Essays on asset pricing with financial frictions

Poulsen, Thomas Kjær Doctoral Thesis Essays on asset pricing with financial frictions PhD Series, No. 19.2019 Provided in Cooperation with: Copenhagen Business School (CBS) Suggested Citation: Poulsen, Thomas Kjær (2019) : Essays on asset pricing with financial frictions, PhD Series, No. 19.2019, ISBN 978-87-93744-81-3, Copenhagen Business School (CBS), Frederiksberg, https://hdl.handle.net/10398/9734 This Version is available at: https://hdl.handle.net/10419/222893 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ ESSAYS ON ASSET PRICING WITH FINANCIAL FRICTIONS Thomas Kjær Poulsen PhD School in Economics and Management PhD Series 19.2019 PhD Series 19-2019 ESSAYS ON ASSET PRICING WITH FINANCIAL FRICTIONS COPENHAGEN BUSINESS SCHOOL SOLBJERG PLADS 3 DK-2000 FREDERIKSBERG DANMARK WWW.CBS.DK ISSN 0906-6934 Print ISBN: 978-87-93744-80-6 Online ISBN: 978-87-93744-81-3 Essays on Asset Pricing with Financial Frictions Thomas Kjær Poulsen A thesis presented for the degree of Doctor of Philosophy Supervisor: Kristian R. Miltersen PhD School in Economics and Management Copenhagen Business School Thomas Kjær Poulsen Essays on Asset Pricing with Financial Frictions 1st edition 2019 PhD Series 19.2019 © Thomas Kjær Poulsen ISSN 0906-6934 Print ISBN: 978-87-93744-80-6 Online ISBN: 978-87-93744-81-3 The PhD School in Economics and Management is an active national and international research environment at CBS for research degree students who deal with economics and management at business, industry and country level in a theoretical and empirical manner. All rights reserved. No parts of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without permission in writing from the publisher. Preface This thesis represents the product of my PhD studies at the Department of Finance and the Center for Financial Frictions (FRIC) at Copenhagen Business School (CBS). In the process of writing this thesis, I have been fortunate to benefit from the advice, feedback, and support from many more people than I can possibly mention here. This long list of people, however, includes some who deserve special recognition. First and foremost, I owe a large intellectual debt to my advisors Kristian R. Miltersen and Jens Dick-Nielsen. I am deeply indebted to Kristian for teaching me how to do research and for being an outstanding advisor throughout my studies. It has been a great pleasure and a privilege to benefit from Kristian’s guidance, constructive suggestions, and not least encouragement over the years. I would also like to thank Jens for our many inspiring discussions which helped me sharpen and clarify my research ideas. Second, I am grateful to my co-author Peter Feldh¨utter for our excellent cooperation on understanding the cross-sectional variation in bid-ask spreads. My other work has also benefited extensively from Peter’s many insights and valuable suggestions. I am also indebted to Lasse Heje Pedersen for always providing honest and constructive feedback on my research. Peter and Lasse helped me prepare for the academic job market and their tireless efforts to sharpen my presentation and writing skills made me a much stronger candidate. Third, I would like to thank Hui Chen for sponsoring my visit at Massachusetts Institute of Technology and for discussing my research ideas. My fellow PhD students and colleagues made my daily life at CBS a pleasure by contributing to an outstanding research and social environment. I also thank Niels Joachim Gormsen for our countless debates on almost any topic. Finally, my partner Julie deserves special thanks. Her endless support and encouragement at times when I needed it the most made it possible to complete this thesis. I am also grateful to my friends for bearing with me in stressful times and to my family for always believing in me. Thomas Kjær Poulsen Copenhagen, April 2019 iii iv Summaries in English Essay 1: Does Debt Explain the Investment Premium? The first essay presents new empirical findings which are inconsistent with prominent theories on the investment premium. The investment premium is the positive stock return differential between firms with low and high asset growth. Asset growth is the annual percentage change in total assets and is typically interpreted as the firm’s investments. The investment premium is an integral part of recent factor models which are fundamental tools for both finance academics and practitioners. In the essay I present three new empirical findings. First, I show that firms with low asset growth on average have higher financial leverage. To the extent that firms with higher leverage have higher returns, cross-sectional differences in leverage account for part of the investment premium. Second, I document that there is no investment premium among zero-leverage firms. Third, I find that the investment premium increases with firms’ refinancing intensities which are the ratio of short-term debt to total debt. These findings reflect firms’ financing decisions and are inconsistent with prominent theories using firms’ investment decisions to explain the investment premium. In the literature there are two prominent theories on why the investment premium exists. On the one hand, rational theories suggest that the investment premium reflects firms’ investment decisions (e.g. Cochrane (1991,1996), Li et al. (2009), Liu et al. (2009), Berk et al. (1999), and Fama and French (2015)). On the other hand, behavioral theories argue that the investment premium reflects mispricing as investors do not properly incorporate information on firms’ investment decisions into asset prices (e.g. Titman et al. (2004) and Cooper et al. (2008)). These theories share two important features. First, they predict that the investment premium should also exist among zero-leverage firms. Second, they cannot explain why the investment premium should depend on refinancing intensities. To explain my empirical findings I develop a new model in which firms not only make investment decisions as in the existing literature but also make financing decisions. The model shows that the investment premium reflects both leverage and refinancing intensities consistent with my empirical findings. In sum, I find that debt-related risks explain part of the investment premium. v Essay 2: Why Does Debt Dispersion Affect Yield Spreads? The second essay investigates the well-known negative relationship between corporate bond yield spreads and debt dispersion. Yield spreads measure firms’ debt financing costs and debt dispersion is the extent to which firms divide their total debt financing into several debt issues. Understanding the determinants of yield spreads remains an important task not only for finance academics but also for finance practitioners to inform corporate policies. In the essay I examine two possible explanations of the negative relationship between yield spreads and debt dispersion. First, theories of rollover risk argue that firms with more dispersed debt have lower yield spreads when they spread out the debt maturity dates across time. The reason is that firms mitigate the adverse effects of deteriorating capital market conditions by limiting the amount of debt that matures at a given point in time. By spreading out the repayment of debt over multiple time periods, the firm can reduce its default risk and therefore also the yield spread. Second, theories of strategic debt service suggest that more dispersed debt increases renegotiation frictions which determine how difficult it is to renegotiate the firm’s debt. In these models equity holders can threaten to default strategically with a view to obtain debt concessions. Higher renegotiation frictions reduce equity holders’ incentive to default strategically. This strategic default effect reduces the probability of default and therefore also the yield spread. Empirically, measures of debt maturity dispersion and proxies for renegotiation frictions are often highly correlated. Both rollover risk and strategic debt service models can therefore explain the negative relationship between yield spreads and debt dispersion. To disentangle these two candidate explanations from each other I examine how the relationship depends on the level of financial constraints. In rollover risk models yield spreads should decrease more with debt maturity dispersion for financially constrained firms because they more exposed to capital market conditions. I document empirically that the negative relationship is more pronounced for financially constrained firms consistent with rollover risk theories. In strategic debt service models the relationship between yield spreads and renegotiation frictions is determined by a trade-off between two opposing effects. On the one hand, higher renegotiation frictions reduce yield spreads through the strategic default effect. On the other hand, higher renegotiation frictions also increase expected liquidation costs in bankruptcy because renegotiations are more likely to fail. This recovery effect decreases recovery rates and increases yield spreads. I show theoretically that financial constraints strengthen the recovery effect because equity holders in financially constrained firms default more often. The relationship between yield spreads and renegotiation frictions should therefore be less negative for financially constrained firms. My empirical results contradict this prediction. vi Essay 3: What Determines Bid-Ask Spreads in Over-the-Counter Markets? with Peter Feldh¨utter The third essay studies the cross-sectional variation in bid-ask spreads, measured by realized transaction costs, in the U.S. corporate bond market. We use the variation to test over-the-counter (OTC) theories of why the bid-ask spread arises. Bid-ask spreads are often used to measure market liquidity. Market liquidity influences bond prices and therefore directly affects firms’ debt financing costs. Our findings shed new light on the ability of OTC theories to explain the cross-sectional variation of bond bid-ask spreads. Our analysis begins by documenting patterns in the cross-section of bid-ask spreads across bond maturity and rating. When we sort in one dimension alone, we find that average spreads increase with bond maturity and credit risk consistent with findings from the existing literature. When we double-sort on maturity and rating, however, a surprising pattern emerges. Spreads for investment grade bonds increase strongly in maturity, while spreads for speculative grade bonds show no clear relation. For short-maturity bonds, spreads increase in credit risk while for long-maturity bonds, spreads for bonds rated AA+ or AAA are substantially higher than other investment grade bonds. We compare these documented patterns in bid-ask spreads to the variation in proxies motivated by theories of the bid-ask spread in OTC markets. We consider four theories based on inventory, dealer network, search-and-bargaining frictions, and asymmetric information and examine the extent to which the variation in proxies explains the variation in bid-ask spreads. We find that dealer inventory is the most important determinant of the variation in bid-ask spreads. In inventory models dealers provide immediacy to investors and charge a bid-ask spread to compensate for the risk that the bond price may decline while it is in the dealer’s inventory. We also find that models based on dealer networks explain part of the variation in bid-ask spreads especially for speculative grade bonds. In these models, the dealers’ position in the network of other dealers as well as the number of dealers involved in intermediating a trade determines the bid-ask spread. We also find that search-and-bargaining frictions and asymmetric information models have limited explanatory power for bid-ask spreads. In search-and-bargaining models the bid-ask spread depends on the easy of finding counterparties to trade with and the strength of their bargaining power over the transaction price. In asymmetric information models some investors have private information about the value of the security and the dealer charges a bid-ask spread to compensate for losses incurred when trading with informed counterparties. Taken together, we document new facts about the cross-sectional variation in bid-ask spreads and provide new evidence on the ability of OTC theories to explain the variation. vii 1.1 Related Literature ................................ 70 2 Testable Hypotheses ................................... 71 2.1 Rollover Risk ................................... 71 2.2 Strategic Debt Service .............................. 72 3 Data and Variables .................................... 73 3.1 Data Sources ................................... 73 3.2 Sample Selection ................................. 74 3.3 Main Variables .................................. 75 3.4 Merging the Data ................................ 76 3.5 Summary Statistics and Correlations ...................... 77 4 Empirical Results ..................................... 78 4.1 Yield Spreads and Debt Dispersion ....................... 79 4.2 The Effect of Financial Constraints ....................... 80 4.3 Robustness Checks ................................ 83 5 Conclusion ........................................ 83 A Rollover Risk Model ................................... 85 B Strategic Debt Service Model .............................. 88 C Definition of Variables .................................. 93 Tables and Figures ....................................... 97 Internet Appendix ....................................... 104 3 What Determines Bid-Ask Spreads in Over-the-Counter Markets? 111 1 Introduction ........................................ 112 2 Data ............................................ 115 3 Cross-Sectional Variation in Bid-Ask Spreads ..................... 116 4 Empirical Measures .................................... 119 4.1 Measures ..................................... 119 4.2 Relation Between Measures ........................... 121 5 Empirical Results ..................................... 122 5.1 Testing Theories of the Bid-Ask Spread .................... 122 5.2 Joint Prediction in Panel Regression ...................... 126 5.3 Matched Trades ................................. 127 6 Conclusion ........................................ 129 A Empirical Measures: Implementation Details ..................... 131 B Regression Results with Simulated Transaction Prices ................ 136 Tables .............................................. 138 Bibliography 157 xiv Introduction This thesis consists of three self-contained essays, which study how financial frictions influence the pricing of equities, corporate bonds, and transaction costs. In the first essay I consider asset pricing implications of firms’ investment and financing decisions for the cross-section of equity returns. I show that risks related to firms’ debt structures explain a substantial fraction of the investment premium i.e. the finding that firms with low asset growth deliver high average stock returns. In the second essay I investigate why debt dispersion — the extent to which firms divide their total debt financing into several debt issues — affect yield spreads on corporate bonds. I document that the negative relationship between yield spreads and debt dispersion is more pronounced for financially constrained firms and show that this finding is consistent with theories of rollover risk. The third essay (co-authored with Peter Feldh¨utter) presents new facts on the cross-section of bid-ask spreads in the corporate bond market. We find that models based on dealer inventory and dealer networks explain a large fraction of the variation in bid-ask spreads while models based on search-and-bargaining frictions and asymmetric information have limited explanatory power. Does Debt Explain the Investment Premium? The first essay studies the pervasive empirical phenomenon in the stock market called the investment premium. The investment premium is the positive stock return differential between firms with low and firms with high asset growth where asset growth is the annual percentage change in total assets. In this essay I present three new empirical findings. First, I find that the investment premium reflects differences in financial leverage. Second, I document that there is no investment premium among zero-leverage firms. And third, I find that the magnitude of the investment premium increases with firms’ refinancing intensities which are the ratio of short-term debt to total debt. These three findings are important because they are inconsistent with prominent explanations of the investment premium. In the literature there are two prominent theories on why the investment premium exists. On the one hand, rational theories argue that the investment premium reflects firms’ investment decisions (e.g. the q-theory of investment including Cochrane (1991,1996), Li et al. (2009), Liu 1 et al. (2009), real option models such as Berk et al. (1999), and the dividend discount model from Fama and French (2015)). On the other hand, behavioral theories argue that the investment premium reflects mispricing as investors do not properly incorporate information on firms’ investment decisions into asset prices (e.g. Titman et al. (2004) and Cooper et al. (2008)). Both of these theories share two important features. First, they predict a positive return differential between zero-leverage firms with low and high asset growth. Second, they cannot explain why the return differential increases with firms’ refinancing intensities. My empirical results are therefore inconsistent with these theories and offer a novel perspective on the economic interpretation of the investment premium. To explain my empirical findings I develop a new model in which firms not only make endogenous investment decisions as in the existing literature but they also make endogenous financing decisions. The model shows that the investment premium reflects both leverage and refinancing intensities consistent with my empirical findings. Taken together, the novelty of the first essay rests in showing that debt-related risks explain part of the investment premium. Why Does Debt Dispersion Affect Yield Spreads? While the first essay studies asset pricing in equity markets, the second essay considers asset pricing in corporate bond markets. In particular, I investigate the well-known negative relationship between yield spreads and debt dispersion1. Yield spreads measure firms’ debt financing costs and debt dispersion is the extent to which firms divide their total debt financing into several debt issues. I document empirically that the negative relationship between yield spreads and debt dispersion is more pronounced for financially constrained firms. This cross-sectional variation is crucial for understanding why debt dispersion affects yield spreads. In the essay I examine two candidate explanations for the negative relationship between yield spreads and debt dispersion. On the one hand, theories of rollover risk argue that firms with more dispersed debt have lower yield spreads when they spread out debt maturity dates across time (e.g. Choi et al. (2018)). On the other hand, theories of strategic debt service suggest that more dispersed debt increases renegotiation frictions, which determine how difficult it is to renegotiate the firm’s debt, and reduce equity holders’ incentive to threaten to default strategically (e.g. Davydenko and Strebulaev (2007)). In both models debt dispersion reduces yield spreads but for different reasons. To disentangle these two candidate explanations from each other I analyze the effects of financial constraints. In rollover risk models yield spreads should decrease more with debt maturity 1See e.g. Davydenko and Strebulaev (2007), Dass and Massa (2014), and Nagler (2019). 2 dispersion for financially constrained firms because they more exposed to capital market conditions. In strategic debt service models I show that the relationship should be less negative for financially constrained firms. I document empirically that the negative relationship is more pronounced for financially constrained firms consistent with theories of rollover risk. What Determines Bid-Ask Spreads in Over-the-Counter Markets? Unlike the first two essays that study asset pricing implications for corporate securities, the third essay examines the cost of trading financial securities. More precisely, we study the cross-sectional variation in bid-ask spreads, measured by realized transaction costs, in the U.S. corporate bond market. It is well-documented in the literature that average bid-ask spreads increase in bond maturity and credit risk when considering one dimension alone2. Our first contribution is to document two new facts about bid-ask spreads by double-sorting on both bond rating and maturity. First, we find that bid-ask spreads do not increase with maturity for speculative grade bonds. Second, we show that long-maturity bonds rated AAA or AA+ have significantly higher spreads than other investment grade bonds. Our results are robust to excluding the financial crisis, adding time fixed effects, and holds separately for bonds issued by financial and non-financial firms. Our second contribution is to examine the relative importance of different over-the-counter (OTC) theories ability to explain the variation in bid-ask spreads. We consider four theories based on dealer inventory, dealer networks, search-and-bargaining frictions, and asymmetric information. We find that dealer inventory is the most important determinant of the variation in bid-ask spreads. Dealer network models also explain part of the variation, especially for speculative grade bonds. Lastly, we find that search-and-bargaining frictions and asymmetric information models have limited explanatory power for bid-ask spreads. 2See e.g. Edwards et al. (2007), Dick-Nielsen et al. (2012), and Goldstein and Hotchkiss (2018). 3 4 Chapter 1 Does Debt Explain the Investment Premium? Thomas Kjær Poulsen* Abstract The investment premium — the finding that firms with low asset growth deliver high average returns — is an integral part of recent factor models. I document empirically that the investment premium (1) reflects financial leverage, (2) does not exist among zero-leverage firms, and (3) increases with firms’ refinancing intensities. This new evidence challenges prominent explanations of the investment premium including the q-theory of investment and behavioral finance. To explain the evidence, I develop a model in which firms make both optimal investment and financing decisions. The model shows that the investment premium reflects both leverage and refinancing intensities consistent with my empirical findings. *Center for Financial Frictions (FRIC), Department of Finance, Copenhagen Business School, Solbjerg Plads 3, DK-2000 Frederiksberg, E-mail: [email protected]. I am grateful to Hui Chen, Jens Dick-Nielsen, Peter Feldh¨utter, Nils Friewald (discussant), Thomas Geelen, Lasse Heje Pedersen, Kristian R. Miltersen, Christian Wagner, and Ramona Westermann for helpful comments and discussions. In addition, I thank seminar participants at the PhD Nordic Finance Workshop 2017, BI Norwegian Business School, Copenhagen Business School, Erasmus School of Economics, University of Oxford (Sa¨ıd Business School), Universit´e Paris-Dauphine, University of Toronto Scarborough, Stockholm School of Economics, and Vienna University of Economics and Business (WU) for their comments. Any remaining errors are solely my own. Support from the Center for Financial Frictions (FRIC), grant no. DNRF102, is gratefully acknowledged. 5 1 Introduction Firms with low asset growth have higher expected stock returns than firms with high asset growth1. This return differential is the investment premium from the five-factor Fama and French (2015) model and the q-factor model by Hou et al. (2015). Factor models are fundamental tools for both finance academics and finance professionals. The lack of agreement on the economic interpretation of the factors calls for more empirical evidence to inform asset pricing theories. In this paper, I study the investment factor and document that the investment premium (1) reflects financial leverage, (2) does not exist among zero-leverage firms, and (3) increases with firms’ refinancing intensities. This cross-sectional variation reflects firms’ financing decisions and is inconsistent with prominent theories using firms’ investment decisions to explain the investment premium. On the one hand, rational theories suggest that the investment premium reflects firms’ investment decisions (e.g. the q-theory of investment including Cochrane (1991,1996), Li et al. (2009), Liu et al. (2009), real option models such as Berk et al. (1999), and the dividend discount model from Fama and French (2015)). On the other hand, behavioral theories argue that the investment premium reflects mispricing as investors do not properly incorporate information on firms’ investment decisions into asset prices (e.g. Titman et al. (2004) and Cooper et al. (2008)). Both of these theories share two important features. First, they predict a positive return differential between zero-leverage firms with low and high asset growth. Second, they cannot explain why the return differential increases with firms’ refinancing intensities. My empirical results are therefore inconsistent with these theories and offer a novel perspective on the economic interpretation of the investment premium. I begin my empirical analysis by confirming a strong negative relationship between asset growth and leverage consistent with the findings by Lang et al. (1996). Doshi et al. (2018) argue that leverage explains a substantial fraction of several cross-sectional anomalies. To control for leverage, I use their methodology to unlever stock returns and find that the investment premium decreases from 0.32% per month with levered returns to 0.15% with unlevered returns. If firms’ investment decisions fully explain the investment premium and if financing decisions are irrelevant, the investment premium should also exist among zero-leverage firms. I use portfolio sorts to document that the return differential between zero-leverage firms with low and high asset growth is −0.11% per month and statistically insignificant. Next, I consider levered firms’ refinancing intensities and analyze how the return differential between low and high asset-growth firms depends on this financing decision. I measure refinancing 1See e.g. Fairfield et al. (2003), Hirshleifer et al. (2004), Titman et al. (2004), Richardson et al. (2005), Anderson and Garvia-Feij´oo (2006), Fama and French (2006,2015), Cooper et al. (2008), Lyandres et al. (2008), Xing (2008), Polk and Sapienza (2009), and Aharoni et al. (2013). 6 intensity by the ratio of debt maturing within one year to total debt and find that the return differential increases monotonically from 0.12% per month for firms with low refinancing intensities to 0.64% for firms with high refinancing intensities. This increase in the return differential of 0.52% is statistically significant and remains almost the same measured in risk-adjusted returns when I control for exposures to common risk-factors (market, size, value, momentum, profitability, and investments). When I control for leverage, the unlevered return differential between low and high asset-growth firms increases with refinancing intensities by 0.33%. Leverage therefore explains some of the cross-sectional return differential but refinancing intensities remain informative about the investment premium. My empirical results show that the investment premium reflects both leverage and refinancing intensities. In the time-series, I regress (levered) investment factor returns on two factors constructed based on leverage and refinancing intensities. These two factors explain 36% of the time-series variation in the investment factor. I develop a corporate finance model to study the impact of leverage and refinancing intensities on the investment premium. Specifically, I integrate the growth option from Diamond and He (2014) into the Friewald et al. (2018) model and study implications of firms’ investment and financing decisions for expected stock returns. Consistent with my empirical results, the model shows that the investment premium reflects both leverage and refinancing intensities. The model features a firm with risky debt and a growth option to increase the growth rate of assets-in-place. Equity holders determine the firm’s investment and default policies to maximize the value of equity. Debt overhang arises because debt and equity holders share the value from the firm’s investments, whereas equity holders pay the entire investment cost. The firm can issue more short-term debt to improve investment incentives and reduce debt overhang at the expense of increasing rollover risk. Rollover risk arises because the firm retires maturing debt at principal value and issues new debt at market value. Equity holders finance the difference between the principal and market value of debt by issuing new equity. The model shows that investment decisions have implications for expected stock returns. Equity holders capture a lower share of the value from the firm’s investments the more risky the firm’s debt and vice versa. When the firm has sufficiently risky debt, equity holders’ share of the value from the firm’s investments is too low to justify paying the investment cost. Since equity holders determine the investment policy, the firm does not invest when it has sufficiently risky debt. In the model, both the riskiness of debt and the expected stock return increase with leverage. Firms therefore invest when they have low leverage and expected stock returns are low, whereas firms do not invest when they have high leverage and expected stock returns are high. The model predicts 7 that firms with low asset growth have higher leverage and higher expected stock returns relative to firms with high asset growth consistent with my empirical findings. The firm jointly determines optimal leverage and debt maturity by choosing a mix between short-term and long-term bonds. This financing decision reflects a trade-off between investment incentives, rollover risk, and reduced-form debt benefits that reflect tax shields, reduction of agency costs, and/or reduction of information asymmetries. If the firm has no debt benefits, it optimally chooses zero leverage to improve investment incentives. Zero-leverage firms have no debt overhang and always invest because the growth option has positive net present value (NPV). This means that there is no cross-sectional variation in their investment policies and they all have the same leverage ratio of zero. For this reason, their investment decisions remain uninformative about expected stock returns and there is no return differential between zero-leverage firms with low and high asset growth. If the firm has debt benefits, it chooses an optimal mix of short and long-term debt at inception. The fraction of short-term debt to total debt determines the refinancing intensity and the firm commits to keep the debt principal values constant through time. Over time, leverage changes with fluctuations in the market value of equity, whereas the refinancing intensity remains fixed. While expected stock returns increase with both leverage for a given refinancing intensity and likewise with the refinancing intensity for a given leverage, the model features an important interaction effect. Expected stock returns increase faster with refinancing intensities for firms with high leverage relative to firms with low leverage because short-term debt amplifies rollover risk. Since firms invest when they have low leverage and do not invest when they have high leverage, this interaction effect predicts that the return differential between firms with low and high asset growth increases with refinancing intensities. 1.1 Related Literature My paper is related to Friewald et al. (2018) who study implications of firms’ financing decisions for the cross-section of expected stock returns. They find that leverage and refinancing intensities explain a substantial fraction of the size and value factors. Doshi et al. (2018) also find that the size and value factors reflect leverage. These two papers do not focus on the investment factor. Prominent theories using firms’ investment decisions to explain the investment factor do not consider financing decisions. My contribution is to study implications of both investment and financing decisions for expected stock returns. Rational theories on the investment factor include three main explanations. First, the q-theory of investment predicts that firms invest more when expected stock returns are lower and vice 8 versa. All else equal, firms invest more when discount rates are lower because the NPV of new projects is higher (e.g. Cochrane (1991,1996), Li et al. (2009), Liu et al. (2009)2, and Hou et al. (2015)). Second, real option models show that risky growth options have higher expected returns than less risky assets-in-place. When the firm invests, the importance of growth options relative to assets-in-place decreases and the expected stock return decreases as well (e.g. Berk et al. (1999), Carlson et al. (2004), Gomes et al. (2003), and Cooper (2006)). Third, Fama and French (2006, 2015) rewrite the dividend discount model and show that firms with higher expected growth in book equity have lower expected stock returns. They argue that growth in book equity reflects investments. Behavioral theories on the investment factor include two main explanations. First, Cooper et al. (2008) build on the idea from Lakonishok et al. (1994) that investors extrapolate past performance too far into the future when they value stocks. If firms with high asset growth performed well in the past, investors expect them to continue to do so in the future. Investors overvalue stocks in these firms to the extent that they cannot live up to the high growth expectations going forward. When realized asset growth falls short of expectations, the market corrects the initial overvaluation and these stocks have low returns. Second, Titman et al. (2004) argue that investors fail to recognize that high asset growth may reflect over-investment (see Jensen and Meckling (1976) and Jensen (1986)). Investors therefore tend to overvalue firms with high asset growth. The subsequent low stock returns to high asset-growth firms reflect that the market corrects the initial over-valuation. My paper also relates to the corporate finance literature on debt overhang and rollover risk which does not consider implications for expected stock returns. Hackbarth and Mauer (2012), Dockner et al. (2012), Sundaresan et al. (2014), Diamond and He (2014), and Chen and Manso (2017) study the debt overhang problem described by Myers (1977) using the conceptual framework from Leland (1994b), Leland (1994a), Leland and Toft (1996), Leland (1998), and Goldstein et al. (2001). The literature on rollover risk include He and Xiong (2012b), He and Milbradt (2014), and Chen et al. (2018) and mainly focuses on credit risk implications of debt rollover and bond market illiquidity. 2 Data and Summary Statistics I obtain monthly stock returns from the Center for Research in Security Prices (CRSP) and annual firm characteristics from COMPUSTAT. I use the CRSP-COMPUSTAT linking table to merge the two data sets. At the end of June in year t, I calculate accounting based variables using information 2In Liu et al. (2009), the firm finances investments using both equity and one-period debt. This model features a leverage effect but the firm cannot choose its debt maturity. Liu et al. (2009) use leverage to improve the quantitative fit of the model and do not analyze the relationship between investments and leverage. 9 debt. Since capital markets reevaluate the firm’s prospects as part of the valuation of new debt issuances, firms with short-term debt should have lower agency costs. In turn, the over-investment hypothesis from Titman et al. (2004) predicts a smaller return differential for firms with high refinancing intensities because they have lower agency costs. My results directly contradict this prediction. The dividend discount model, real option models, the q-theory of investment, and the overextrapolation hypothesis do not feature any directly testable predictions on refinancing intensities. Li and Zhang (2010) and Lam and Wei (2011) point out that it is challenging to disentangle candidate explanations of the investment premium in the data. For example, q-theory predicts that the return differential should increase with investment frictions because frictions make investment less responsive to changes in the discount rate. Behavioral theories predict a larger return differential in firms with stocks that have high limits-to-arbitrage because rational investors find it more challenging to step in and correct the mispricing. If measures of investment frictions, limitsto-arbitrage, and refinancing intensities are highly correlated then it is challenging to disentangle the predictions from each other. To explore this possibility, I calculate Spearman rank correlations between measures of investment frictions, limits-to-arbitrage, and refinancing intensities. Li and Zhang (2010) and Lam and Wei (2011) use several proxies to measure investment frictions and limits-to-arbitrage. They hypothesize that firms with high investment frictions have smaller asset size, lower payout rates, and are younger. Firms with high limits-to-arbitrage have high idiosyncratic stock volatility, low stock price, high bid-ask spread, high Amihud (2002) illiquidity measure, and low dollar volume. Appendix A contains a detailed description of all variables. Table 6 presents Spearman rank correlations between these measures and refinancing intensities. Consistent with Li and Zhang (2010) and Lam and Wei (2011), I find high correlations between measures of investment frictions and measures of limits-to-arbitrage. However, Table 6 shows only modest correlations between refinancing intensities and these measures. This finding suggests that refinancing intensities convey information not captured by investment frictions or limits-toarbitrage. [INSERT TABLE 6] It is also not clear from the theoretical literature on debt maturity that we should expect firms with short-term debt to have high investment frictions. For example, Diamond (1991) predicts an inverse U-shape between debt maturity and credit risk when firms trade off lower borrowing costs of short-term debt against higher refinancing risk. Chen et al. (2013) show that firms with higher exposure to systematic risk choose longer debt maturities. Dangl and Zechner (2015) find that short-term debt typically increases firms’ debt capacities. To the extent that higher credit risk, 16 higher systematic risk, and lower debt capacity are associated with higher investment frictions, we should not expect firms with short-term debt to have high investment frictions. For the limits-to-arbitrage measures, it is not clear from the literature how and if they should be related to debt maturity. Chen et al. (2013) and Friewald et al. (2018) show that firms with higher idiosyncratic volatility issue more short-term debt because long-term debt becomes relatively more expensive. Since stocks with high idiosyncratic volatility have high limits-to-arbitrage, it is challenging to disentangle the predictions based on limits-to-arbitrage and refinancing intensities using this measure. Taken together, my results suggest that the higher return differential among firms with high refinancing intensities does not simply reflect higher investment frictions or higher limits-to-arbitrage. 3.4 Time-Series Variation in the Investment Factor My cross-sectional results show that the investment premium reflects leverage and refinancing intensities. In this section, I study to what extent leverage and refinancing intensities explain the time-series variation in the investment factor. I follow Fama and French (2015) and construct the investment factor as follows. At the end of each June, I independently double-sort stocks into two portfolios based on size and into three portfolios based on asset growth rates using NYSE breakpoints. This procedure generates a crosssection of 2 ×3 = 6 portfolios. The investment factor is the average return on the two low asset-growth portfolios (small and big) minus the average return on the two high asset-growth portfolios using value-weighted portfolios. I use the same procedure to construct two factors based on leverage and refinancing intensities. The leverage factor is the average return on the two highleverage portfolios (small and big) minus the average return on the two low-leverage portfolios. The refinancing-intensity factor is long stocks with high refinancing intensities and short stocks with low refinancing intensities. I regress the time-series of investment factor returns on the two factors based on leverage and refinancing intensities and present the results in Table 7. [INSERT TABLE 7] The first column in Table 7 shows that the investment premium in my sample is 0.32% per month and statistically significant. In column (2), I regress investment factor returns on the leverage factor and find that the intercept decreases to 0.23% and remains statistically significant. The investment factor has positive loading on the leverage factor and the adjusted R2of the regression is 34.16%. When I only include the refinancing-intensity factor in the regression then the loading is close to zero and statistically insignificant while the intercept is virtually unchanged. 17 This finding suggests that refinancing intensities alone has no explanatory power for the timeseries variation of the investment factor. When I include both factors in the regression, the loading on each factor is positive and statistically significant. The adjusted R2increases to 35.82% and suggests that leverage and refinancing intensities jointly explain a significant fraction of the investment premium. 3.5 Robustness Checks This section summarizes robustness checks which I include in the Internet Appendix. Table IA.1IA.4 show that my results are robust to using equal-weighted portfolios. In addition to zeroleverage firms, Strebulaev and Yang (2013) also consider firms with zero long-term debt, almost zero-leverage firms, and firms with non-positive net debt7. I also analyze the return differential between firms with low and high asset growth for these firm types. I only report the results for firms with non-positive net debt in the Internet Appendix because it gives the largest sample and the other firm types give similar results (result are available upon request). My sample of firms with non-positive net debt features 518,505 firm-month observations from 7,741 unique firms. In an average year, firms with non-positive net debt constitute 30.31% of all firms and account for 23.83% of total market capitalization. Table IA.5 shows that the return differential between low and high asset-growth firms remains close to zero and statistically insignificant. The number of portfolios to sort stocks into is arguably an arbitrary choice. I therefore also conduct the independent double-sorts based on refinancing intensities and asset growth for a different number of portfolios. I keep the number of portfolios based on asset growth fixed to ensure that each portfolio contains a reasonable number of stocks. The difference between the return differential in firms with low and high refinancing intensities should increase with the number of portfolios because the difference between the average refinancing intensity in the highest and lowest portfolio increases as well. Table IA.6 shows that the return differential increases with the number of portfolios. In the main analysis, I use independent portfolio double-sorts to analyze the relationship between asset growth and refinancing intensities. The number of stocks in each portfolio can therefore vary considerably. My sample features a large cross-section of stocks and the portfolio with the lowest number of stocks in the 5 ×5 sorts contains 62 stocks on average and the lowest number of stocks is 29. To mitigate the concern that the portfolios are not well-diversified, I repeat the main analysis using conditional double-sorts. At the end of each June, I first sort stocks into five 7Firms with zero long-term debt have DLT T = 0, almost zero-leverage firms have DLC+DLT T AT ≤5%, and firms with non-positive net debt have DLT T +DLC −CHE ≤0. Capitalized acronyms correspond to annual COMPUSTAT items. 18 portfolios based on refinancing intensities and then into five portfolios based on asset growth rates. The remainder of the portfolio analysis is identical to the independent double-sorts. I also perform conditional double-sorts by first sorting on asset growth and subsequently sorting on refinancing intensities. The results are qualitatively similar and I present these results in Table IA.7-IA.10. I also consider different measures of refinancing intensities and asset growth. Almeida et al. (2012) and Gopalan et al. (2014) calculate the refinancing intensity with the ratio of debt maturing within one year to total assets. Lipson et al. (2011) show that the change in total assets, which I use to measure asset growth, largely subsumes other measures of asset growth. Nonetheless, I also consider the investment-to-asset ratio from Lyandres et al. (2008) as a further robustness check of my results8. Table IA.11-IA.16 show that my results are qualitatively similar with these measures but quantitatively less pronounced. Finally, I also repeat the main analysis using Fama and MacBeth (1973) regressions. The dependent variable is either the excess stock return or the unlevered excess stock return in month t+ 1 while the independent variables are characteristics in month t. I present the time-series averages of monthly coefficient estimates from cross-sectional Fama and MacBeth (1973) regressions in Table IA.17-IA.19 in the Internet Appendix. For the cross-sectional regressions, I use either ordinary least squares estimates (equal-weighted) or weighted least squares with the market value of equity as the weighting scheme (value-weighted). The value-weighted Fama and MacBeth (1973) regressions mitigate the influence of small stocks. Table IA.17 shows that the negative coefficient estimates on asset growth are substantially smaller with unlevered excess returns compared to (levered) excess returns. This result supports my finding that leverage explains a substantial fraction of the investment premium. In addition, Table IA.18 shows that the coefficient estimates on asset growth are statistically insignificant for zero-leverage firms. This result means that there is no investment premium for zero-leverage firms. To analyze how the investment premium depends on firms’ refinancing intensities, I regress future returns on asset growth, refinancing intensities, and the interaction between asset growth and refinancing intensities. The coefficient estimates on the interaction term are negative and economically large suggesting that the investment premium is more pronounced for firms with high refinancing intensities but the coefficient estimates are statistically insignificant. 8At the end of June in year t, the refinancing intensity is given by DD1t−1 ATt−1and the investment-to-asset ratio is ∆P P EGTt−1+∆INV Tt−1 ATt−2. Capitalized acronyms correspond to annual COMPUSTAT items. 19 4 The Model In this section, I develop a corporate finance model by integrating the investment option from Diamond and He (2014) into the Friewald et al. (2018) model. The purpose of the model is to study the impact of leverage and refinancing intensities on the investment premium. Friewald et al. (2018) study implications of firms’ financing decisions for the cross-section of expected stock returns and do not consider investment decisions. Diamond and He (2014) do not analyze implications for expected stock returns. My contribution is to study implications of both investment and financing decisions for expected stock returns within a unified model. 4.1 Firm Fundamental The firm has assets-in-place that generate cash flows at a rate of Xt>0. The cash flows follow a geometric Brownian motion under the equivalent martingale measure Q: dXt=˜ itXtdt +σXtdZt(1) where ˜ itis the risk-neutral growth rate, σis the volatility, and dZtis the increment of a standard Brownian motion {Zt: 0 ≤t < ∞} under Q. One can show that the value of the firm’s assets-inplace share their dynamics with Xtbecause assets-in-place denote a claim to the entire cash flow stream. I refer to the firm’s cash flows and assets-in-place interchangeably in the remainder of the paper. At each instant in time, the equity holders endogenously determine the growth rate ˜ itof assetsin-place. The growth rate can take two values ˜ it={0, i}with i > 0. When ˜ it= 0 the firm does not invest and when ˜ it=ithe firm invests. The firm pays an instantaneous investment cost λiXtdt when it invests. Diamond and He (2014) show that equity holders use a threshold investment strategy i.e. they invest when the current cash flow Xtexceeds an endogenous investment boundary Xi. If the firm always invests, the expected present value of the cash flow stream is: EQ tZ∞ t e−r(s−t)(Xs−λiXs) ds=1−λi r−iXt If the firm never invests, the expected present value of the cash flow stream is Xt r. I follow Diamond and He (2014) and assume λr < 1 to ensure that the growth option has positive net present value. When λr < 1, a zero-leverage firm will always choose to invest because the market value of the firm with investments 1−λi r−iXtis strictly greater than the market value of the firm without investments Xt r. A levered firm with risky debt, however, will not always invest because of debt overhang. 20 4.2 Debt and Equity The firm chooses a mix between short-term zero-coupon bonds (S) and long-term zero coupon bonds (L) at time t= 0 similar to Friewald et al. (2018). Each bond type j={S, L}has an aggregate principal value Pjand the total principal value corresponds to P=PS+PL. Each bond matures at a random point in time and the maturity event follows a Poisson occurrence with intensity φj. Each bond therefore has an expected maturity of 1/φjyears as in Cheng and Milbradt (2012), He and Xiong (2012a), and Chen et al. (2018). I assume that φS> φLto ensure that Shas a shorter expected maturity than L. I follow Friewald et al. (2018) and assume that the firm obtains a flow of debt benefits kφjPj with scaling factor k > 0 when it issues debt9. Short-term debt offers more debt benefits relative to long-term debt since φS> φLto reflect lower fixed issuance costs, better market liquidity, and the potential to reduce agency costs and/or information asymmetries (see for example Flannery (1986), Diamond (1991), Datta et al. (2005), Brockman et al. (2010), He and Milbradt (2014), Chen et al. (2013), and Cust´odio et al. (2013)). Intuitively, this relative advantage of short-term debt reflects the additional benefits over and above the fact that short-term debt improves investment incentives. The firm commits to keep the aggregate principal values constant through time. This stationary debt structure implies that at each instant in time, the firm retires an expected principal amount of φSPS+φLPLand issues new bonds to keep the principal values constant10. The newlyissued zero-coupon bonds sell at market value and have the same principal value and seniority as the retired bonds they replace. When the market value of debt differs from the principal value, the firm incurs expected rollover losses of Pjφj[Dj(Xt)−Pj] where Dj(Xt) denotes the market value of bond j11. Maturing debt holders receive the full principal value while equity holders finance rollover losses by issuing new equity. Debt rollover therefore features a conflict of interests between equity and debt holders. When cash flows decrease, equity holders service debt payments as long as the option value of keeping the firm alive remains positive. For some positive starting value of the cash flow process, X0, the firm defaults when Xtreaches a lower endogenous default boundary XB. The absolute priority rule applies and the firm loses its growth option in bankruptcy. Debt holders recover the 9This assumption ensures that the firm has an incentive to issue debt. The Diamond and He (2014) model features no debt benefits and instead allows the firm to choose its optimal debt maturity for a fixed (sub-optimal) amount of debt. The implications of the firm’s investment and financing decisions for expected stock returns, however, remain qualitatively the same in the Diamond and He (2014) model and in the model I present. 10Leland (1994a), Leland and Toft (1996), and Leland (1998) likewise assume stationary debt structures. 11The firm always incur rollover losses with zero-coupon bonds. If the firm instead issues fixed-rate coupon bonds at par values at time t= 0 then the firm may face both rollover gains and losses at time t > 0. This feature, however, does not qualitatively affect the results and I therefore consider zero-coupon bonds to keep the model as simple as possible. 21 value of assets-in-place without investments proportionally to their share of the total principal i.e. proportional to Pj/P. These assumptions translate into the following value-matching conditions at XB: E(XB)=0, Dj(XB) = XB rθj(2) where E(Xt) is the market value of equity, ris the risk-free rate, and θjis the fraction of debt j to total debt i.e. θj=Pj/P. The firm’s investment policy introduces an additional conflict of interest between equity and debt holders. When the firm invests, the higher asset growth tends to push the firm away from the default boundary over time. Debt holders benefit from the firm’s investments because debt becomes safer and hence more valuable. Equity holders pay the entire investment cost but only capture part of the value from the firm’s investments. The equity holders therefore have low incentives to invest when a large share of the value from the firm’s investments accrues to debt holders. Debt overhang implies a non-investment region when XB< Xt< Xiwhere the firm does not invest despite the fact that investment at each instant in time maximizes firm value. This non-investment region reflects that equity holders maximize the value of equity and not the value of the firm. I provide the technical details for the valuation of debt and equity in closed-form in Appendix B. 4.3 Default and Investment Boundaries Equity holders determine the endogenous default and investment boundaries to maximize the value of equity following the inaugural debt issue. The two boundaries satisfy the following smooth pasting conditions: ∂E(X) ∂X X=XB = 0,∂E(X) ∂X X=Xi =λ(3) These smooth pasting conditions give rise to a system of non-linear equations, which I solve numerically for the default and investment boundaries. The boundaries characterize the optimal default and investment policies for a given choice of principal values Pj={PS, P L}. 4.4 Optimal Leverage and Refinancing Intensity At time t= 0, the firm chooses the principal amounts of short and long-term debt to maximize the value of the firm. The optimal principal amounts Pj∗solve the maximization problem: {PS∗, PL∗}= arg max PS,PLE(X0) + D(X0)(4) 22 subject to the constraints from equation (3) and the requirements that Dj(XB)< Pj/(1 + r/φj) for j={S, L}. This requirement ensures that there is an interior optimum refinancing intensity. Intuitively, the requirement states that the firm cannot issue risk-free debt which would eliminate the debt overhang problem. The optimal principal amounts are not available in closed-form and must be determined numerically. By choosing the principal amounts of short and long-term debt, the firm jointly chooses optimal leverage and refinancing intensity. Consistent with the measures of leverage and refinancing intensities from the empirical analysis above, I define the firm’s leverage ratio L(Xt) as: L(Xt) = P P+E(Xt)(5) and I measure the firm’s refinancing intensity by the ratio of short-term debt principal to total debt principal: θS=PS PS+PL(6) 4.5 Expected Stock Return I derive the value of debt and equity from the Q–dynamics of the cash flow process Xtin Appendix B. The calculation of the expected stock return requires the P–dynamics of Xt. For simplicity, I assume a constant risk premium ξand remain silent on the structure of the pricing kernel that determines the value of the underlying cash flow process in equation (1). The expected stock return is therefore given by: EP t[Rt] = r+βtξ(7) where the conditional equity beta is: βt=dlogE(Xt) dXt 5 Model Predictions In this section, I parameterize the model and explain the trade-off between investment incentives, debt benefits, and rollover risk that determines optimal leverage and refinancing intensity. Next, I consider implications of investment and financing decisions for the cross-section of expected stock returns. 23 5.1 Optimal Leverage and Refinancing Intensity I use the parameter values from Diamond and He (2014) and Friewald et al. (2018) and set X0= 1, r= 10%, σ= 15%, i= 7%, and k= 1%. At time t= 0, the firm determines the optimal mix between a short-term zero-coupon bond with one-year expected maturity (φS= 1) and a long-term zero-coupon bond with ten-year expected maturity (φL= 0.1) to maximize firm value. For a given level of the investment cost λ, I consider the firm’s optimal choices of leverage and refinancing intensity. [INSERT FIGURE 1] Panel A in Figure 1 shows optimal leverage as a function of the investment cost λ12. This relationship reflects the firm’s trade-off between investment incentives and debt benefits. On the one hand, the value of debt benefits increases as the firm issues more debt. On the other hand, the value of the growth option decreases with the amount of debt because debt distorts investment incentives. As λincreases, it becomes more expensive to invest and the value of the growth option decreases. In turn, the firm has greater incentive to exploit debt benefits compared to improving investment incentives. The optimal leverage therefore increases with λ. Panel B in Figure 1 displays the optimal principal values of short-term debt PSand long-term debt PLas a function of λ. Consistent with the findings on optimal leverage in Panel A, the total amount of debt P=PS+PLincreases with λ. The figure also shows that the amount of long-term debt increases with λwhereas the amount of short-term debt decreases. This finding has implications for the firm’s refinancing intensity. Panel C in Figure 1 displays the optimal refinancing intensity θSas a function of λ. This relationship reflects the firm’s trade-off between rollover risk and investment incentives. On the one hand, the firm improves investment incentives by using more short-term debt relative to longterm debt. This feature comes from the fact that the value of short-term debt is less sensitive to the firm’s assets-in-place compared to long-term debt. Short-term debt holders therefore share less of the benefits from the firm’s investments with equity holders when assets-in-place increase. On the other hand, the firm’s rollover risk increases with the amount of short-term debt relative to long-term debt. Short-term debt holders share fewer losses with equity holders when assets-in-place decrease and the firm therefore defaults earlier. Since the value of the growth option decreases 12Friewald et al. (2018) emphasize that it is challenging to match the level of several measures from their model (most importantly leverage ratios) with corresponding measures in the real world. I face the same challenge because I extend their model by incorporating the investment option from Diamond and He (2014). Similar to Friewald et al. (2018), the purpose of my theoretical analysis is to study the structural relationships between key variables in a stylized model and to consider implications for expected stock returns. I refer to Strebulaev and Whited (2012) for a more elaborate discussion on the general challenges corporate finance models have in terms of matching real-world quantities. 24 with λ, the firm has greater incentive to reduce rollover risk compared to improving investment incentives the higher the value of λ. For this reason, the optimal refinancing intensity decreases with λ. Panel D in Figure 1 depicts the investment and default boundaries as functions of λ. The investment boundary Xilies above the default boundary XBwhen λ > 0. As λincreases, it becomes more expensive to invest and the firm endogenously chooses higher leverage and lower refinancing intensity. This financing choice impairs investment incentives and Xiincreases. Since the value of the growth option decreases with λ, equity holders become less willing to keep the firm alive when assets-in-place deteriorate and this tends to increase XB. The fact that the firm endogenously chooses higher leverage also tends to increase XB. The lower refinancing intensity, however, reduces rollover risk and tends to decrease XB. Nonetheless, the two former effects dominate the latter and XBincreases with λ. In the limiting case where λ→0 then Xi→XB because the firm always invests when the investment cost approaches zero. In this case, the model reduces to Friewald et al. (2018) as a special case. 5.2 Expected Stock Returns The previous section considered the firm’s optimal financing decisions at time t= 0. At time t > 0 most firms deviate from their optimal capital structures (see e.g. Leary and Roberts (2005) and Strebulaev (2007)). In this section, I therefore consider implications of firms’ investment and financing decisions for the cross-section of expected stock returns at time t > 0. First, I explore the relationship between investments and expected stock returns which gives rise to a return differential consistent with the investment premium. Second, I investigate the return differential among zeroleverage firms. Third, I analyze how the return differential depends on firms’ refinancing intensities. Investments and Expected Stock Returns I set the asset risk-premium to ξ= 1% and analyze the relationship between the firm’s investment policy and expected stock returns at time t > 0. The model has a constant risk-free rate and I refer to the expected excess stock return as the expected stock return below. Consider a single firm with λ= 9.5 which chooses its optimal leverage and refinancing intensity at time t= 0. The firm’s refinancing intensity remains fixed over time but leverage does not. At time t > 0, the firm’s current leverage deviates from its optimal leverage whenever Xt6=X0. The firm invests when Xt≥Xi= 0.67 and defaults when Xt=XB= 0.61. Debt overhang makes equity holders unwilling to invest when XB< Xt< Xieven though the growth option has positive NPV. [INSERT FIGURE 2] 25 Measures of Investment Frictions ATtTotal assets at the end of June in year tis given by ATt−1i.e. ”Assets - Total” from the fiscal year ending in year t−1. AGEtAge is the number of years a firm has appeared in COMPUSTAT at the end of the previous fiscal year. PAYtPayout at the end of June in year tis the tercile ranking of the payout ratio: Payout Ratiot=PRSTKCt−1+DV Pt−1+DV Ct−1 OIBDPt−1 where PRSTKCt−1is ”Purchase of Common and Preferred Stock”, DV Pt−1is ”Dividends - Preferred/Preference”, DV Ct−1is ”Dividends Common/Ordinary”, and OIBDPt−1is ”Operating Income Before Depreciation” at the end of the fiscal year ending in t−1. For firms with non-positive OIBDPt−1, I include those with positive distributions in the high payout tercile and those with zero distributions in the low payout tercile. Measures of Limits-to-Arbitrage IV OLtIdiosyncratic stock volatility is estimated from daily stock returns over the last year ending in June in year t. I run time-series regressions of each stock’s daily realized returns on market returns obtained from Kenneth French’s website and use the standard deviation of the residuals to measure idiosyncratic volatility. I require at least 200 observations in the estimation window. PRCtPrice is the stock price at the end of June in year t from CRSP. BAtBid-ask spread is the time-series average of daily stock bid-ask spreads over the last year ending in June in year t. I calculate daily bid-ask spreads as : Bid-Ask Spreadt=ASKt−BIDt 1 2(ASKt+BIDt) where ASKtis the end-of-day ask price and BIDtis the end-of-day bid price from CRSP. AMtAmihud (2002) illiquidity measure is the time-series average of absolute daily returns divided by daily dollar trading volume over the past year ending in June in year tfrom CRSP. 32 Measures of Limits-to-Arbitrage (continued) DV OLtDollar volume is the time-series average of daily trading volumes calculated as stock price times trading volume over the past year ending in June in year tfrom CRSP. 33 B Valuations of Debt and Equity In this appendix, I derive the value of debt and equity. For simplicity, I omit time subscripts such that X=Xtthroughout the derivations. Debt Value The market value of debt, Dj(X), for j={S, L}is the solution to the ordinary differential equation (ODE): rDj=1 2σ2X2Dj XX +˜ iXDj X+φj[Pj−Dj] (B.1) where I write Dj=Dj(X) and use subscripts to denote partial derivatives. The equation states that the required return on the left-hand side must equal the expected return on the right-hand side. The first two terms is the expected change in the value of debt when Xfluctuates where ˜ iis the asset growth rate determined by equity holders which depends on X. The third term is the change in debt value from retiring maturing debt at principal value and issuing new debt at market value. Diamond and He (2014) show that equity holders follow a threshold investment strategy: the firm invests when X≥Xiand it does not invest when XB< X < Xi. The general solution to equation (B.1) is therefore given by: Dj(X) =    dj 1X−γj 1+pj, X ≥Xi dj 2X−γj 2+dj 3Xδj 2+pj, XB< X < Xi (B.2) where pj=Pj 1+r/φjis the default-free debt value and the exponents are given by: γj 1=(i−1 2σ2) + q(i−1 2σ2)2+ 2σ2(r+φj) σ2>0 γj 2=−1 2σ2+q1 4σ4+ 2σ2(r+φj) σ2>0 (B.3) δj 2= 1 2σ2+q1 4σ4+ 2σ2(r+φj) σ2>1 34 The value-matching condition at XBtogether with the continuity and differentiability conditions at Xidetermine the three coefficients dj 1,dj 2and dj 3: Dj(XB) = XB rθj lim X↑Xi Dj(X) = lim X↓Xi Dj(X) (B.4) lim X↑Xi Dj X(X) = lim X↓Xi Dj X(X) which are then given by: dj 1=dj 2Xγj 1−γj 2 i+dj 3Xγj 1+δj 2 i dj 2=dj 3 γj 1+δj 2 γj 2−γj 1 Xγj 2+δj 2 i(B.5) dj 3=θjXB/r −pj γj 1+δj 2 γj 2−γj 1 Xγj 2+δj 2 iX−γj 2 B+Xδj 2 B Equity Value The market value of equity, E(X), satisfies the equation: rE = max ˜ i∈{0,i} 1 2σ2X2EXX +˜ iXEX+X−λ˜ iX +kX j φjPj−X j φj[Pj−Dj] (B.6) where I have omitted the optimal default policy. The equation states that the required return on the left-hand side must equal the expected return on the right-hand side given equity holders’ optimal investment strategy. The first two terms is the expected change in the value of equity when Xfluctuates. The third and fourth terms are the cash flows to equity holders per unit time from the firm’s cash flow minus the investment cost. The fifth term is the debt benefits and the sixth term is debt rollover costs. It is challenging to solve equation (B.6) directly, because it depends on the debt values Dj(X). Instead, I value the equity claim as the residual between the levered firm value and debt value. The general solution to the unlevered firm value, V(X), is given by: V(X) =      v1X−γ3+X(1 −λi) r−i, X ≥Xi v2X−γ4+v3Xδ4+X r, XB< X < Xi (B.7) where the expected present value of the earnings stream is X(1−λi) r−iwhen the firm always invests 35 and X rwhen the firm never invests. The exponents are given by: γ3=(i−1 2σ2) + q(i−1 2σ2)2+ 2σ2r σ2>0 γ4=−1 2σ2+q1 4σ4+ 2σ2r σ2>0 (B.8) δ4= 1 2σ2+q1 4σ4+ 2σ2r σ2>1 The value-matching condition at XBtogether with the continuity and differentiability conditions at Xidetermine the coefficients v1,v2and v3: V(XB) = XB r lim X↑Xi V(X) = lim X↓Xi V(X) (B.9) lim X↑Xi VX(X) = lim X↓Xi VX(X) which are then given by: v1=−i(1 −λr) r(r−i)X1+γ3 i−v3Xγ4+δ4 BXγ3−γ4 i+v3Xγ3+δ4 i v2=−v3Xγ4+δ4 B(B.10) v3=(1 + γ3)i(1−λr) r(r−i)Xγ4+1 i (γ3+δ4)Xδ4+γ4 i−(γ3−γ4)Xγ4+δ4 B The general solution to the value of debt benefits, B(X), is given by: B(X) =            b1X−γ3+kX j φjPj r, X ≥Xi b2X−γ4+b3Xδ4+kX j φjPj r, XB< X < Xi (B.11) where kPj φjPj ris the expected present value of receiving the debt benefits in perpetuity. The value-matching condition at XBtogether with the continuity and differentiability conditions at Xi 36 determine the coefficients b1,b2and b3: B(XB)=0 lim X↑Xi B(X) = lim X↓Xi B(X) (B.12) lim X↑Xi BX(X) = lim X↓Xi BX(X) which are then given by: b1=−b3Xγ4+δ4 BXγ3−γ4 i−kX j φjPj rXγ4 BXγ3−γ4 i+b3Xγ3+δ4 i b2=−b3Xγ4+δ4 B−kX j φjPj rXγ4 B(B.13) b3=(γ3−γ4)kPj φjPj rXγ4 B (γ3+δ4)Xδ4+γ4 i−(γ3−γ4)Xγ4+δ4 B Given the unlevered firm value from equation (B.7), the value of debt benefits from equation (B.11), and the debt values from equation (B.2), the equity value is the residual: E(X) = V(X) + B(X)−X j Dj(X) (B.14) 37 Table 1: Summary Statistics and Correlations This table shows summary statistics and correlations for the variables I use in the main empirical analysis. Panel A reports time-series averages of the cross-sectional mean, standard deviation, 25%–quantile, median, and 75%–quantile of monthly excess returns, annual asset growth rates (AG), refinancing intensities (RI ), and leverage (LEV ) in percent. I calculate AG as the change in total assets from the fiscal year ending in t−2 to the fiscal year ending in t−1 divided by total assets from t−2. RI is the ratio of debt maturing within one year to total debt in t−1. LEV is the ratio of total debt to the sum of total debt and the market value of equity at the end of December in t−1. ME is the market value of equity in millions of USD measured at the end of June in year t. Before I calculate summary statistics, I winsorize asset growth rates each month at the 1st and 99th percentiles. Panel B presents time-series averages of the monthly cross-sectional Spearman rank correlations. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). Panel A: Summary Statistics Mean SD Q25 Median Q75 Excess return (RET) 0.94 16.27 -7.04 -0.26 7.05 Asset growth rate (AG) 18.54 47.70 -1.99 7.70 22.00 Refinancing intensity (RI ) 13.27 19.18 1.56 5.73 16.13 Leverage (LEV ) 25.45 23.10 5.59 19.75 40.07 Size (ME) 1,753 8,492 44 177 723 Panel B: Spearman Rank Correlations RET AG RI LEV ME Excess return (RET) 1.00 Asset growth rate (AG) 0.00 1.00 Refinancing intensity (RI ) -0.01 -0.06 1.00 Leverage (LEV ) 0.00 -0.14 -0.17 1.00 Size (ME) 0.05 0.21 -0.22 -0.08 1.00 38 Table 2: Portfolios Independently Sorted by Size and Asset Growth At the end of each June, I independently double-sort stocks into two portfolios based on size (ME) and into three portfolios based on asset growth rates (AG) using NYSE breakpoints. This procedure generates a cross-section of 2×3 = 6 portfolios. For both small and big firms, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B and C show value-weighted average asset growth rates and leverage ratios in percent. Panel D presents monthly value-weighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1−Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 High AG Low-High AG t-stat Panel A: Excess Returns Small 0.94 0.97 0.53 0.41 (4.87) Big 0.78 0.63 0.54 0.24 (1.79) Average 0.86 0.80 0.54 0.32 (3.63) Panel B: Asset Growth Small -8.63 7.48 53.11 -61.74 (-59.23) Big -4.08 7.54 37.62 -41.71 (-53.82) Average -6.35 7.51 45.37 -51.72 (-59.68) Panel C: Leverage Small 30.22 23.88 20.01 10.21 (53.92) Big 25.80 19.44 15.41 10.38 (42.10) Average 28.01 21.66 17.71 10.29 (54.85) Panel D: Unlevered Excess Returns Small 0.62 0.73 0.42 0.21 (2.76) Big 0.55 0.50 0.45 0.10 (0.82) Average 0.59 0.62 0.43 0.15 (1.86) 39 Table 3: Portfolios of Zero-Leverage Firms Independently Sorted by Size and Asset Growth At the end of each June, I independently double-sort zero-leverage firms into two portfolios based on size (ME) and into two portfolios based on asset growth rates (AG) using NYSE breakpoints. This procedure generates a cross-section of 2 ×2 = 4 portfolios. For both small and big firms, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B shows value-weighted asset growth rates in percent. Panel C presents the average number of stocks in each portfolio and Panel D shows the minimum number of stocks in each portfolio. I define firm ias zero-leverage if in both years t−2 and t−1 the outstanding amounts of both short-term debt (DLC ) and long-term debt (DLTT) equal zero. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG High AG Low-High AG t-stat Panel A: Excess Returns Small 0.80 0.67 0.12 (0.84) Big 0.44 0.77 -0.34 (-1.42) Average 0.62 0.72 -0.11 (-0.72) Panel B: Asset Growth Small -3.69 45.11 -48.80 (-46.29) Big 2.10 37.44 -35.34 (-37.64) Average -0.80 41.27 -42.07 (-45.87) Panel C: Average Number of Stocks Small 141 100 Big 18 40 Panel D: Minimum Number of Stocks Small 27 15 Big 3 6 40 Table 4: Portfolios Independently Sorted by Refinancing Intensitites and Asset Growth At the end of each June, I independently double-sort stocks into five portfolios based on refinancing intensities (RI ) and into five portfolios based on asset growth rates (AG) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. In each asset-growth quintile, I construct a High-Low RI portfolio that buys the High RI portfolio and sells the Low RI portfolio. I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B shows value-weighted average leverage ratios in percent. Panel C presents monthly valueweighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month t and Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 3 4 High AG Low-High AG t-stat Panel A: Excess Returns Low RI 0.70 0.81 0.76 0.79 0.57 0.12 (0.62) 2 0.90 0.81 0.65 0.70 0.47 0.43 (2.27) 3 0.76 0.80 0.75 0.50 0.31 0.45 (2.52) 4 0.87 0.68 0.56 0.72 0.36 0.51 (3.16) High RI 1.11 0.77 0.77 0.66 0.46 0.64 (3.46) High-Low RI 0.41 -0.04 0.01 -0.12 -0.11 0.52 (2.60) t-stat (2.62) (-0.28) (0.08) (-0.81) (-0.70) Panel B: Leverage Low RI 26.97 20.60 18.38 15.49 14.84 12.13 (37.04) 2 31.52 25.87 20.86 18.31 18.43 13.09 (30.61) 3 30.06 25.10 21.18 17.81 22.40 7.66 (16.50) 4 33.95 25.69 21.88 18.88 20.82 13.13 (27.02) High RI 28.97 21.57 19.70 15.13 11.85 17.11 (41.05) High-Low RI 2.00 0.97 1.32 -0.36 -2.98 4.98 (12.27) t-stat (4.67) (2.63) (2.28) (-0.93) (-12.76) Panel C: Unlevered Excess Returns Low RI 0.46 0.62 0.62 0.66 0.47 -0.01 (-0.08) 2 0.58 0.59 0.50 0.56 0.38 0.19 (1.21) 3 0.51 0.57 0.57 0.42 0.18 0.32 (2.13) 4 0.56 0.49 0.41 0.60 0.26 0.30 (2.24) High RI 0.72 0.59 0.58 0.56 0.40 0.32 (1.87) High-Low RI 0.26 -0.03 -0.04 -0.10 -0.07 0.33 (1.93) t-stat (2.05) (-0.22) (-0.30) (-0.75) (-0.51) 41 Table IA.1: Portfolios Independently Sorted by Size and Asset Growth: EqualWeighted Returns At the end of each June, I independently double-sort stocks into two portfolios based on size (ME) and into three portfolios based on asset growth rates (AG) using NYSE breakpoints. This procedure generates a cross-section of 2×3 = 6 portfolios. For both small and big firms, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B and C show value-weighted average asset growth rates and leverage ratios in percent. Panel D presents monthly value-weighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1−Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 High AG Low-High AG t-stat Panel A: Excess Returns Small 1.35 1.09 0.55 0.80 (8.61) Big 0.90 0.85 0.59 0.31 (2.90) Average 1.13 0.97 0.57 0.56 (6.70) Panel B: Asset Growth Small -11.65 7.29 57.29 -68.94 (-61.53) Big -5.30 7.50 44.73 -50.03 (-46.21) Average -8.48 7.40 51.01 -59.48 (-55.29) Panel C: Leverage Small 30.87 26.09 22.56 8.31 (43.54) Big 28.97 21.99 17.38 11.60 (67.82) Average 29.92 24.04 19.97 9.95 (58.84) Panel D: Unlevered Excess Returns Small 0.81 0.77 0.37 0.44 (5.97) Big 0.59 0.64 0.47 0.12 (1.27) Average 0.70 0.70 0.42 0.28 (3.87) 48 Table IA.2: Portfolios of Zero-Leverage Firms Independently Sorted by Size and Asset Growth: Equal-Weighted Returns At the end of each June, I independently double-sort zero-leverage firms into two portfolios based on size (ME) and into two portfolios based on asset growth rates (AG) using NYSE breakpoints. This procedure generates a cross-section of 2 ×2 = 4 portfolios. For both small and big firms, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Panel A presents monthly equal-weighted means of excess returns in percentage points. Panel B shows equal-weighted asset growth rates in percent. Panel C presents the average number of stocks in each portfolio and Panel D shows the minimum number of stocks in each portfolio. I define firm ias zero-leverage if in both years t−2 and t−1 the outstanding amounts of both short-term debt (DLC ) and long-term debt (DLTT) equal zero. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG High AG Low-High AG t-stat Panel A: Excess Returns Small 1.24 0.88 0.35 (2.61) Big 0.48 0.76 -0.28 (-1.62) Average 0.86 0.82 0.04 (0.31) Panel B: Asset Growth Small -6.91 46.77 -53.68 (-54.19) Big 1.37 37.45 -36.08 (-38.61) Average -2.77 42.11 -44.88 (-48.49) Panel C: Average Number of Stocks Small 141 100 Big 18 40 Panel D: Minimum Number of Stocks Small 27 15 Big 3 6 49 Table IA.3: Portfolios Independently Sorted by Refinancing Intensitites and Asset Growth: Equal-Weighted Returns At the end of each June, I independently double-sort stocks into five portfolios based on refinancing intensities (RI ) and into five portfolios based on asset growth rates (AG) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. In each asset-growth quintile, I construct a High-Low RI portfolio that buys the High RI portfolio and sells the Low RI portfolio. I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents monthly equal-weighted means of excess returns in percentage points. Panel B shows equal-weighted average leverage ratios in percent. Panel C presents monthly equalweighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month t and Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 3 4 High AG Low-High AG t-stat Panel A: Excess Returns Low RI 1.08 1.06 0.90 0.90 0.37 0.71 (4.37) 2 1.17 1.14 0.95 0.77 0.47 0.70 (4.72) 3 1.17 1.12 0.90 0.76 0.35 0.82 (5.93) 4 1.27 1.29 1.02 1.00 0.39 0.88 (6.91) High RI 1.45 1.16 1.14 1.00 0.39 1.06 (7.82) High-Low RI 0.38 0.11 0.24 0.10 0.03 0.35 (2.47) t-stat (3.09) (0.96) (2.34) (0.99) (0.25) Panel B: Leverage Low RI 31.42 27.87 23.87 22.08 22.46 8.96 (40.39) 2 44.40 37.93 32.45 29.53 30.14 14.26 (69.61) 3 44.38 38.20 32.56 29.80 30.46 13.93 (64.47) 4 40.67 35.74 31.15 27.63 28.63 12.04 (41.49) High RI 29.16 24.87 21.68 18.49 17.65 11.52 (52.28) High-Low RI -2.26 -2.99 -2.20 -3.59 -4.82 2.56 (13.84) t-stat (-10.03) (-16.72) (-12.72) (-28.43) (-25.05) Panel C: Unlevered Excess Returns Low RI 0.57 0.73 0.64 0.68 0.22 0.35 (3.03) 2 0.56 0.62 0.60 0.52 0.29 0.28 (2.96) 3 0.52 0.58 0.57 0.49 0.18 0.34 (4.01) 4 0.59 0.76 0.66 0.67 0.17 0.41 (4.83) High RI 0.85 0.79 0.85 0.79 0.26 0.59 (5.50) High-Low RI 0.28 0.06 0.22 0.10 0.04 0.24 (2.37) t-stat (3.12) (0.76) (2.72) (1.28) (0.41) 50 Table IA.4: Long-Short Portfolios Independently Sorted by Refinancing Intensitites and Asset Growth: Equal-Weighted Returns At the end of each June, I independently double-sort stocks into five portfolios based on refinancing intensities (RI ) and into five portfolios based on asset growth rates (AG) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. For each of these five long-short portfolios, I calculate monthly equal-weighted means in percentage points of alpha estimates from regressing excess returns on the market (MKT), the three FamaFrench factors (MKT, SMB, HML), the four factors including momentum (MKT, SMB, HML, UMD), and the five Fama-French factors (MKT, SMB, HML, RMW, CMA). I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents the results for risk-adjusted levered returns and Panel B shows the results for risk-adjusted unlevered returns. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, ∗∗∗ when p < 0.01, and t-statistics are in parenthesis. CAPM α3-factor α4-factor α5-factor α Panel A: Risk-Adjusted Returns Low RI 0.80∗∗∗ 0.63∗∗∗ 0.58∗∗∗ 0.61∗∗∗ (4.99) (4.13) (3.74) (4.19) 2 0.75∗∗∗ 0.50∗∗∗ 0.45∗∗∗ 0.39∗∗∗ (5.00) (3.68) (3.27) (2.83) 3 0.83∗∗∗ 0.66∗∗∗ 0.66∗∗∗ 0.62∗∗∗ (5.94) (4.99) (4.82) (4.77) 4 0.91∗∗∗ 0.74∗∗∗ 0.74∗∗∗ 0.70∗∗∗ (7.10) (6.09) (5.92) (5.85) High RI 1.14∗∗∗ 0.95∗∗∗ 0.90∗∗∗ 0.92∗∗∗ (8.55) (7.66) (7.16) (7.74) High-Low RI 0.34∗∗ 0.32∗∗ 0.32∗∗ 0.31∗∗ (2.39) (2.19) (2.17) (2.09) Panel B: Risk-Adjusted Unlevered Returns Low RI 0.48∗∗∗ 0.37∗∗∗ 0.32∗∗∗ 0.37∗∗∗ (4.40) (3.54) (2.98) (3.76) 2 0.40∗∗∗ 0.29∗∗∗ 0.23∗∗∗ 0.23∗∗∗ (4.76) (3.65) (2.84) (2.95) 3 0.45∗∗∗ 0.40∗∗∗ 0.36∗∗∗ 0.40∗∗∗ (5.82) (5.23) (4.56) (5.31) 4 0.51∗∗∗ 0.44∗∗∗ 0.40∗∗∗ 0.44∗∗∗ (6.45) (5.70) (5.09) (5.86) High RI 0.74∗∗∗ 0.62∗∗∗ 0.54∗∗∗ 0.58∗∗∗ (7.57) (6.60) (5.75) (6.56) High-Low RI 0.26∗∗ 0.24∗∗ 0.22∗∗ 0.21∗ (2.52) (2.35) (2.11) (1.94) 51 Table IA.5: Portfolios of Firms with Non-Positive Net Debt Independently Sorted by Size and Asset Growth At the end of each June, I independently double-sort firms with non-positive net debt into two portfolios based on size (ME) and into two portfolios based on asset growth rates (AG) using NYSE breakpoints. This procedure generates a cross-section of 2 ×2 = 4 portfolios. For both small and big firms, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B shows value-weighted asset growth rates in percent. Panel C presents the average number of stocks in each portfolio and Panel D shows the minimum number of stocks in each portfolio. I define firm ias a firm with non-positive net debt if in both years t−2 and t−1 the sum of short-term debt (DLC) and long-term debt (DLTT) minus cash and short-term investments (CHE) is non-positive. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG High AG Low-High AG t-stat Panel A: Excess Returns Small 0.82 0.66 0.16 (1.65) Big 0.59 0.62 -0.03 (-0.18) Average 0.71 0.64 0.07 (0.64) Panel B: Asset Growth Small -2.47 48.12 -50.59 (-38.53) Big 3.54 31.43 -27.88 (-31.56) Average 0.54 39.78 -39.24 (-37.73) Panel C: Average Number of Stocks Small 430 349 Big 53 107 Panel D: Minimum Number of Stocks Small 78 55 Big 17 36 52 Table IA.6: Long-Short Portfolios Independently Sorted by Refinancing Intensities and Asset Growth with Different Number of Portfolios At the end of each June, I independently double-sort stocks into Nportfolios based on firms’ refinancing intensities (RI ) and into five portfolios based on firms’ asset growth rates (AG). This procedure generates a cross-section of N×5 portfolios. In each refinancing quantile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. Next, I calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. For this portfolio, I calculate the monthly value-weighted mean in percentage points of excess returns and alpha estimates from regressing value-weighted excess returns on the market (MKT), the three Fama-French factors (MKT, SMB, HML), the four factors including momentum (MKT, SMB, HML, UMD), and the five Fama-French factors (MKT, SMB, HML, RMW, CMA). I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, ∗∗∗ when p < 0.01, and t-statistics are in parenthesis. Levered Returns Unlevered Returns 3×5 5 ×5 7 ×5 3 ×5 5 ×5 7 ×5 Excess return 0.38∗∗ 0.52∗∗∗ 0.78∗∗∗ 0.24 0.33∗0.57∗∗∗ (2.12) (2.60) (3.65) (1.56) (1.93) (2.99) CAPM α0.41∗∗ 0.58∗∗∗ 0.79∗∗∗ 0.28∗0.41∗∗ 0.64∗∗∗ (2.28) (2.88) (3.68) (1.86) (2.39) (3.36) 3-factor α0.42∗∗ 0.56∗∗∗ 0.76∗∗∗ 0.29∗0.39∗∗ 0.64∗∗∗ (2.33) (2.77) (3.48) (1.92) (2.30) (3.36) 4-factor α0.55∗∗∗ 0.61∗∗∗ 0.78∗∗∗ 0.41∗∗∗ 0.45∗∗∗ 0.66∗∗∗ (3.05) (2.97) (3.49) (2.68) (2.59) (3.37) 5-factor α0.42∗∗ 0.52∗∗ 0.68∗∗∗ 0.31∗∗ 0.38∗∗ 0.60∗∗∗ (2.26) (2.49) (3.05) (2.00) (2.14) (3.07) 53 Table IA.7: Portfolios Sequentially Sorted by Refinancing Intensitites and Asset Growth At the end of each June, I sequentially double-sort stocks first into five portfolios based on refinancing intensities (RI ) and then into five portfolios based on asset growth rates (AG) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. In each asset-growth quintile, I construct a High-Low RI portfolio that buys the High RI portfolio and sells the Low RI portfolio. I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B shows value-weighted average leverage ratios in percent. Panel C presents monthly value-weighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 3 4 High AG Low-High AG t-stat Panel A: Excess Returns Low RI 0.73 0.76 0.76 0.73 0.56 0.17 (0.94) 2 0.88 0.81 0.63 0.71 0.48 0.40 (2.18) 3 0.81 0.82 0.76 0.46 0.32 0.49 (2.72) 4 0.89 0.67 0.58 0.65 0.48 0.41 (2.44) High RI 1.11 0.81 0.79 0.69 0.44 0.67 (3.53) High-Low RI 0.38 0.05 0.03 -0.04 -0.12 0.50 (2.45) t-stat (2.30) (0.31) (0.17) (-0.24) (-0.76) Panel B: Leverage Low RI 26.35 21.22 17.74 13.84 16.04 10.31 (28.22) 2 31.08 25.20 20.06 18.51 18.67 12.41 (29.50) 3 29.88 25.16 20.37 18.11 22.91 6.97 (15.19) 4 34.23 26.14 21.76 19.34 20.53 13.70 (28.71) High RI 28.75 23.12 20.57 15.16 12.22 16.53 (38.92) High-Low RI 2.40 1.90 2.83 1.32 -3.83 6.22 (14.66) t-stat (5.87) (5.77) (5.54) (3.49) (-14.24) Panel C: Unlevered Excess Returns Low RI 0.50 0.58 0.62 0.63 0.45 0.05 (0.33) 2 0.56 0.60 0.50 0.57 0.39 0.17 (1.08) 3 0.56 0.58 0.60 0.38 0.19 0.36 (2.37) 4 0.56 0.48 0.44 0.51 0.37 0.20 (1.43) High RI 0.73 0.60 0.60 0.58 0.37 0.35 (2.07) High-Low RI 0.23 0.01 -0.02 -0.05 -0.07 0.30 (1.71) t-stat (1.68) (0.09) (-0.18) (-0.38) (-0.49) 54 Table IA.8: Long-Short Portfolios Sequentially Sorted by Refinancing Intensitites and Asset Growth At the end of each June, I sequentially double-sort stocks first into five portfolios based on refinancing intensities (RI ) and then into five portfolios based on asset growth rates (AG) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. For each of these five long-short portfolios, I calculate monthly value-weighted means in percentage points of alpha estimates from regressing excess returns on the market (MKT), the three FamaFrench factors (MKT, SMB, HML), the four factors including momentum (MKT, SMB, HML, UMD), and the five Fama-French factors (MKT, SMB, HML, RMW, CMA). I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents the results for risk-adjusted levered returns and Panel B shows the results for risk-adjusted unlevered returns. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, ∗∗∗ when p < 0.01, and t-statistics are in parenthesis. CAPM α3-factor α4-factor α5-factor α Panel A: Risk-Adjusted Returns Low RI 0.24 -0.07 -0.16 -0.29∗ (1.29) (-0.43) (-0.93) (-1.88) 2 0.50∗∗∗ 0.19 0.14 -0.13 (2.77) (1.15) (0.86) (-0.85) 3 0.55∗∗∗ 0.35∗∗ 0.32∗0.22 (3.05) (2.04) (1.79) (1.29) 4 0.48∗∗∗ 0.23 0.34∗∗ 0.06 (2.88) (1.52) (2.27) (0.39) High RI 0.77∗∗∗ 0.42∗∗ 0.41∗∗ 0.10 (4.13) (2.56) (2.46) (0.63) High-Low RI 0.54∗∗∗ 0.49∗∗ 0.57∗∗∗ 0.39∗ (2.62) (2.39) (2.72) (1.83) Panel B: Risk-Adjusted Unlevered Returns Low RI 0.18 -0.07 -0.15 -0.27∗ (1.12) (-0.51) (-1.03) (-1.95) 2 0.33∗∗ 0.09 0.06 -0.15 (2.22) (0.65) (0.45) (-1.20) 3 0.46∗∗∗ 0.31∗∗ 0.26∗0.22 (3.06) (2.15) (1.76) (1.49) 4 0.34∗∗∗ 0.16 0.24∗∗ 0.04 (2.60) (1.36) (1.98) (0.34) High RI 0.55∗∗∗ 0.26∗0.26∗0.00 (3.47) (1.88) (1.83) (-0.04) High-Low RI 0.37∗∗ 0.34∗0.41∗∗ 0.26 (2.13) (1.91) (2.30) (1.43) 55 Table IA.9: Portfolios Sequentially Sorted by Asset Growth and Refinancing Intensitites At the end of each June, I sequentially double-sort stocks first into five portfolios based on asset growth rates (AG) and then into five portfolios based on refinancing intensities (RI ) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. In each asset-growth quintile, I construct a High-Low RI portfolio that buys the High RI portfolio and sells the Low RI portfolio. I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents monthly value-weighted means of excess returns in percentage points. Panel B shows value-weighted average leverage ratios in percent. Panel C presents monthly value-weighted means of unlevered excess returns in percentage points. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The parentheses contain t-statistics. Low AG 2 3 4 High AG Low-High AG t-stat Panel A: Excess Returns Low RI 0.70 0.86 0.77 0.82 0.59 0.12 (0.60) 2 0.93 0.77 0.62 0.70 0.43 0.50 (2.69) 3 0.71 0.82 0.72 0.51 0.35 0.35 (2.09) 4 0.92 0.74 0.55 0.69 0.35 0.57 (3.48) High RI 1.14 0.73 0.75 0.69 0.48 0.66 (3.69) High-Low RI 0.44 -0.13 -0.02 -0.12 -0.11 0.54 (2.70) t-stat (2.70) (-0.86) (-0.13) (-0.83) (-0.68) Panel B: Leverage Low RI 27.10 21.33 18.67 15.67 14.39 12.71 (34.54) 2 31.59 26.07 20.91 17.56 18.12 13.47 (34.02) 3 31.02 25.25 21.39 17.77 22.51 8.51 (17.65) 4 33.61 25.46 21.93 18.62 21.35 12.26 (24.60) High RI 27.54 22.15 19.44 15.63 12.64 14.90 (34.47) High-Low RI 0.44 0.82 0.77 -0.04 -1.75 2.19 (4.43) t-stat (0.93) (2.24) (1.37) (-0.10) (-6.71) Panel C: Unlevered Excess Returns Low RI 0.46 0.66 0.63 0.69 0.49 -0.03 (-0.16) 2 0.62 0.55 0.49 0.57 0.34 0.28 (1.76) 3 0.48 0.59 0.54 0.43 0.25 0.23 (1.60) 4 0.58 0.53 0.40 0.58 0.23 0.35 (2.65) High RI 0.77 0.56 0.57 0.57 0.42 0.35 (2.16) High-Low RI 0.31 -0.10 -0.06 -0.12 -0.07 0.38 (2.17) t-stat (2.31) (-0.84) (-0.46) (-0.88) (-0.49) 56 Table IA.10: Long-Short Portfolios Sequentially Sorted by Refinancing Intensitites and Asset Growth At the end of each June, I sequentially double-sort stocks first into five portfolios based on asset growth rates (AG) and then into five portfolios based on refinancing intensities (RI ) using NYSE breakpoints. In each refinancing quintile, I construct a Low-High AG portfolio that buys the Low AG portfolio and sells the High AG portfolio. For each of these five long-short portfolios, I calculate monthly value-weighted means in percentage points of alpha estimates from regressing excess returns on the market (MKT), the three FamaFrench factors (MKT, SMB, HML), the four factors including momentum (MKT, SMB, HML, UMD), and the five Fama-French factors (MKT, SMB, HML, RMW, CMA). I also calculate the return differential of buying the Low-High AG portfolio for firms with high refinancing intensities and selling the Low-High AG portfolio for firms with low refinancing intensities. Panel A presents the results for risk-adjusted levered returns and Panel B shows the results for risk-adjusted unlevered returns. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, ∗∗∗ when p < 0.01, and t-statistics are in parenthesis. CAPM α3-factor α4-factor α5-factor α Panel A: Risk-Adjusted Returns Low RI 0.20 -0.14 -0.25 -0.46∗∗∗ (1.02) (-0.82) (-1.41) (-2.90) 2 0.56∗∗∗ 0.28 0.21 -0.07 (3.00) (1.60) (1.16) (-0.46) 3 0.43∗∗ 0.24 0.21 0.10 (2.53) (1.46) (1.27) (0.61) 4 0.67∗∗∗ 0.44∗∗∗ 0.50∗∗∗ 0.28∗ (4.11) (2.87) (3.23) (1.85) High RI 0.76∗∗∗ 0.44∗∗∗ 0.39∗∗ 0.11 (4.30) (2.78) (2.46) (0.80) High-Low RI 0.56∗∗∗ 0.58∗∗∗ 0.65∗∗∗ 0.57∗∗∗ (2.77) (2.82) (3.07) (2.69) Panel B: Risk-Adjusted Unlevered Returns Low RI 0.12 -0.16 -0.25∗-0.44∗∗∗ (0.74) (-1.05) (-1.65) (-3.20) 2 0.42∗∗∗ 0.21 0.14 -0.05 (2.76) (1.47) (0.98) (-0.35) 3 0.35∗∗ 0.21 0.17 0.10 (2.52) (1.62) (1.23) (0.78) 4 0.50∗∗∗ 0.33∗∗∗ 0.38∗∗∗ 0.22∗ (4.02) (2.90) (3.25) (1.95) High RI 0.54∗∗∗ 0.27∗∗ 0.23∗0.01 (3.58) (2.00) (1.68) (0.10) High-Low RI 0.42∗∗ 0.43∗∗ 0.48∗∗∗ 0.46∗∗ (2.37) (2.40) (2.66) (2.48) 57 Table IA.17: FM Regressions: Asset Growth and Leverage This table presents the results of Fama and MacBeth (1973) regressions of future excess returns on the logarithm of asset growth (AG), beta (β), the logarithm of the market value of equity (ME), the logarithm of the book-to-market ratio (BM ), and the logarithm of operating profitability (OP). For the cross-sectional regressions, I use either ordinary least squares estimates (equal-weighted) or weighted least squares with the market value of equity as the weighting scheme (value-weighted). I estimate βas in Fama and French (1992) while BM and OP are calculated as in Fama and French (2015). Panel A presents the results for excess returns and Panel B shows the results for unlevered excess returns. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The t-statistics in parenthesis are adjusted following Newey and West (1987) using six lags. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. Value-weighted Equal-weighted (1) (2) (3) (4) Panel A: Excess Returns Log(1+AG) -0.66∗∗ -0.36∗∗ -1.41∗∗∗ -1.11∗∗∗ (-2.35) (-2.19) (-7.71) (-9.45) β-0.08 -0.05 (-0.25) (-0.17) Log(ME) -0.08∗∗ -0.13∗∗∗ (-2.29) (-4.14) Log(BM) 0.15 0.20∗∗∗ (1.64) (2.96) Log(1+OP) 0.87∗∗∗ 0.43∗∗ (3.39) (2.58) Adj. R20.01 0.10 0.00 0.03 N3025.35 2786.96 3025.35 2786.96 Panel B: Unlevered Excess Returns Log(1+AG) -0.42 -0.21 -0.86∗∗∗ -0.75∗∗∗ (-1.60) (-1.45) (-5.95) (-8.44) β-0.09 -0.11 (-0.32) (-0.52) Log(ME) -0.06∗∗ -0.08∗∗∗ (-2.07) (-3.45) Log(BM) 0.02 0.04 (0.26) (0.67) Log(1+OP) 0.56∗∗ 0.32∗∗ (2.56) (2.15) Adj. R20.02 0.10 0.00 0.03 N3025.35 2786.96 3025.35 2786.96 64 Table IA.18: FM Regressions: Asset Growth and Zero-Leverage Firms This table presents the results of Fama and MacBeth (1973) regressions of future excess returns on the logarithm of asset growth (AG), beta (β), the logarithm of the market value of equity (ME), the logarithm of the book-to-market ratio (BM ), and the logarithm of operating profitability (OP) for zero-leverage firms. For the cross-sectional regressions, I use either ordinary least squares estimates (equal-weighted) or weighted least squares with the market value of equity as the weighting scheme (value-weighted). I estimate βas in Fama and French (1992) while BM and OP are calculated as in Fama and French (2015). I define firm ias zero-leverage if in both years t−2 and t−1 the outstanding amounts of both short-term debt (DLC) and long-term debt (DLTT) equal zero. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The t-statistics in parenthesis are adjusted following Newey and West (1987) using six lags. The convention for p-values is: ∗ when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. Value-weighted Equal-weighted (1) (2) (3) (4) Log(1+AG) 0.78 0.29 -0.25 -0.17 (1.22) (0.48) (-0.71) (-0.49) β0.78∗0.22 (1.72) (0.66) Log(ME) 0.07 -0.21∗∗∗ (1.13) (-4.48) Log(BM) 0.26∗0.34∗∗∗ (1.94) (3.79) Log(1+OP) 1.25∗∗ 0.97∗∗∗ (2.41) (2.61) Adj. R20.05 0.16 0.01 0.03 N297.71 284.86 297.71 284.86 65 Table IA.19: FM Regressions: Asset Growth and Refinancing Intensitites This table presents the results of Fama and MacBeth (1973) regressions of future excess returns on the logarithm of asset growth (AG), refinancing intensities (RI ), and their interaction. For the cross-sectional regressions, I use either ordinary least squares estimates (equal-weighted) or weighted least squares with the market value of equity as the weighting scheme (value-weighted). In specifications (2) and (4), I also include beta (β), the logarithm of the market value of equity (ME), the logarithm of the book-to-market ratio (BM ), and the logarithm of operating profitability (OP) in the regressions. I estimate βas in Fama and French (1992) while BM and OP are calculated as in Fama and French (2015). Panel A presents the results for excess returns and Panel B shows the results for unlevered excess returns. I follow Doshi et al. (2018) and calculate unlevered excess returns as RE,i(t)(1 −Li(t−1)) where RE,i(t) is the excess return for firm iin month tand Li(t−1) is the leverage ratio of firm iat the end of month t−1. The sample period is from July 1970 to June 2016 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The t-statistics in parenthesis are adjusted following Newey and West (1987) using six lags. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. Value-weighted Equal-weighted (1) (2) (3) (4) Panel A: Excess Returns Log(1+AG) -0.73∗∗ -0.33∗-1.45∗∗∗ -1.07∗∗∗ (-2.47) (-1.80) (-7.42) (-7.63) RI 0.41 0.40 0.45∗∗ 0.42∗∗∗ (1.18) (1.52) (2.12) (3.13) Log(1+AG)*RI -0.96 -1.30 -0.11 -0.48 (-1.16) (-1.48) (-0.28) (-1.06) Controls N Y N Y Adj. R20.02 0.10 0.01 0.03 N2643.23 2428.12 2643.23 2428.12 Panel B: Unlevered Excess Returns Log(1+AG) -0.50∗-0.20 -0.77∗∗∗ -0.63∗∗∗ (-1.90) (-1.28) (-5.52) (-6.64) RI 0.43 0.43∗0.50∗∗ 0.65∗∗∗ (1.39) (1.76) (2.33) (4.62) Log(1+AG)*RI -0.69 -1.02 -0.23 -0.56 (-0.96) (-1.34) (-0.80) (-1.57) Controls N Y N Y Adj. R20.02 0.11 0.01 0.03 N2643.23 2428.12 2643.23 2428.12 66 Chapter 2 Why Does Debt Dispersion Affect Yield Spreads? Thomas Kjær Poulsen* Abstract I study predictions of rollover risk models and strategic debt service models on the negative relationship between corporate bond yield spreads and debt dispersion. Rollover risk models predict a more negative relationship for financially constrained firms, whereas strategic debt service models predict a less negative relationship. To test these predictions I run panel regressions of yield spreads on debt dispersion interacted with measures of financial constraints. I find that the relationship between yield spreads and debt dispersion is more negative for financially constrained firms consistent with rollover risk models. *Center for Financial Frictions (FRIC), Department of Finance, Copenhagen Business School, Solbjerg Plads 3, DK-2000 Frederiksberg, E-mail: [email protected]. I am grateful to Jens Dick-Nielsen, Peter Feldh¨utter, and Kristian R. Miltersen for helpful comments and discussions. In addition, I thank seminar participants at Copenhagen Business School. Any remaining errors are solely my own. Support from the Center for Financial Frictions (FRIC), grant no. DNRF102, is gratefully acknowledged. 67 1 Introduction A central question in the corporate bond literature is why some bonds have higher yield spreads than others. Yield spreads directly determine firms’ debt financing costs and influence both financing and investment decisions. Understanding the determinants of yield spreads is therefore important not only for finance academics but also for finance professionals to inform corporate financial policies. In the literature there is a well-established negative relationship between yield spreads and debt dispersion (see e.g. Davydenko and Strebulaev (2007), Dass and Massa (2014), and Nagler (2019)). In this paper, I examine two possible explanations for this negative relationship: rollover risk and strategic debt service. According to both theories debt dispersion reduces yield spreads but for different reasons. Theories of rollover risk argue that firms with more dispersed debt maturities have lower yield spreads because they are less likely to default (e.g. Choi et al. (2018)). Theories of strategic debt service argue that higher renegotiation frictions, which determine how difficult it is to renegotiate the firm’s debt, reduce equity holders’ incentive to default strategically and therefore results in lower yield spreads (e.g. Davydenko and Strebulaev (2007)). Empirically, measures of debt maturity dispersion and proxies for renegotiation frictions are often highly correlated. I therefore refer to these measures jointly as debt dispersion. To disentangle these two candidate explanations from each other I examine how the relationship between yield spreads and debt dispersion depends on the level of financial constraints. I exploit the fact that financially constrained firms are more exposed to capital market conditions (see e.g. Gomes et al. (2006), Whited and Wu (2006), Livdan et al. (2009), and Li (2011)). In rollover risk models yield spreads should decrease more with debt maturity dispersion for financially constrained firms because they are more exposed to capital market conditions. In strategic debt service models the relationship between yield spreads and renegotiation frictions should be less negative for financially constrained firms. To derive this hypothesis I extend the strategic debt service model by Davydenko and Strebulaev (2007). Davydenko and Strebulaev (2007) show that the relationship between yield spreads and renegotiation frictions is determined by a trade-off between two opposing effects. On the one hand, renegotiation frictions reduce the incentive for equity holders to threaten to default strategically with a view to obtain debt concessions. This strategic default effect decreases yield spreads because the probability of default decreases. On the other hand, renegotiation frictions also increase expected liquidation costs in bankruptcy because renegotiations are more likely to fail. This recovery effect increases yield spreads because expected recovery rates decrease. When equity holders have high bargaining power vis-´a-vis debt holders, the strategic default effect dominates and vice versa. 68 To analyze the effects of financial constraints in strategic debt service models I make two extensions to the Davydenko and Strebulaev (2007) model. First, I assume that financially constrained firms borrow at higher rates consistent with the empirical evidence that financially constrained firms face higher costs of capital because they are more exposed to capital market conditions (see e.g. Gomes et al. (2006), Whited and Wu (2006), Livdan et al. (2009), and Li (2011)). Second, I assume that firms refinance maturing debt by issuing new debt. The model shows that financial constraints strengthen the recovery effect because equity holders default more often as higher borrowing costs make it more expensive to refinance maturing debt. When equity holders have low bargaining power and the recovery effect dominates, higher financial constraints increase the recovery effect and make the relationship between yield spreads and renegotiation frictions more positive. When equity holders have high bargaining power, the relationship between yield spreads and renegotiation frictions should be less negative for financially constrained firms because the higher recovery effect offsets the strategic default effect. In fact the higher recovery effect may dominate for high levels of financial constraints such that the relationship between yield spreads and renegotiation frictions becomes positive. In the empirical analysis I use Enhanced TRACE transaction data from 1 July 2002 to 30 June 2017 to compute yield spreads. I follow Choi et al. (2018) and measure debt maturity dispersion based on an inverse Herfindahl index of the firm’s outstanding debt principal shares within specific maturity buckets. To proxy for renegotiation frictions I use the normalized number of bond issues similar to Davydenko and Strebulaev (2007). These two variables have a correlation coefficient of 0.76. My results are robust to using other measures of debt maturity dispersion and proxies for renegotiation frictions. I regress yield spreads on either debt maturity dispersion or the normalized number of bond issues and control for well-known determinants from the literature. The coefficient estimates are negative and statistically significant. A one standard deviation increase in debt maturity dispersion (normalized number of bond issues) decreases yield spreads by 14.4 (12.7) basis points (bps) on average, which corresponds to almost 10% of the median yield spread. I also divide the sample into four groups based on bond ratings and run the same regression within each rating group. The absolute value of the coefficient estimates on debt maturity dispersion and the normalized number of bond issues increase with credit risk and remain statistically significant except for bonds rated AAA-AA. These findings are consistent with Davydenko and Strebulaev (2007), Dass and Massa (2014), and Nagler (2019). To analyze the effects of financial constraints I consider three of the most widely used indexes of financial constraints. The WW index from Whited and Wu (2006), the SA index by Hadlock 69 and Pierce (2010), and the KZ index used in Lamont et al. (2001) which builds on Kaplan and Zingales (1997). Higher index values correspond to higher levels of financial constraints. I interact these measures of financial constraints with either maturity dispersion or the normalized number of bond issues and regress yield spreads on the interaction variable and a set of controls. For all three measures, the coefficient estimate on the interaction variable is negative and mostly statistically significant. The relationship between yield spreads and debt dispersion is therefore more negative for financially constrained firms consistent with theories of rollover risk. For example, a one standard deviation increase in debt maturity dispersion (normalized number of bond issues) decreases yield spreads by up to 47.4 (22.2) bps on average for financially constrained firms. Taken together, my findings show that the negative relationship between yield spreads and debt dispersion reflects rollover risk rather than strategic debt service concerns. My results are useful for understanding the survey evidence in Servaes and Tufano (2006) that firms’ debt maturity decisions are mainly driven by a desire to mitigate rollover risk. 1.1 Related Literature This paper belongs to the literature on debt maturity dispersion. Choi et al. (2018) study the firm’s decision to spread out debt maturity dates across time. They document that firms increase debt maturity dispersion when they anticipate higher rollover risk and that maturities on newly issued debt depend on pre-existing maturity profiles. Dass and Massa (2014) find that firms with more dispersed maturities have lower yield spreads and attribute this finding to higher demand from institutional investors that economize on information-collection costs. Nagler (2019) also finds a negative relationship between yield spreads and maturity dispersion using a sample of S&P 500 firms. Davydenko and Strebulaev (2007) study the effects of strategic actions on yield spreads and argue that dispersed debt proxies for renegotiation frictions. They document a negative relationship between yield spreads and renegotiation frictions and show how this finding is consistent with strategic debt service models. None of these papers consider the impact of financial constraints. My paper also contributes to the literature on debt maturity choice and rollover risk. Barclay and Smith (1995), Guedes and Opler (1996), and Stohs and Mauer (1996) study the determinants of average debt maturities while Gopalan et al. (2014) analyze the relationship between yield spreads and rollover risk. Diamond and He (2014) examine the effects of short and long-term debt on the debt overhang problem. He and Xiong (2012b), He and Milbradt (2014), and Chen et al. (2018) investigate how bond market illiquidity affects yield spreads through the debt rollover channel. Xu (2017) shows that firms often use early refinancing to extend debt maturity especially among speculative-grade firms. Harford et al. (2014) find that firms with more refinancing risk 70 increase their cash holdings to mitigate rollover risk. None of these papers focus on debt maturity dispersion. Finally, my paper also relates to the literature on strategic debt service. Anderson and Sundaresan (1996), Mella-Barral and Perraudin (1997), Fan and Sundaresan (2000), and Hege and Mella-Barral (2005) study how strategic debt service influences the pricing of debt and equity in contingent claims models. Christensen et al. (2014) consider strategic debt service when debt holders can reject non-credible threats by equity holders. Hackbarth et al. (2007) analyze the optimal mixture of public debt and bank debt when firms can renegotiate the bank debt outside of formal bankruptcy. Arnold and Westermann (2017) develop a model in which the firm can renegotiate debt both in financial distress and outside of distress. 2 Testable Hypotheses This section presents testable hypotheses to guide the empirical analysis. I hypothesize the relationship between yield spreads and debt dispersion based on theories of rollover risk and strategic debt service. In Appendix A and B I formally derive the testable hypotheses in extended versions of the rollover risk model by Choi et al. (2018) and the strategic debt service model by Davydenko and Strebulaev (2007). 2.1 Rollover Risk In rollover risk models firms face the risk that capital market conditions deteriorate when they have to redeem maturing debt. If conditions in capital markets deteriorate, the cost of refinancing maturing debt increases and in the most extreme case it may be impossible to raise new financing. The firm could therefore be forced to cut back on investments and/or liquidate assets to repay maturing debt. When the firm cannot repay its debt, debt holders recover less than their principal value due to liquidation costs in bankruptcy. To mitigate the adverse effects of deteriorating capital market conditions firms can divide their total debt financing needs into smaller debt issues and spread out their maturity dates across time. If capital markets deteriorate, firms with dispersed debt maturities are less likely to default compared to firms with concentrated debt maturities that have to refinance a larger amount of debt. All else equal, bonds issued by firms with dispersed debt maturities therefore have lower yield spreads relative to firms with concentrated debt maturities. Financially constrained firms are more exposed to capital market conditions and find it more difficult and/or costly to raise new financing in capital markets. All else equal, the effect of debt maturity dispersion on yield spreads is therefore more pronounced for financially constrained firms. 71 This prediction supports the following hypothesis: HYPOTHESIS 1: The relationship between yield spreads and debt maturity dispersion is more negative for financially constrained firms. 2.2 Strategic Debt Service In strategic debt service models equity holders can threaten to default strategically with a view to obtain debt concessions. Debt holders have incentives to renegotiate the debt because they can avoid liquidation costs in bankruptcy. Hart and Moore (1998) and Fan and Sundaresan (2000) identify two opposing effects that determine how the possibility to renegotiate debt affects yield spreads. On the one hand, the possibility to renegotiate enables debt holders to avoid liquidation cost they would otherwise incur ex post default. This recovery effect reduces yield spreads because expected recovery rates increase. On the other hand, the possibility to renegotiate may induce equity holders to default strategically more often. This strategic default effect increases yield spreads because the probability of default increases. The possibility to renegotiate therefore has an ambiguous impact on yield spreads. Davydenko and Strebulaev (2007) examine the relationship between yield spreads and renegotiation frictions to infer how the possibility to renegotiate the firm’s debt affects yield spreads. Renegotiation frictions determine how difficult it is to renegotiate between equity and debt holders. Suppose that qmeasures the difficulty of renegotiating and let sdenote the yield spread. The derivative φ=∂s/∂q measures the sensitivity of yield spreads to renegotiation frictions. Davydenko and Strebulaev (2007) argue that if φ > 0, it can either be because the strategic default effect is non-existent or because the recovery effect dominates the strategic default effect. Intuitively, higher renegotiation frictions reduce equity holders’ incentives to default strategically which decrease yield spreads (i.e. the strategic default effect). However, higher renegotiation frictions also increase expected liquidation costs which increase yield spreads (i.e. the recovery effect). Davydenko and Strebulaev (2007) also argue that if φ < 0, it must indicate that the strategic default effect exists and dominates the recovery effect. If liquidation costs are strictly positive, the relative bargaining power of debt and equity holders determines whether the strategic default effect or the recovery effect dominates. When equity holders have all the bargaining power, they capture the entire bargaining surplus. In this case there is no recovery effect because debt holders cannot capture any surplus from bargaining. The strategic default effect therefore dominates meaning that φ < 0. Under these conditions higher renegotiation frictions decrease yield spreads because equity holders have lower incentives to default strategically (i.e. the default probability decreases). 72 Suppose instead that debt holders have all the bargaining power. Equity holders have no incentive to default strategically as they cannot capture any surplus from bargaining. In this case there is no strategic default effect meaning that the recovery effect dominates and φ > 0. Under these conditions higher renegotiation frictions increase yield spreads because the expected liquidation costs increases (i.e. the recovery rate decreases). Gertner and Scharfstein (1991) and Bolton and Scharfstein (1996) show that free-rider and coordination problems make renegotiations more difficult when they involve many parties with competing interests. Davydenko and Strebulaev (2007) construct proxies for renegotiation frictions based on the firm’s debt structure. Their measures include the normalized number of outstanding bond issues, a dispersion measure based on outstanding principal values, the ratio of outstanding public debt to total debt, and the ratio of short-term debt to total debt. In the Internet Appendix I show that empirically these proxies for renegotiations frictions are often highly correlated with measures of debt maturity dispersion. Importantly, the trade-off between the recovery and the strategic default effect depends on the level of financial constraints. Suppose that financially constrained firms borrow at higher rates and that firms refinance maturing debt by issuing new debt. Financial constraints then strengthen the recovery effect because equity holders default more often as higher borrowing costs increase the cost of refinancing maturing debt. When equity holders have low bargaining power such that φ > 0, higher financial constraints increase the recovery effect and make the relationship between yield spreads and renegotiation frictions more positive. When equity holders have high bargaining power, the relationship between yield spreads and renegotiation frictions should be less negative for financially constrained firms because the higher recovery effect offsets the strategic default effect. I summarize this prediction in the following hypothesis: HYPOTHESIS 2: The relationship between yield spreads and renegotiation frictions is less negative for financially constrained firms. 3 Data and Variables This section describes the data, sample requirements, and how I construct the main variables used in the empirical analysis. I also present summary statistics and correlations. 3.1 Data Sources I obtain bond characteristics and ratings together with the amount outstanding from Mergent Fixed Income Securities Database (FISD). The amount outstanding data is available from April 1995 and records all changes in the principal amount outstanding for each bond issue over its 73 on Log(amount outstanding). The coefficients on Equity volatility and Leverage are positive and statistically significant consistent with e.g. Davydenko and Strebulaev (2007). The results also show that firms with high cash-to-debt ratios typically have higher yield spreads consistent with Harford et al. (2014) who show that risky firms choose higher cash holdings to mitigate rollover risk. I also find that more profitable firms with higher return on assets have lower yield spreads while the coefficient estimates on book-to-market is mainly positive but statistically insignificant except for A-rated bonds. [INSERT TABLE 5] Table 5presents estimates of equation (1) for the full sample and by bond rating when I use the normalized number of bond issues to proxy for renegotiation frictions. The results are almost identical to those in Table 4because debt maturity dispersion and the normalized number of bond issues are highly positively correlated. For example, the coefficient estimate of β1is −1.273 and highly statistically significant for the full sample. A one standard deviation increase in the normalized number of bond issues decreases the yield spread by 12.7 bps on average. This economic magnitude is substantially higher compared to Davydenko and Strebulaev (2007) who find that a one standard deviation increase in their proxies for renegotiation frictions decrease average yield spreads by 1 −8 bps. I also find that the absolute magnitude of the coefficient estimate on the normalized number of bond issues tends to increase with the level of credit risk. These findings are consistent with strategic debt service models. My results confirm that yield spreads decrease with debt dispersion. In rollover risk models this negative relationship reflects that firms with dispersed debt maturities have less rollover risk and therefore lower default risk and yield spreads. In models of strategic debt service higher renegotiation frictions reduce equity holders’ incentive to default strategically because bargaining is more difficult. When this strategic default effect dominates, higher renegotiation frictions result in lower yield spreads. The results in Table 4and 5are therefore consistent with both explanations. 4.2 The Effect of Financial Constraints I now investigate how the relationship between yield spreads and debt dispersion depends on the level of firms’ financial constraints. Whited and Wu (2006), Hadlock and Pierce (2010), and Kaplan and Zingales (1997) divide firms into five groups based on financial constraints when they construct their indexes. In each quarter, I divide my sample into five groups based on the level of each financial constraint index. I construct a dummy variable which equals one when the firm belongs to the top quintile of the financial constraints index and equals zero otherwise. Next, I 80 estimate the following regression: Y ield spreadijt =β0+β1Dispersionj,t−1+β2HF Cj,t−1+β3Dispersionj,t−1HFCj,t−1 +δControlsij,t−1+γit +ijt (2) where Y ield spreadijt is the yield spread on bond iissued by firm jmeasured in quarter t, and Dispersionj,t−1is either the debt maturity dispersion or the normalized number of bond issues measured at the end of quarter t−1, HF Cj,t−1is a dummy variable equal to one when the firm belongs to the high-financial-constraints quintile, Controlsij,t−1is a vector of control variables, and γit is a quarter times rating fixed effect. I use the same set of control variables and fixed effects as in equation (1) and continue to cluster standard errors by firm and quarter. In addition, I also use the financial constraints index values themselves to estimate the following regression: Y ield spreadijt =β0+β1Dispersionj,t−1+β2FCIj,t−1+β3Dispersionj,t−1FCIj,t−1 +δControlsij,t−1+γit +ijt (3) where FCIj,t−1is the financial constraint index value for firm jat time t−1. The remaining variables are the same as in equation (2). For equations (2) and (3), the coefficient estimate of β3 should be negative according to Hypothesis 1 but positive according to Hypothesis 2. [INSERT TABLE 6] Panel A in Table 6presents estimates of equation (2) for the three different measures of financial constraints when I use debt maturity dispersion as explanatory variable. The coefficient estimates on Maturity dispersion remain negative and statistically significant in all specifications when controlling for financial constraints. This finding means that debt maturity dispersion is not simply another measure of financial constraints already captured by the three indexes. The coefficient estimates on both the WW and SA indexes are positive and statistically significant meaning that more financially constrained firms on average have higher yield spreads. The KZ index has a negative coefficient estimate in some specifications akin to the finding by Lamont et al. (2001) that firms with higher KZ index values have lower average stock returns. Importantly, the coefficient on the interaction variable between Maturity dispersion and HFC is negative using all three measures of financial constraints. This finding means that the relationship between yield spreads and debt maturity dispersion is more negative for financially constrained firms consistent with rollover risk models. For example, a one standard deviation increase in debt 81 maturity dispersion decreases yield spreads by 47.4 bps on average (3.00 ∗(−0.035 −0.123) = −0.474) for financially constrained firms using the WW index. In Panel B, I use the actual index values of financial constraints to estimate equation (3) and obtain virtually the same results as in Panel A. The coefficient estimate on β3using the SA index is statistically insignificant in Panel A. The SA index is based on a combination of firm age and firm size measured by total assets. To calculate the index firm age is capped at 37 years while total assets are capped at $4.5 billions measured in 2004 dollars. These thresholds may not be reasonable for my sample of listed firms with rated corporate bonds because these firms are much older and larger than the average firm. In fact 45% of the observations in my sample have the lowest possible SA index value because firms exceed the size and/or age thresholds. In untabulated results I replace the FCI variable in equation (3) with either firm size or firm age. The coefficient estimates on β3are now positive (because larger firms and older firms are less constrained) and have t-statistics of 5.62 when I use firm size and 1.86 when I use firm age. When I use dummy variables instead as in equation (2) the coefficient estimates on β3remain positive and have t-statistics of 2.39 for both size and age. These results provide additional evidence on the effects of financial constraints consistent with Hennessy and Whited (2007) who argue that firm size is the most important proxy for financial constraints. [INSERT TABLE 7] Table 7presents estimates of equation (2) and (3) when I use the normalized number of bond issues as explanatory variable. Again, the results are almost identical to Table 6because of the high correlation between debt maturity dispersion and the normalized number of bond issues. For example, the coefficient estimate on the interaction variable between Norm. no. of issues and HFC is negative using all three measures of financial constraints. A one standard deviation increase in the normalized number of bond issues decreases yield spreads by 22.2 bps on average (0.10 ∗(−1.062 −1.174) = −0.222) for financially constrained firms using the KZ index. Panel B shows that the coefficient estimates on β3remain negative when I use the actual index values of financial constraints to estimate equation (3). In untabulated results I replace FCI with firm size or firm age and obtain positive coefficient estimates with t-statistics of 1.86 and 1.59, respectively. These findings show that the relationship between yield spreads and renegotiation frictions is more negative for financially constrained firms in contrast to the prediction from strategic debt service models. Taken together, my findings support Hypothesis 1 and are inconsistent with Hypothesis 2. The empirical evidence supports rollover risk models in which the effect of debt maturity dispersion on yield spreads is more pronounced for financially constrained firms. My results are inconsistent 82 with strategic debt service models because these models predict a less negative relationship between yield spreads and renegotiation frictions for firms with higher levels of financial constraints. 4.3 Robustness Checks In the main analysis I use the inverse Herfindahl measure to quantify debt maturity dispersion. Choi et al. (2018) point out that this measure may not capture all aspects of firms’ debt maturity profiles. For example, this measure does not distinguish between maturity dates in the near future and maturity dates in the more distant future. Moreover, the inverse Herfindahl measure may be affected by the longest feasible maturity a firm can issue. For example, if a firm cannot issue debt with maturities greater than five years then the Herfindahl index will be greater than or equal to 0.2. To alleviate these concerns, Choi et al. (2018) develop two additional dispersion measures: an inverse weighted Herfindahl index that gives more weight to short-term debt and a dispersion measure based on the distance from a perfectly dispersed debt maturity profile. As a robustness check I repeat the main analysis using both of these dispersion measures. The results are similar to those presented above and a full summary can be found in the Internet Appendix together with a detailed explanation on how to construct the additional dispersion measures. I also consider other proxies for renegotiation frictions than the normalized number of bond issues. Davydenko and Strebulaev (2007) also use an inverse Herfindahl index of bond principal values, the fraction of public debt to total debt, and the fraction of short-term debt to total debt to proxy for renegotiation frictions. I present the results using these proxies in the Internet Appendix which are broadly similar to those presented above. 5 Conclusion In this paper, I document that the negative relationship between yield spreads and debt dispersion is more pronounced for financially constrained firms. I show that this finding supports theories of rollover risk where dispersed debt maturities reduce default risk and therefore also yield spreads. The negative relationship is more pronounced for financially constrained firms because they are more exposed to capital market conditions. The negative relationship between yield spreads and debt dispersion could also be consistent with theories of strategic debt service. In these models dispersed debt proxies for renegotiation frictions which reduce equity holders’ incentive to default strategically. This strategic default effect tends to decrease yield spreads. However, renegotiation frictions also increase expected liquidation costs in bankruptcy. This recovery effect tends to increase yield spreads. I show that the recovery effect is more pronounced for financially distressed firms because they have higher default risk. As 83 a result, the relationship between yield spreads and renegotiation frictions should be less negative for financially constrained firms. This prediction is inconsistent with the empirical evidence found in this paper. Taken together, my results shed new light on how and why debt maturity profiles are priced in the cross-section of yield spreads. My results are useful for understanding the survey evidence in Servaes and Tufano (2006) that firms’ debt maturity decisions are mainly driven by a desire to mitigate rollover risk. Moreover, the empirical evidence rationalizes the findings by Choi et al. (2018) that firms increase debt maturity dispersion when they anticipate higher rollover risk and explains why maturities on newly issued debt depend on pre-existing maturity profiles. It remains an interesting question to explore how demand from institutional investors as in Dass and Massa (2014) may be related to firms’ financial constraints. I leave this question for future research. 84 Appendices A Rollover Risk Model In this section, I include liquidation costs and risky debt into the rollover risk model by Choi et al. (2018) to derive Hypothesis 1. For ease of exposition, I do not consider growth options and issuance costs of debt as in Choi et al. (2018) but only focus on the pricing of debt. The model has three time periods separated by four dates t0,t1,t2, and t3. The firm is initially all-equity financed and has assets in place with a market value of A. At time t0, the firm invests in a project which requires a capital outlay of I > A. This project generates three cash flows: an intermediate cash flow cat both times t1and t2together with a final cash flow Iat time t3. The risk-free rate is zero. The firm finances the required investment spending I−Aat time t0by issuing oneor twoperiod debt with the same seniority. In turn the firm must roll over its debt before time t3. At times t1and t2, the debt market may freeze with probability δ. If the debt market freezes, the firm cannot roll over maturing debt and must repay the debt holders from intermediate cash flows or default on the debt. The principal value of maturing debt is Bso the firm repays the debt when B≤cand defaults when B > c in case the debt market freezes. When the firm defaults, debt holders recover a fraction (1 −α) of the debt principal where αreflects liquidation costs in bankruptcy. Now, consider two firms with different initial debt structures. Firm Dissues two bonds at time t0with the same principal value BD 1=BD 2= (I−A)/2. Bond 1 matures at time t1and bond 2 matures at time t2such that the firm has a perfectly dispersed debt maturity profile. Firm C only issues one bond with principal value BC= (I−A) and therefore has a perfectly concentrated debt maturity profile. This firm is indifferent between choosing maturity date t1or t2because the probability of a debt market freeze remains the same in both periods. Without loss of generality I therefore assume that the bond matures at time t2. I require that I−A > c > (I−A)/2 and that any excess cash remaining after rolling over debt is paid out as dividends to the equity holders in each time period together with the restriction that 85 the firm cannot issue new equity. The first inequality entails that the intermediate cash flow cis insufficient to repay the debt principal for Firm C. Firm Cwill therefore default in case the debt market freezes. The second inequality states that firm Dcan repay the debt principal out of the intermediate cash flow and therefore do not default if the debt market freezes. Firm D’s debt is risk-free because the firm never defaults. The market value of its total debt DDis therefore equal to the total principal value: DD=BD 1+BD 2=I−A(A.1) Firm Cmay default at time t2in which case the debt holders recover less than the principal value due to liquidation costs. Firm C’s debt is therefore risky and has a market value of: DC= (I−A)−δα(I−A) (A.2) where the first term is the risk-free value and the second term is the expected present value of liquidation costs. Firm Dand Crepresent the two extremes of perfectly dispersed and perfectly concentrated debt maturity profiles, respectively. One way to think about firms with intermediate debt maturity dispersion is to consider a weighted average between these two extremes. Let DIdenote the market value of a bond issued by a firm with intermediate debt maturity dispersion: DI=qDD+ (1 −q)DC =q(I−A) + (1 −q)(I−A)−δα(I−A)(A.3) where qdenotes the weight in the perfectly dispersed debt maturity profile. Differentiating DI with respect to qyields: ∂DI ∂q =δα(I−A)>0 (A.4) meaning that bond prices increase with the level of debt maturity dispersion. Conversely, yield spreads decrease with debt maturity dispersion. Gomes et al. (2006), Whited and Wu (2006), Livdan et al. (2009), and Li (2011) find that financially constrained firms face higher cost of capital. Based on their findings, I assume that the probability that a given firm experiences a debt market freeze has two components: δ=δM+δI where δMreflects the market-wide probability and δIreflects an idiosyncratic part. Since financially constrained firms are more exposed to capital market conditions, I assume that δIincreases with the level of financial constraints. 86 HYPOTHESIS 1: Differentiating ∂DI ∂q with respect to δyields ∂DI ∂q∂δ =α(I−A)>0 (A.5) meaning that bond prices increase more with debt maturity dispersion when δis higher i.e. when the firm is more financially constrained. Conversely, the relationship between yield spreads and debt maturity dispersion is more negative for financially constrained firms. I note that the model also gives rise to an additional testable hypothesis on the effect of liquidation costs. The derivative ∂DI ∂q∂α =δ(I−A)>0 meaning that the relationship between yield spreads and debt maturity dispersion should be more negative the higher the level of liquidation costs. I do not focus on this hypothesis in the paper because strategic debt service models generate the same prediction and it is therefore not possible to distinguish the two models from each other based on this prediction. 87 B Strategic Debt Service Model In this section, I extend the strategic debt service model by Davydenko and Strebulaev (2007) by introducing costly financial constraints. In particular, I assume that financially constrained firms borrow at higher rates and that firms refinance maturing debt by issuing new debt. I then use the extended model to derive Hypothesis 2. The firm has assets-in-place that follows a geometric Brownian motion under the equivalent martingale measure Q: dVt= (r−β)Vtdt +σVtdZt(B.1) where ris the risk-free rate, βis the payout ratio, σis the volatility, and dZtis the increment of a standard Brownian motion {Zt: 0 ≤t < ∞} under Q. The firm is financed by both debt and equity. If the firm defaults and the claims are settled in bankruptcy court, the firm incurs proportional liquidation costs of αV where Vis the market value of assets at default. Alternatively, the debt and equity holders can renegotiate the debt contract at no cost by agreeing on a debt-for-equity swap. Renegotiation fails with probability q for exogenous reasons in which case the claims are settled in bankruptcy court according to the absolute priority rule. The parameter qreflects frictions that impede the renegotiation process such as having dispersed debt holders. In renegotiation, the equity and debt holders play a Nash bargaining game with bargaining power ηand 1−ηrespectively. Fan and Sundaresan (2000) show that this game results in an optimal sharing rule where equity holders get ηαVRand debt holders get (1 −ηα)VRwhere VRdenotes the market value of assets at the endogenous debt renegotiation boundary. The firm issues zero-coupon bonds with an aggregate principal value B. Each bond mature with Poisson intensity mmeaning that the expected time-to-maturity is 1 mas in Cheng and Milbradt (2012), He and Xiong (2012a), Chen et al. (2018), Friewald et al. (2018), and Nagler (2019). The firm commits to keep the aggregate principal value constant through time. At each instant in time, the firm therefore repays an expected principal amount mB and immediately issues new bonds to keep the aggregate principal value constant. Debt holders may require a premium δin excess of the risk-free rate when they discount cash flows. The parameter δreflects that debt holders require higher compensation when they lend to financially constrained firms. This assumption is consistent with my empirical findings in Table 6and 7that bonds issued by financially constrained firms typically have higher yield spreads. 88 The market value of debt D(V) is the solution to the ordinary differential equation (ODE): (r+δ)D=1 2σ2V2DV V + (r−β)V DV+m(B−D) (B.2) where subscripts denote partial derivatives. The equation states that the required return on the left-hand side must equal the expected return on the right-hand side. The first two terms is the expected change in the value of debt when Vfluctuates. The third term is the change in debt value from retiring maturing debt at principal value and issuing new debt at market value. The general solution to equation (B.2) is given by: D(V) = d2Vγ+mB r+m+δ(B.3) where γ=1 2−r−β σ2−s1 2−r−β σ22 +2(r+m+δ) σ2<0 (B.4) and the coefficient d2is determined by the value-matching condition at the renegotiation boundary VR: D(VR) = (1 −q)(1 −ηα)VR+q(1 −α)VR(B.5) which is given by: d2= (1 + qα(η−1) −ηα)V1−γ R−mB r+m+δV−γ R(B.6) The market value of debt is therefore given by: D(V) = mB r+m+δ−mB r+m+δ−(1 + qα(η−1) −ηα)VRV VRγ (B.7) where the first term is the risk-free value of debt and the second term is the expected present value of renegotiation and liquidation costs. The market value of equity E(V) is the solution to the differential equation: rE =1 2σ2V2EV V + (r−β)V EV+βV −m(B−D) (B.8) The equation states that the required return on the left-hand side must equal the expected return on the right-hand side. The first two terms is the expected change in the value of equity when V fluctuates. The third term is the cash flow paid to equity holders per unit time and the fourth term is debt rollover costs. 89 Table 1: Summary Statistics on Bonds This table presents summary statistics for the entire sample and by bond rating. The data frequency is quarterly and Appendix C contains a detailed description of how I construct all variables. Yield spread,Bid-ask spread, and Coupon rate are measured in percent. Time-to-maturity,Bond age, and Avg. firm maturity are measured in years. Amount outstanding is in millions of US dollars and Equity volatility is in annualized percent. Leverage,Cash/debt, and Return on assets are measured in percent. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). I report sample averages and include standard deviations in parentheses. Bond Rating All AAA-AA A BBB SPEC Yield spread 2.15 0.76 1.10 1.90 4.51 (2.01) (0.53) (0.78) (1.37) (2.47) Maturity dispersion 5.00 6.09 5.63 5.33 3.14 (3.00) (2.71) (2.86) (3.17) (2.05) Norm. no. of issues 0.21 0.25 0.23 0.22 0.15 (0.10) (0.09) (0.09) (0.10) (0.10) Bid-ask spread 0.38 0.36 0.38 0.37 0.39 (0.44) (0.42) (0.43) (0.46) (0.44) Coupon rate 5.97 4.70 5.37 5.91 7.35 (1.83) (1.88) (1.69) (1.66) (1.43) Time-to-maturity 9.32 9.51 9.94 9.82 7.52 (8.01) (8.77) (8.81) (8.40) (5.05) Bond age 4.40 4.67 4.67 4.26 4.19 (3.98) (4.75) (4.13) (3.65) (4.03) Avg. firm maturity 9.93 10.88 10.98 10.27 7.57 (4.28) (4.19) (4.35) (4.29) (3.15) Amount outstanding 574.95 827.18 638.93 551.99 436.54 (514.30) (711.49) (527.03) (500.92) (358.58) Equity volatility 30.37 21.28 25.16 29.88 41.54 (17.20) (9.77) (12.63) (15.28) (21.73) Leverage 28.53 15.84 20.57 28.54 43.71 (16.88) (11.42) (11.22) (13.67) (18.89) Cash/debt 36.79 82.68 44.54 28.94 23.38 (55.82) (91.05) (60.81) (43.95) (36.70) Return on assets 3.66 4.61 4.13 3.53 2.91 (1.87) (2.00) (1.67) (1.73) (1.98) Book/market 0.47 0.29 0.35 0.50 0.63 (0.31) (0.15) (0.19) (0.29) (0.41) Firms 1,153 75 286 527 616 Bonds 5,785 631 1,828 2,683 1,694 N60,012 5,147 17,181 24,411 13,273 96 Table 2: Summary Statistics on Financial Constraints Indexes This table presents summary statistics for the entire sample and by bond rating. The data frequency is quarterly and Appendix C contains a detailed description of how I construct the variables. The indexes for financial constraints are from Whited and Wu (2006) (WW ), Hadlock and Pierce (2010) (SA), and Kaplan and Zingales (1997) (KZ). Data are from COMPUSTAT. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). I report sample averages and include standard deviations in parentheses. Bond Rating All AAA-AA A BBB SPEC WW index -4.35 -4.95 -4.62 -4.31 -3.84 (0.61) (0.57) (0.51) (0.50) (0.52) SA index -4.30 -4.49 -4.41 -4.29 -4.07 (0.43) (0.27) (0.34) (0.44) (0.49) KZ index -4.37 -12.61 -5.16 -3.61 -1.54 (9.67) (13.25) (7.88) (9.17) (9.13) Firms 1,153 75 286 527 616 Bonds 5,785 631 1,828 2,683 1,694 N60,012 5,147 17,181 24,411 13,273 97 Table 3: Correlations This table shows Pearson correlation coefficients between all variables. Appendix C contains a detailed description of how I construct all variables. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). YS MD NNI BA CR MAT AGE FMAT AMT VOL LEV CD ROA BM WW SA KZ Yield spread (YS) 1.00 Maturity dispersion (MD) -0.28 1.00 Norm. no. of issues (NNI) -0.26 0.76 1.00 Bid-ask spread (BA) 0.26 -0.03 -0.01 1.00 Coupon rate (CR) 0.44 -0.23 -0.21 0.11 1.00 Log(time-to-maturity) (MAT) 0.08 0.12 0.02 0.22 0.14 1.00 Log(bond age) (AGE) -0.00 0.04 0.02 0.16 0.37 -0.09 1.00 Avg. firm maturity (FMAT) -0.20 0.42 0.25 0.10 -0.08 0.42 0.11 1.00 Log(amt. outstanding) (AMT) -0.14 0.15 0.01 -0.17 -0.26 0.12 -0.25 0.16 1.00 Equity volatility (VOL) 0.63 -0.18 -0.13 0.21 0.30 -0.03 -0.01 -0.13 -0.13 1.00 Leverage (LEV) 0.52 -0.05 -0.01 0.07 0.39 -0.05 0.03 -0.17 -0.10 0.38 1.00 Cash/debt (CD) -0.14 -0.02 -0.05 -0.00 -0.18 0.03 -0.04 0.08 0.10 -0.05 -0.41 1.00 Log(1+ret. on assets) (ROA) -0.29 -0.00 -0.04 -0.06 -0.18 0.03 -0.08 0.08 0.07 -0.22 -0.45 0.12 1.00 Log(book/market) (BM) 0.28 -0.10 -0.08 0.06 0.26 -0.00 0.05 -0.05 -0.08 0.29 0.40 -0.09 -0.48 1.00 WW index (WW) 0.36 -0.45 -0.37 -0.01 0.27 -0.06 -0.11 -0.34 -0.41 0.25 0.14 -0.08 0.02 0.01 1.00 SA index (SA) 0.24 -0.29 -0.29 -0.05 0.18 -0.03 -0.14 -0.19 -0.03 0.14 0.15 -0.03 0.03 0.01 0.29 1.00 KZ index (KZ) 0.15 -0.07 -0.04 0.03 0.26 -0.02 0.05 -0.06 -0.14 0.14 0.29 -0.44 -0.12 0.19 0.07 0.03 1.00 98 Table 4: Yield Spreads and Debt Maturity Dispersion This table presents pooled OLS regression results with the quarterly yield spread in percent as the dependent variable. Appendix C contains a detailed description of how I construct all variables. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The regression for the full sample includes quarter times rating fixed effects (QTR*RAT) while regressions for each rating group include quarter fixed effects (QTR). Standard errors are clustered by firm and quarter with tstatistics in parenthesis. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. Bond Rating All AAA-AA A BBB SPEC Maturity dispersion -0.048∗∗∗ 0.001 -0.034∗∗∗ -0.048∗∗∗ -0.090∗∗∗ (-5.83) (0.08) (-4.59) (-3.76) (-3.33) Bid-ask spread 0.407∗∗∗ 0.074∗∗∗ 0.183∗∗∗ 0.390∗∗∗ 0.774∗∗∗ (7.82) (2.62) (5.06) (5.12) (8.17) Coupon rate 0.198∗∗∗ 0.078∗∗∗ 0.112∗∗∗ 0.154∗∗∗ 0.330∗∗∗ (14.59) (6.39) (9.36) (10.17) (9.62) Log(time-to-maturity) 0.150∗∗∗ 0.199∗∗∗ 0.188∗∗∗ 0.199∗∗∗ 0.218∗∗ (5.27) (8.54) (7.42) (5.34) (2.41) Log(bond age) -0.130∗∗∗ -0.009 -0.017 -0.067∗∗∗ -0.176∗∗∗ (-6.99) (-0.57) (-1.09) (-3.21) (-5.11) Avg. firm maturity -0.014∗∗∗ -0.009∗-0.005 -0.018∗∗∗ -0.030∗ (-3.57) (-1.74) (-1.06) (-3.58) (-1.91) Log(amount outstanding) -0.104∗∗∗ -0.041∗∗ -0.066∗∗∗ -0.121∗∗∗ -0.110∗ (-4.20) (-2.38) (-3.19) (-3.91) (-1.71) Equity volatility 0.032∗∗∗ 0.015∗∗∗ 0.009∗∗∗ 0.027∗∗∗ 0.038∗∗∗ (10.78) (4.60) (3.77) (7.27) (11.26) Leverage 0.024∗∗∗ 0.014∗∗∗ 0.009∗∗∗ 0.019∗∗∗ 0.031∗∗∗ (11.00) (4.25) (3.10) (6.28) (10.49) Cash/debt 0.001∗∗∗ -0.000 -0.000 0.001∗∗∗ 0.002∗∗ (3.10) (-0.52) (-0.00) (2.78) (2.00) Log(1+return on assets) -3.747∗∗∗ 0.952 -1.592∗∗ -5.266∗∗∗ -8.740∗∗∗ (-3.41) (0.81) (-2.10) (-3.92) (-3.81) Log(book/market) -0.008 0.012 0.060∗∗ -0.011 0.040 (-0.30) (0.48) (1.99) (-0.27) (0.79) Fixed effects QTR*RAT QTR QTR QTR QTR N60,012 5,147 17,181 24,411 13,273 Adj. R20.788 0.682 0.653 0.639 0.670 99 Table 5: Yield Spreads and Renegotiation Frictions This table presents pooled OLS regression results with the quarterly yield spread in percent as the dependent variable. Appendix C contains a detailed description of how I construct all variables. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). The regression for the full sample includes quarter times rating fixed effects (QTR*RAT) while regressions for each rating group include quarter fixed effects (QTR). Standard errors are clustered by firm and quarter with tstatistics in parenthesis. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. Bond Rating All AAA-AA A BBB SPEC Norm. no. of issues -1.273∗∗∗ -0.115 -0.918∗∗∗ -1.350∗∗∗ -1.321∗∗ (-6.39) (-0.39) (-3.79) (-5.88) (-2.44) Bid-ask spread 0.414∗∗∗ 0.073∗∗∗ 0.185∗∗∗ 0.399∗∗∗ 0.796∗∗∗ (7.94) (2.60) (5.15) (5.29) (8.37) Coupon rate 0.196∗∗∗ 0.077∗∗∗ 0.111∗∗∗ 0.156∗∗∗ 0.334∗∗∗ (15.00) (6.34) (8.96) (10.61) (9.75) Log(time-to-maturity) 0.149∗∗∗ 0.199∗∗∗ 0.187∗∗∗ 0.196∗∗∗ 0.222∗∗ (5.17) (8.47) (7.35) (5.20) (2.45) Log(bond age) -0.135∗∗∗ -0.011 -0.023 -0.076∗∗∗ -0.186∗∗∗ (-7.45) (-0.68) (-1.40) (-3.50) (-5.56) Avg. firm maturity -0.019∗∗∗ -0.008∗-0.008∗-0.023∗∗∗ -0.040∗∗ (-4.99) (-1.78) (-1.81) (-4.46) (-2.53) Log(amount outstanding) -0.119∗∗∗ -0.044∗∗ -0.079∗∗∗ -0.140∗∗∗ -0.127∗ (-4.76) (-2.31) (-3.85) (-4.43) (-1.95) Equity volatility 0.033∗∗∗ 0.015∗∗∗ 0.010∗∗∗ 0.028∗∗∗ 0.038∗∗∗ (11.08) (4.60) (3.86) (7.60) (11.36) Leverage 0.023∗∗∗ 0.014∗∗∗ 0.008∗∗∗ 0.019∗∗∗ 0.030∗∗∗ (10.97) (3.62) (2.59) (6.39) (10.24) Cash/debt 0.001∗∗∗ -0.000 -0.000 0.001∗∗∗ 0.002∗ (3.04) (-0.39) (-0.03) (2.87) (1.84) Log(return on assets) -3.874∗∗∗ 0.822 -1.743∗∗ -5.001∗∗∗ -8.608∗∗∗ (-3.62) (0.76) (-2.16) (-3.78) (-3.66) Log(book/market) -0.008 0.008 0.069∗∗ -0.007 0.035 (-0.30) (0.33) (2.21) (-0.17) (0.70) Fixed effects QTR*RAT QTR QTR QTR QTR N60,012 5,147 17,181 24,411 13,273 Adj. R20.788 0.683 0.651 0.638 0.668 100 Table 6: Debt Maturity Dispersion and Financial Constraints This table presents pooled OLS regression results with the quarterly yield spread in percent as the dependent variable. Appendix C contains a detailed description of how I construct all variables. The indexes for financial constraints are from Whited and Wu (2006) (WW ), Hadlock and Pierce (2010) (SA), and Kaplan and Zingales (1997) (KZ). In Panel A, I use a dummy variable (HFC) that equals 1 when the financial constraints index level in a given quarter belongs to the top quintile and equals zero otherwise. In Panel B, I use the actual values of the financial constraints indexes. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). All regressions include quarter times rating fixed effects and all control variables from Table 4. Standard errors are clustered by firm and quarter with t-statistics in parenthesis. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. WW Index SA Index KZ Index Panel A: Financial Constraints Dummy Maturity dispersion -0.041∗∗∗ -0.035∗∗∗ -0.045∗∗∗ -0.043∗∗∗ -0.048∗∗∗ -0.037∗∗∗ (-5.13) (-4.51) (-5.46) (-5.16) (-5.92) (-4.54) High fin. constraints (HFC) 0.215∗∗∗ 0.551∗∗∗ 0.178∗∗∗ 0.292∗∗∗ -0.066 0.211∗∗ (4.20) (6.42) (4.06) (3.76) (-1.18) (2.54) Maturity dispersion*HFC -0.123∗∗∗ -0.030 -0.057∗∗∗ (-5.27) (-1.51) (-4.25) Controls Y Y Y Y Y Y Quarter*Rating FE Y Y Y Y Y Y N60,012 60,012 60,012 60,012 60,012 60,012 Adj. R20.790 0.791 0.789 0.790 0.788 0.790 Panel B: Financial Constraints Index Maturity dispersion -0.040∗∗∗ -0.339∗∗∗ -0.044∗∗∗ -0.198∗∗ -0.048∗∗∗ -0.052∗∗∗ (-4.72) (-6.40) (-5.23) (-2.25) (-5.83) (-5.64) Fin. constraints index (FCI) 0.185∗∗∗ 0.424∗∗∗ 0.164∗∗∗ 0.307∗∗∗ -0.004∗∗ 0.001 (3.67) (6.58) (3.61) (3.97) (-2.03) (0.51) Maturity dispersion*FCI -0.065∗∗∗ -0.035∗-0.001∗∗ (-5.90) (-1.79) (-2.23) Controls Y Y Y Y Y Y Quarter*Rating FE Y Y Y Y Y Y N60,012 60,012 60,012 60,012 60,012 60,012 Adj. R20.790 0.792 0.789 0.790 0.789 0.789 101 Table 7: Renegotiation Frictions and Financial Constraints This table presents pooled OLS regression results with the quarterly yield spread in percent as the dependent variable. Appendix C contains a detailed description of how I construct all variables. The indexes for financial constraints are from Whited and Wu (2006) (WW ), Hadlock and Pierce (2010) (SA), and Kaplan and Zingales (1997) (KZ). In Panel A, I use a dummy variable (HFC) that equals 1 when the financial constraints index level in a given quarter belongs to the top quintile and equals zero otherwise. In Panel B, I use the actual values of the financial constraints indexes. Data are from Enhanced TRACE, Federal Reserve Bank, Mergent FISD, COMPUSTAT, and CRSP. The sample period covers 1 July 2002 to 30 June 2017 where I have excluded financials (SIC codes 6000-6999) and utilities (SIC codes 4900-4999). All regressions include quarter times rating fixed effects and all control variables from Table 4. Standard errors are clustered by firm and quarter with t-statistics in parenthesis. The convention for p-values is: ∗when p < 0.10, ∗∗ when p < 0.05, and ∗∗∗ when p < 0.01. WW Index SA Index KZ Index Panel A: Financial Constraints Dummy Norm. no. of issues -1.036∗∗∗ -0.877∗∗∗ -1.186∗∗∗ -1.111∗∗∗ -1.271∗∗∗ -1.062∗∗∗ (-5.36) (-4.15) (-5.99) (-5.51) (-6.45) (-5.54) High fin. constraints (HFC) 0.219∗∗∗ 0.335∗∗∗ 0.181∗∗∗ 0.258∗∗∗ -0.076 0.163 (4.25) (4.30) (4.11) (3.22) (-1.31) (1.40) Norm. no. of issues*HFC -0.729∗-0.432 -1.174∗∗ (-1.75) (-0.92) (-2.16) Controls Y Y Y Y Y Y Quarter*Rating FE Y Y Y Y Y Y N60,012 60,012 60,012 60,012 60,012 60,012 Adj. R20.789 0.789 0.789 0.789 0.788 0.788 Panel B: Financial Constraints Index Norm. no. of issues -1.034∗∗∗ -3.204∗∗∗ -1.134∗∗∗ -4.078∗∗ -1.283∗∗∗ -1.370∗∗∗ (-5.30) (-2.74) (-5.63) (-2.16) (-6.51) (-6.26) Fin. constraints index (FCI) 0.197∗∗∗ 0.293∗∗∗ 0.162∗∗∗ 0.291∗∗∗ -0.004∗∗ 0.002 (3.98) (4.41) (3.54) (3.99) (-2.24) (0.53) Norm. no. of issues*FCI -0.499∗-0.684 -0.030∗ (-1.95) (-1.61) (-1.67) Controls Y Y Y Y Y Y Quarter*Rating FE Y Y Y Y Y Y N60,012 60,012 60,012 60,012 60,012 60,012 Adj. R20.789 0.790 0.789 0.789 0.788 0.788 102 Figure A.1: The Effects of Renegotiation Frictions δ=0.02 δ=0 0.2 0.4 0.6 0.8 1.0 q 0.50 0.55 0.60 VR (A) Renegotiation boundary (η= 0.05) δ=0.02 δ=0 0.2 0.4 0.6 0.8 1.0 q 0.60 0.65 0.70 0.75 0.80 0.85 0.90 VR (B) Renegotiation boundary (η= 0.95) δ=0 δ=0.02 0.2 0.4 0.6 0.8 1.0 q 100 200 300 400 s (C) Yield spreads (η= 0.05) δ=0.02 δ=0 0.2 0.4 0.6 0.8 1.0 q 200 250 300 350 400 450 s (D) Yield spreads (η= 0.95) q=0.8 q=0.2 0.01 0.02 0.03 0.04 δ 100 150 200 250 300 ∂s/∂q (E) Spread sensitivity (η= 0.05) q=0.2 q=0.8 0.01 0.02 0.03 0.04 δ 200 400 600 ∂s/∂q (F) Spread sensitivity (η= 0.95) This figure shows the effects of renegotiation frictions qon yield spreads for different levels of financial constraints δ. Panel A, C, and E have η= 0.05 while Panel B, D, and F have η= 0.95. The remaining parameter values are r= 0.05, β= 0.03, σ= 0.2, α= 0.45, m= 0.2, B= 0.75, and V0= 1. The y-axes in panels C to F are in basis points. 103 Internet Appendix for: Why Does Debt Dispersion Affect Yield Spreads? Abstract This Internet Appendix contains the robustness checks mentioned in the paper. First, I explain the construction of the additional measures of debt maturity dispersion and renegotiation frictions. Second, I present summary statistics and correlations. Third, I repeat the regression analysis from the paper with the additional measures of debt maturity dispersion and renegotiation frictions. 104 Definition of Variables This section contains the detailed variable descriptions. The capitalized acronyms correspond to quarterly COMPUSTAT data items and subscripts refer to the calendar time. Debt Maturity Dispersion WMD1tThe weighted maturity dispersion measure gives more weight to short-term debt. I use the weighting scheme from Choi et al. (2018), namely, yi=1 i/P25 i=1 1 ifor maturities up to i= 25 years and yi= 0 otherwise. Let ωi=yixi/Piyixidenote the weighted principal share of bond isuch that the Weighted Herfindahlj=Pi(ωi)2and the weighted dispersion for firm jis: WMD1j= 1/Weighted Herfindahlj MD2tThis maturity dispersion distance measure from Choi et al. (2018) is based on the average squared deviation between the firm’s observed debt maturity profile and a perfectly dispersed debt maturity profile. The perfectly dispersed profile has a principal share of 1/tmax jmaturing in each maturity bucket where tmax jis the longest maturity of the currently outstanding bonds measured at the time of issuance. The distance from the perfectly dispersed debt maturity profile is: DISTj=1 tmax j tmax j X i=1 wj,i −1 tmax j!2 where wj,i is firm j’s principal share maturing in bucket i. The dispersion measure at time t is then given by MD2j=−log(DISTj+ 0.001). Renegotiation Frictions BDtThe bond dispersion measure is based on the principal shares of outstanding bonds. Let Bidenote the principal value of bond iissued by firm jsuch that the principal shares are zi=Bi/PiBi. The bond dispersion measure is then given by: BDt= 1 −X i (zi)2 PDtThe ratio of public debt to total debt at the end of quarter tis: PDt=PiBi DLCQt+DLTTQt where Biis the principal value of bond i,DLCQtis ”Debt in Current Liabilities”, and DLTTQtis ”Long-Term Debt - Total”. STDtThe ratio of short-term debt to total debt at the end of quarter tis: STDt=DLCQt DLCQt+DLTTQt where DLCQtis ”Debt in Current Liabilities” and DLTTQtis ”Long-Term Debt - Total”. 105 1 Introduction Market liquidity of the corporate bond market is important as it affects bond prices and thus the funding cost of firms, and bid-ask spreads (measured as realized transaction costs) are typically used when measuring liquidity.1Despite the importance of the bid-ask spread in understanding the functioning of the market, we have a limited understanding of why it arises in the first place. There are a number of theories of over-the-counter (OTC) frictions that have been proposed as explanations for the size and cross-sectional variation of bond bid-ask spreads, but despite the extensive theoretical literature, there is little empirical literature examining the relative importance of different theories in explaining bid-ask spreads. We fill this gap by presenting new evidence on the cross-sectional variation in corporate bond bid-ask spreads and testing leading theories’ ability to explain this variation. The paper begins by documenting new facts about bid-ask spreads in the U.S. corporate bond market using the Academic TRACE dataset for U.S. corporate bonds for the period 2002-2015. This data set has anonymized dealer identities and allows us to follow the trail through the dealer network of a bond being sold by an investor until the bond is ultimately being bought by another investor, so-called round-trip intermediation chains. For each chain we calculate the investor buy price minus the investor sell price divided by the mid-price. Schestag et al. (2016) show that there is a high correlation between realized transaction costs and dealer bid-ask spreads in the U.S. corporate bond market, and we therefore call our estimates for bid-ask spreads. We sort bid-ask spreads according to bond maturity and rating. Sorting in one dimension we find that average spreads increase in bond maturity and credit risk, confirming previous results in the literature. When double-sorting on maturity and rating, a surprising pattern emerges. Spreads for investment grade bonds increase strongly in maturity, while spreads for speculative grade bonds show no clear relation. For short-maturity bonds spreads increase in credit risk, while for longmaturity bonds spreads for bonds rated AA+ or AAA, which we call Safe bonds, are substantially higher than other investment grade bonds. We show that these patterns are robust to excluding the financial crisis, adding time fixed effects, and holds separately for bonds issued by financial and non-financial firms. We use the documented patterns in bid-ask spreads to test theories of the bid-ask spread in OTC markets. To do so, we construct proxies motivated by theories of OTC frictions and examine the extent to which the variation in proxies explains the variation in bid-ask spreads. 1Examples of research finding that liquidity impacts bond prices include Bao et al. (2011), Friewald et al. (2012), Dick-Nielsen et al. (2012), and Acharya et al. (2013). Recent research that uses transaction costs to measure corporate bond liquidity include Aquilina and Suntheim (2016), Adrian et al. (2017), Trebbi and Xiao (2017), Bessembinder et al. (2018), and Choi and Huh (2018). 112 In inventory models the dealer acts as an intermediary providing immediacy for investors and the bid-ask spread arises as a compensation for inventory risk. The bid-ask spread in the classic models of Stoll (1978) and Ho and Stoll (1983) is proportional to asset volatility and we use bond return volatility as a proxy for inventory risk. We regress actual bid-ask spreads on bond volatilities and calculate predicted bid-ask spreads from the regression estimates. Predicted spreads are increasing in maturity for investment grade bonds. Also, predicted spreads are increasing in credit risk for short-maturity bonds and show a U-shaped pattern for long-maturity bonds. Thus, patterns in predicted spreads are consistent with those in actual spreads. The average difference between predicted and actual spreads grows for increasingly credit risky speculative grade bonds, showing that the importance of other factors than inventory increases in credit risk. Duffie et al. (2005) introduce search-and-bargaining models to explain bid-ask spreads in OTC markets. A seller searches for dealers sequentially, and once a seller meets a dealer, they negotiate bilaterally over the price and their strength of negotiation depends on their outside options, in particular how easily the seller can find other dealers. We use completion time of round-trip intermediation chains as a proxy for the easy of finding counterparties. As a proxy for dealer bargaining power we follow Friewald and Nagler (2018) and compute a bond-specific HerfindahlHirschman (HH) index based on dealers’ trading volume in the past month. We find that neither proxy, and thus predicted spreads based on any of them, varies much across maturity. Furthermore, we analyse matched intermediation chains, i.e. where the chain is completed within one minute and likely prearranged by the dealer(s). Search-and-bargaining models predict that there is no difference between spreads of matched chains vs unmatched chains, but actual spreads of matched chains are much smaller than those of unmatched chains. Taken together, our results suggest that search-and-bargaining frictions have limited explanatory power in explaining bid-ask spreads. In information-based models, such as Copeland and Galai (1983) and Glosten and Milgrom (1985), the market maker’s concern is that some investors have private information about the value of the security and she does not know whether she trades with an informed or uninformed investor. To protect herself, the market maker charges a bid-ask spread. To construct our proxy, we exploit that debt and equity are claims on the same asset, the firm, and therefore private information should affect both equity and bond bid-ask spreads, albeit to a different degree. Specifically, we calculate the equity bid-ask spread of the bond issuer and compute an implied bond bid-ask spread based on the equity spread and the ratio of bond and equity price sensitivities to changes in firm value. We find that predicted spreads are much smaller than actual spreads for all maturities and ratings. The reason for this underprediction is twofold. First, the size of equity spreads is an upper bound on the size of bond spreads, because equity is more information-sensitive than debt, and 113 equity spreads are on average more than three times smaller than bond spreads. Second, bond returns are much less sensitive to changes in firm value than equity returns. Finally, recent empirical research, among others Li and Sch¨urhoff (2018), Maggio et al. (2017), and Hollifield et al. (2017), finds that how a bond travels through the dealer network is important for bid-ask spreads. In particular, how many dealers are involved in an intermediation chain and the centrality of those dealers have an impact on spreads. We calculate the average markup charged by each dealer and for each chain we calculate a predicted spread by adding the average markups of the dealers involved in the chain. Predicted spreads for long-maturity bonds show a U-shaped pattern in the relation between spreads and rating, broadly consistent with the pattern in actual spreads. Furthermore, the positive relation between actual spreads and credit risk for short-maturity bonds is also largely matched by predicted spreads. In both cases, however, the slope in the relation is smaller for predicted spreads than for actual spreads. In stark contrast to actual spreads, there is no relation between spreads and bond maturity for investment grade bonds. Overall, our results suggest that the network of dealers plays a significant role in determining spreads across rating but not across maturity. We also examine the relation between actual spreads and our measures in a panel regression. Two measures stand out in terms of R2, bond volatility and predicted dealer network spread. This is consistent with our results when we average across rating and maturity, namely that dealer inventory and dealer network are most important in explaining spreads. When we estimate the regression separately for investment grade and speculate grade bonds, dealer inventory is most important for investment grade bonds while the dealer network is dominant in explaining spreads of speculative grade bonds. Taken together, we find that inventory models explain a significant amount of the variation of bid-ask spreads, in particular across bond maturity. The network of dealers provides additional explanatory power, mainly for speculative grade bonds. We find that search-and-bargaining and asymmetric information have limited explanatory power. Our paper relates to several strands of literature. One strand tests OTC theories and the relation to bid-ask spreads. Feldh¨utter (2012) and He and Milbradt (2014) estimate parameters in search-and-bargaining models by calibrating to actual bid-ask spreads in the credit markets and comparing model-implied spreads to actual spreads across either maturity or rating. We investigate a number of alternative theories, provide more extensive comparisons across maturity and rating, and present further evidence using matched trades. Benmelech and Bergman (2018) test several implications of Dang et al. (2015)’s theory of asymmetric information and find that corporate bond bid-ask spreads (and other liquidity measures) increase in a non-linear pattern as credit quality 114 deteriorates, consistent with the theory. Similar to their results we also document a non-linear relation when we investigate asymmetric information models. However, using another prediction of Dang et al. (2015), that debt is less information-sensitive than equity, we find that only a small part of the bond bid-ask spread can be explained by unlevered equity bid-ask spreads. Another strand of literature investigates the relation between OTC frictions and prices. Using corporate bond data, Friewald and Nagler (2018) study theories of inventory and search-andbargaining, Han and Zhou (2014) study asymmetric information, and Dick-Nielsen and Rossi (2018) study dealer inventory around index exclusions. These papers focus on prices/returns and do not investigate bid-ask spreads. A third strand of literature studies the relation between the dealer network and the bid-ask spread and these papers include Li and Sch¨urhoff (2018), Maggio et al. (2017), and Hollifield et al. (2017). We contribute to this literature by studying how dealer network spreads relate to credit quality and bond maturity. Our paper is also related to a large literature that examines the bid-ask spread of corporate bonds such as Goldstein and Hotchkiss (2018), Edwards et al. (2007), Bessembinder et al. (2006), Goldstein et al. (2007), Schultz (2001), Hong and Warga (2000) and others. We contribute to this literature by studying bid-ask spreads across both bond maturity and rating and testing OTC theories of the bid-ask spread. 2 Data We use a transaction data set for the U.S. corporate bond market, called Academic TRACE, which is provided by the Financial Industry Regulatory Authority (FINRA) and covers all transactions conducted by designated dealers. The data contain dealer identities, in anonymised form, for every transaction. FINRA provides the data with a three-year lag and the data cover the period 2002:072015:06. We account for reporting errors using Dick-Nielsen (2014)’s filter and since our focus is on transaction costs of institutional investors we delete trades with a par value below $100,000 as these are commonly viewed as retail transactions. We do, however, also support our findings with results based on retail-sized transactions. We restrict our sample to bonds with fixed coupon rates including zero-coupon bonds and exclude bonds that are callable at a fixed price, putable, convertible, denoted in foreign currency, or have sinking fund provisions. We keep bonds with a make-whole call provision since makewhole calls have little effect on bond prices (see Powers and Tsyplakov (2008) and Bao and Hou (2017)). We collect information on bond characteristics and bond ratings from Mergent Fixed Income Securities Database (FISD).2 2We use Mergent FISD’s ISSUER ID as firm identifier. At a given point in time, we use the most recent rating 115 Table 1shows summary statistics of our data sample for institutional-sized transactions. In total, our sample includes 18.1 million transactions in 23,626 bonds issued by 3,178 firms. We sort bonds into three maturity groups (0-4 years, 4-8 years, and more than 8 years) which we call short, medium, and long maturity. The number of transactions in each maturity group are similar: for short-, medium-, and long-maturity bonds the number is 6.4, 5.5, and 6.2 million, respectively. We divide our sample into seven rating groups (Safe [AAA and AA+], AA [AA and AA-], A, BBB, BB, B, and C [C, CC, and CCC]). Table 1shows that most transactions, 82%, occur in investment grade bonds. There is broad coverage across rating and maturity. For example, the rating/maturity combination with fewest firms, long-maturity bonds issued by Safe firms, nevertheless has 310,568 transactions in 586 bonds issued by 71 firms over the sample period. Examples of Safe bond issuers are Microsoft, Johnson & Johnson, Yale University, Harvard University, New York University, Stanford University, and MIT. Finally, when needed, we obtain firm characteristics from COMPUSTAT, Treasury rates from the Federal Reserve Bank, and equity data from the Center for Research in Security Prices (CRSP). 3 Cross-Sectional Variation in Bid-Ask Spreads We calculate bid-ask spreads by tracking bond prices as a bond travels from a selling investor through the network of dealers until the bond ends in the inventory of a buying investor. Thus, we follow a recent literature on intermediation chains (Maggio et al. (2017), Li and Sch¨urhoff (2018), and Friewald and Nagler (2018)). Specifically, we use the round-trip match algorithm from Li and Sch¨urhoff (2018) to compute realized transaction costs from round-trip intermediation chains. A round-trip intermediation chain starts from an investor who sells bonds to a dealer (CD leg). If the dealer sells all the bonds to another investor (DC leg) then the chain is a CDC chain. If the dealer sells less than all the bonds to a single investor or sells some or all the bonds to several investors then the chain is a CDC-Split chain. The dealer may also sell all the bonds to another dealer (DD leg) who can then sell the bonds either to investors or another dealer. These chains are classified as C(N)DC or C(N)DC-Split where (N) denotes the number of dealers and the name reflects if the initial par size from the CD leg is split into smaller lots in the last leg of the chain i.e. in the DC leg. As in Li and Sch¨urhoff (2018) we restrict order splitting to the last leg of the chain and not in interdealer trades. In case of order splitting, we calculate the par-weighted sales price and the par-weighted transaction date of the DC leg. We use our sample of round-trip intermediation chains to calculate bid-ask spreads from realized from Standard & Poor’s. If this rating is not available, we use the most recent rating from Moody’s. If this rating is also missing, we use the most recent Fitch rating. For bonds that are initially rated by Moody’s or Fitch, we keep the initial rating until a rating becomes available from Standard & Poor’s. 116 transaction costs. For each chain, we calculate the bid-ask spread as the sales price the tail dealer receives from the investor minus the purchase price the head dealer pays to the investor divided by the mid-price of the two. A round-trip intermediation chain may take up to several days to complete during which the bond’s time-to-maturity decreases and its rating can change. We use the first date of the chain (i.e. the day where the dealer buys from the investor) to determine the bond’s time-to-maturity and rating. If a bond has several chains beginning on the same day, we calculate the volume-weighted bid-ask spread using the trading volume from the last leg in the chain. Since we divide our sample into three maturity groups and seven rating groups, we end up with a cross-section of 21 groups in total. Within each of the 21 groups, we winsorize bid-ask spreads at the 1st and 99th percentiles over the entire sample period to mitigate the influence of outliers. We use these winsorized bid-ask spreads in the subsequent analysis. Table 2shows summary statistics of the round-trip intermediation chains for institutional-sized transactions. As was the case with the number of transactions, 82% of the chains are in investment grade bonds. Panel A shows that the average bond age increases with credit risk. For example, the average bond age is 5.65 years when a C-rated bond trades while it is only 2.99 years for a Safe bond. Panel A also shows that the average amount outstanding decreases with credit risk. The average amount outstanding of Safe bonds is more than three times that of C-rated bonds. Finally, we see that the average trade size is higher for Safe bonds and C-rated bonds, but otherwise shows no relation with rating. Table 3presents average bid-ask spreads across maturity and rating for institutional-sized transactions. On average, bid-ask spreads increase with bond maturity: the average bid-ask spread for short-, medium-, and long-maturity bonds is 23.1bps, 36.4bps, and 45.8bps, respectively. The positive relation between bond maturity and bid-ask spreads is well-known in literature (see for example Chakravarty and Sarkar (2003), Edwards et al. (2007), and Feldh¨utter (2012)), and for all investment grade ratings we see the same pattern of increasing bid-ask spreads as maturity increases. However, for speculative grade ratings, there is no clear pattern: although long-maturity bonds have the highest bid-ask spreads, short-maturity bonds have higher bid-ask spreads than medium-maturity bonds. For example, for BB-rated bonds the average bid-ask spread for short-, medium-, and long-maturity bonds is 39.8bps, 33.7bps, and 42.8bps, respectively. Turning to the relation between rating and bid-ask spreads, Table 3reveals a surprising pattern. For short-maturity bonds, the bid-ask spread is 16.3-17.3 bps for ratings above BBB while for lower ratings there is a positive relation between rating and bid-ask spread, increasing from 25.6 bps for BBB bonds to 63.8 bps for the most risky C-rated bonds. For medium-maturity bonds we see that 117 Safe bonds have higher average bid-ask spreads (38.4 bps) than bonds rated AA, A, BBB, and BB (33.7-37.3 bps), while long-maturity Safe bonds have higher spreads (50.4 bps) than bonds in other rating classes (40.2-49.8 bps) except the most risky bonds rated C.3 The finding that long-maturity bonds of the lowest credit risk have substantially higher bid-ask spreads than other investment grade bonds is surprising. Theoretically, research articles studying the relation between credit risk and illiquidity in the corporate bond market imply a positive relation between credit risk and illiquidity (Ericsson and Renault (2006), He and Milbradt (2014), Chen et al. (2018)). Empirically, Edwards et al. (2007) and Goldstein and Hotchkiss (2018) find a monotone and positive relation between bid-ask spreads and credit risk. There are at least two reasons why the high bid-ask spreads for long-maturity Safe bonds has gone unnoticed. First, we double-sort on rating and maturity and the high bid-ask spreads only become apparent for longer-maturity bonds. Second, previous research articles such as Edwards et al. (2007) and Goldstein and Hotchkiss (2018) have a coarser grouping of ratings making the high bid-ask spreads for Safe bonds more difficult to discern. A concern when using average bid-ask spreads over the period 2002-2015 is that bonds with low credit risk trade more often in periods when transaction costs are higher. For example, Acharya et al. (2013) find that there is a flight-to-safety in the U.S. corporate bond market in stress periods, i.e. investors prefer safe corporate bonds in crisis periods. However, Table 4shows that the pattern is present both in the financial crisis 2007-2009 and in the sample period excluding the financial crisis. To further examine the impact of time variation in bid-ask spreads, we estimate a regression with month fixed effects in Table 5. Time fixed effects soak up potential effects of having more observations of bid-ask spreads from bonds with low credit risk in stress periods where bid-ask spreads are generally high. For short-maturity bonds, we see that bid-ask spreads now monotonically increase with credit risk, while the pattern that mediumand long-maturity Safe bonds have higher bid-ask spreads than other investment grade bonds remains unchanged. The standard errors show that the differences in bid-ask spreads for long-maturity Safe bonds and other investment grade bonds are statistically significant. We estimate bid-ask spreads for both financial and non-financial firms and a potential concern is that high bid-ask spreads of long-maturity Safe bonds may be caused by many observations of highly rated financial bonds with high bid-ask spreads and lower-rated non-financial bonds 3Formally, we need to carry out a t-test of differences in mean rather than look at standard errors in individual groups to claim statistical significance. If we do so we find significant differences; a t-test of the difference in mean between the long-maturity Safe and AA groups is 3.11, between long-maturity Safe and A groups is 1.54, between long-maturity Safe and BBB groups is 2.00, and between long-maturity Safe and BB groups is 2.16. Further t-tests are available on request. 118 with low bid-ask spreads. We therefore estimate bid-ask spreads separately for financial and nonfinancial firms in Table 6. The size of bid-ask spreads is similar across maturity and rating (except for C-rated bonds) and, in particular, long-maturity Safe bonds have higher bid-ask spreads than other investment grade bonds for both financials and non-financials. In Table 7, we present average bid-ask spreads for retail-sized transactions (trade sizes below $100,000) across maturity and rating. Our results show that the average bid-ask spread for retailsized transactions is 155.6 bps compared to 34.1 bps for institutional-sized transactions. The finding that bid-ask spreads decrease substantially with trade size is well-documented in the literature by e.g. Edwards et al. (2007) and Schestag et al. (2016). The cross-sectional variation in bid-ask spreads for retail-sized transactions show the same patterns as institutional-sized transactions. The average bid-ask spread for short-, medium-, and long-maturity bonds is 114.3 bps, 158.1 bps, and 240 bps, respectively. For short-maturity bonds, average bid-ask spreads increase with credit risk from 76.5 bps for Safe bonds to 369.6 bps for C-rated bonds. For medium-maturity bonds, the average bid-ask spread for Safe bonds is 151.7 bps which is higher than bonds rated either AA (132 bps) or A (134.4 bps). Also for long-maturity bonds, Safe bonds have higher average bid-ask spreads (224.7 bps) compared to bonds rated AA or A (210.4 and 219.8 bps). Unlike our results for institutional-sized transactions, however, we find that average bid-ask spreads increase with maturity for both investment and speculative grade bonds. 4 Empirical Measures In this section, we discuss theories of the bid-ask spread and define our empirical measures. We leave the implementation details of our measures to Appendix A. 4.1 Measures Inventory costs. In inventory models, the market maker acts as an intermediary providing immediacy for investors by absorbing an imbalanced order flow. Since the asset entails price risk, the market maker has inventory risk and as a compensation for this risk the market maker earns a bid-ask spread. In the classic models of Stoll (1978) and Ho and Stoll (1983) the relative bid-ask spread is proportional to the volatility in the asset’s returns and volatility is the only asset specific component. We therefore test the classic models of inventory by examining the extent to which differences in bond return volatility explains differences in bid-ask spreads. 119 Search and bargaining.Duffie et al. (2005) introduce search-based models to explain bid-ask spreads in OTC markets and these models are used extensively to explain different aspects of bidask spreads and liquidity in general.4In the models, a seller searches for dealers sequentially and trade does not occur immediately. Once a seller meets a dealer, they negotiate bilaterally over the price and their strength of negotiation depends on their outside options, in particular how often they meet other counterparties. A key prediction of search models is that the bid-ask spread is decreasing in the speed with which counterparties find trading partners. This implies that if it is difficult to find counterparties when trading a particular bond, it will take a longer time for the bond to travel from a selling investor through the interdealer network to a buying investor, and bid-ask spreads will be higher. Therefore, we use the average time it takes for a bond to complete a round-trip intermediation chain as a measure for the inverse search intensity and we expect bid-ask spreads to be positively related to the chain time. Another central feature of search based models is the importance of the bargaining power of the dealer in the bilateral negotiation between dealer and investor. We follow Friewald and Nagler (2018) and use a bond-specific Herfindahl-Hirschman index based on customer trading volume of dealers. The intuition is that in a more concentrated market with fewer dealers, the bargaining power of investors is worse and therefore bid-ask spreads are higher. Asymmetric information. Information-based models are introduced in Bageshot (1971), Copeland and Galai (1983), and Glosten and Milgrom (1985). The market maker’s concern is that some investors have private information about the value of the security and she does not know whether she trades with an informed or uninformed investor. To protect herself, the market maker charges a bid-ask spread such that losses from trading with informed investors are offset by gains from trading with uninformed investors, and more private information leads to a larger bid-ask spread. To test the prediction of asymmetric information, we exploit that private information is about the value of the firm and this information therefore affects the bid-ask spread of both equity and debt, albeit to different degrees. Specifically, we measure the bid-ask spread in the equity market and unlever this bid-ask spread to a corresponding predicted bid-ask spread in the bond market. We do so in Merton (1974)’s model of credit risk where we add asymmetric information to the model following Copeland and Galai (1983); we leave the details of the model and the implementation details to Appendix A. The intuition for the bid-ask spread in the model is: if the equity return is three times as sensitive to a change in firm value as the debt return, the bid-ask spread 4Feldh¨utter (2012), He and Milbradt (2014), Vayanos and Weill (2008), Lagos and Rocheteau (2009), Lagos et al. (2009), Duffie et al. (2007), Sambalaibat (2018) and many others. 120 in the equity market is three times as large as in the bond market because a piece of private information moves equity prices three times as much as debt prices.5 Dealer networks. There is a recent empirical literature finding that the network of dealers is central to understanding liquidity in OTC markets (Li and Sch¨urhoff (2018), Maggio et al. (2017), and Hollifield et al. (2017) among others). In particular, the kind of dealer investors trade with, periphery or central dealer, as well as the number of dealers involved in an intermediation chain is important for bid-ask spreads. We examine the importance of the dealer network by estimating a predicted bid-ask spread for a given bond transaction based on how this bond travels through the network.6Specifically, for each dealer we calculate four average markups, across time and bonds, depending on whether the dealer buys from an investor or another dealer and whether the dealer sells to another investor or another dealer. We use the average markups as a proxy for predicted markups. For each round-trip intermediation chain, we then estimate a predicted bid-ask spread by aggregating the predicted markups of the individual dealers involved in the chain. As an example, consider a chain where an investor sells to dealer A, dealer A sells to dealer B, and dealer B ultimately sells to another investor. Assume that on average dealer A earns a markup of 10 bps when buying from an investor and selling to another dealer, while dealer B on average earns a markup of 15 bps when buying from another dealer and selling to an investor. In this case, the predicted bid-ask spread is 25 bps. 4.2 Relation Between Measures Table 8shows the correlations between our measures for institutional-sized transactions. We calculate correlations using observations for which we can calculate all measures, and in particular this implies that the correlations are based on a subset of bonds for which the firm is a public company (since our proxy for asymmetric information requires an equity bid-ask spread). The highest correlation of 31.5% is between unlevered equity bid-ask spreads as a proxy for asymmetric information and bond volatility as a proxy for inventory costs. The positive correlation reflects that they are clearly related, but they also have distinctly different predictions. For instance, consider a firm with low leverage that have issued a safe bond with near-zero default risk. The theoretical prediction from asymmetric information models is a near-zero bid-ask spread 5The prediction of our model is consistent with Dang et al. (2015) who show that debt is less information sensitive than equity. 6We take the structure of the network as exogeneously given. The network structure may arise because of search frictions (Hugonnier et al. (2017), Neklyudov (2014)), relationships (Colliard and Demange (2018)), asymmetric information (Glode and Opp (2016), Babus and Kondor (2018), Chang and Zhang (2018)), or inventory (¨ Usl¨u (2018)). 121 standard search-and-bargaining models, the main drivers of spreads is the search for counterparties and bilateral bargaining and the models abstain from modelling inventory of dealers. A standard feature of the models is that dealers have immediate access to an interdealer market in which they unload their positions, so that they have no inventory at any time (see for example Duffie et al. (2005), Lagos and Rocheteau (2009), Feldh¨utter (2012), and He and Milbradt (2014)). In such models, dealers immediately unload bonds in the interdealer market and all transactions appear as prematched. Therefore, we do not expect to see different bid-ask spreads of matched and unmatched trades. In inventory models, the bid-ask spread arises because the dealer is compensated for the risk that the bond price decreases while the dealer has the bond in inventory. In matched trades there is no such risk and the bid-ask spread in matched trades should be constant across rating and maturity. Bid-ask spreads in asymmetric information models arise because the dealer has to earn a positive profit when trading with uninformed investors to offset trading loses when trading against informed investors. In matched trades, there is no such potential trading losses regardless of whether the counterparty is informed or uninformed and therefore the models predict that the bid-ask spread of matched trades is constant. As noted in footnote 6, there are a number of theories that may explain the network structure, for example search frictions and asymmetric information, and therefore dealer network models do not have clear predictions on matched trades. In our sample, we define matched trades as round-trip intermediation chains completed within one minute. We calculate bid-ask spreads in the same way as for the full sample. Specifically, if a bond has several chains beginning on the same day, we calculate the volume-weighted bid-ask spread. This implies that the sum of matched and unmatched chains is higher than the sum of all chains in Table 1, because if a bond trades in both a matched and in a unmatched chain on a given day, this gives rise to only one volume-weighted chain in the full sample. Finally, we divide our samples of matched and unmatched chains into seven rating groups and three maturity groups similar to our previous analysis. We winsorize bid-ask spreads within each of the 21 ratingmaturity groups, for matched and unmatched chains separately, at the 1st and 99th percentiles over the entire sample. Table 18 shows the bid-ask spread for matched and unmatched chains, respectively. For investment grade bonds, the bid-ask spread of matched chains is a small fraction of the spread of unmatched chains. For example, the bid-ask spread of matched chains for Safe bonds is 5.9 bps while the spread is 31.8 bps for unmatched chains. Furthermore, the spread does not consistently 128 become larger as bond maturity increases. For example, the spread for BBB bonds shows little relation to maturity for matched chains. Since search-and-bargaining models predict that there is no difference in bid-ask spreads of matched and unmatched chains, these results suggest that these models cannot explain the size of bid-ask spreads for speculative grade bonds. In contrast, the large difference between matched and unmatched chains is consistent with models of inventory and asymmetric information. For speculative grade bonds, we see that bid-ask spreads of matched chains increase substantially as credit quality deteriorates and for the lowest C-rated bonds the average bid-ask spread of matched chains is 46.1 bps which is a sizeable 66% of the bid-ask spread of unmatched chains of 69.7 bps. This is consistent with the importance of search-and-bargaining frictions increasing as bonds become more credit risky. 6 Conclusion We estimate bid-ask spreads in the U.S. corporate bond market using realized transaction costs from round-trip intermediation chains and document variation across credit quality and bond maturity. Spreads increase in bond maturity for investment grade bonds, but there is no clear relation for speculative grade bonds. For short-maturity bonds, spreads increase with credit risk while long-maturity Safe bonds have significantly higher spreads than other investment grade bonds. We use the documented patterns to test prominent theories of the bid-ask spread in OTC markets: inventory, search-and-bargaining, asymmetric information, and dealer networks. A key implication of dealer inventory models is that the bid-ask spread is proportional to bond return volatility, and consistent with this implication we find that variation in bond volatilities explains a large part of the variation in bond bid-ask spreads, in particular for investment grade bonds. We also calculate a predicted spread from the dealer network by calculating an average markup for each dealer and estimating a predicted spread for each round-trip intermediation chain by adding the markups of the involved dealers. We find that predicted spreads can also explain part of the variation, especially for speculative grade bonds. We do not find much support for search-and-bargaining models. Our proxies for search-andbargaining models, the time it takes to complete a round-trip intermediation chain and dealer concentration, do not exhibit much variation across bond maturity or rating. Furthermore, we find that matched chains, i.e. chains that are completed within one minute, have much smaller spreads than unmatched chains. Search-based models predict that there is no difference in spreads of matched and unmatched chains. Finally, asymmetric information models predict that the equity bid-ask spread is larger than 129 the bond bid-ask spread because the equity price is more sensitive to information than the bond price, and we exploit this feature to derive a predicted bond bid-ask spread by unlevering the equity bid-ask spread. We find that predicted bond spreads are much too small, in particular for investment grade bonds, suggesting that asymmetric information, at least for investment grade bonds, is not important for determining bid-ask spreads. 130 Appendices A Empirical Measures: Implementation Details This appendix explains implementation details of the measures we use to proxy for central predictions from theories on frictions in OTC markets. A.1 Inventory: bond return volatility We use the WRDS Bond Returns dataset to estimate bond return volatility. This dataset contains monthly bond returns based on cleaned transaction prices from Enhanced and Standard TRACE. We use the monthly return based on the last price at which a bond traded in a given month provided that day falls within the last 5 trading days of the month. If there are no trades in the last five days of the current month or the previous month, the bond return is missing for the month. We estimate bond return volatility as the standard deviation of monthly bond returns in the past 24 months and require at least 12 monthly observations in the two-year estimation window. We use bond return volatility instead of bond return variance as implied by Stoll (1978) and Ho and Stoll (1983) because the distribution of bond volatilities is less skewed. To account for outliers, we winsorize the bond-month observations of bond volatility one-sided at the 98% level. We have also done our analysis using the monthly return based on either (1) the last price at which the bond traded in a given month or (2) the price on the last trading day of the month and these choices give similar results. A.2 Search: chain time We measure chain time as the number of days it takes to complete a round-trip intermediation chain. A chain starts when the head dealer buys bonds from an investor and ends when the tail dealer sells bonds to an investor. The chain time is the number of days between the first and last transaction in the chain. In case of order splitting, we calculate the par-weighted transaction date of the last leg in the chain. For example, assume an investor sells $1mio in par value to a dealer on a Monday. This dealer sells half the amount to an investor on the following Wednesday and 131 the rest to another investor on the following Friday. In this case the chain time is 1 2∗2 + 1 2∗4=3 days. A.3 Bargaining: Herfindahl-Hirschman index for dealer concentration For each bond, we calculate a Herfindahl-Hirschman (HH) index based on bond transactions in the past month. Assume that there are Ndealers transacting in bond jover the last month and dealer itransacts a par value of vi. The market share of dealer iis si=vi PN i=1 viand the HH index at time tis DCj,t = N X i=1 s2 i.(A.1) A.4 Dealer network: predicted bond bid-ask spreads based on the dealer network For each dealer we find all instances in the round-trip intermediation chains where the dealer •buys from an investor and sells to another investor •buys from an investor and sells to a dealer •buys from a dealer and sells to another dealer •buys from a dealer and sells to an investor and in each of the four cases we calculate a dealer-specific average markup, across all chains, where the markup in each leg of the chain is estimated as dealer sell price −dealer buy price mid-price (A.2) where the mid-price is the average of the investor sell price and the investor buy price in the chain. In case of order splitting, the investor buy price is the par-weighted average of investor buy prices. The average markup in each of the four cases serves as the predicted markup for this particular dealer. For each round-trip intermediation chain, we calculate a bid-ask spread predicted by the dealer network in the following way. For each dealer in the chain, we replace the actual markup with the predicted markup, and then calculate the total round-trip markup based on the sum of the predicted dealer markups. As in example, consider a chain where an investor sells to dealer A, dealer A sells to dealer B, and dealer B ultimately sells to another investor. Assume that on average dealer A earns a markup of 10 bps when buying from an investor and selling to another dealer, while dealer B on average earns a markup of 15 bps when buying from another dealer and selling to an investor. In this case the predicted markup is 25 bps. 132 We winsorize predicted bid-ask spreads at the 1% and 99% level. A.5 Asymmetric information: predicted bond bid-ask spread extracted from the equity bid-ask spread We use a model to calculate predicted bond bid-ask spreads from equity bid-ask spreads for the issuing firm. Our model follows Copeland and Galai (1983). We assume that V0is the current value of the firm as perceived by a risk-neutral dealer. The dealer trades a claim on the value of the firm C0and commits to sell a fixed quantity of the claim for KAand buy a fixed quantity for KBwithin a short period of time. Firm value can take on two values in the next period, Vu> V0and Vd< V0, and each value is equally likely. We assume that claim value is monotone in firm value and therefore Cu> C0and Cd< C0. An investor arrives and trades before the next period; after the transaction firm value in the next period is revealed. With probability pthe investor is informed about the value of the firm while with probability 1 −pthe investor trades for liquidity-reasons and is uninformed. It is equally likely that the liquidity-trader will buy or sell. The dealer’s expected revenue from the transaction if the investor is a liquidity-trader is 1 2(KA−C0) + 1 2(C0−KB) (A.3) while the expected revenue if the investor is informed is 1 2(KA−Cu) + 1 2(Cd−KB) (A.4) The dealer revenue in equation (A.4) is negative because the informed investor only trades if he gains a profit. We assume that dealer markets are competitive and therefore the expected dealer profit is zero (1 −p)1 2(KA−C0) + 1 2(C0−KB)+p1 2(KA−Cu) + 1 2(Cd−KB)= 0 (A.5) and simplifying the expression yields KA−KB=p(Cu−Cd).(A.6) Assume that dealer A trades equity while dealer B trades debt and the probabilities in the two markets (of the investor being informed and the liquidity-trader selling) are the same. In this case equation (A.6) holds for both dealers and the ratio between the bid-ask spread in the equity and 133 the debt market is KE A−KE B KD A−KD B =Eu−Ed Du−Dd (A.7) while the ratio between the relative bid-ask spreads is (KE A−KE B)/E0 (KD A−KD B)/D0 =(Eu−Ed)/E0 (Du−Dd)/D0 .(A.8) Equation (A.8) shows that the relative spreads depend on the price sensitivity of debt and equity to changes in firm value: if the percentage change in equity value is twice the percentage change in debt value, the relative bid-ask spread of equity is twice that of debt. Assume now that firm value follows a Geometric Brownian Motion and that the firm has issued one zero-coupon bond with maturity date T, i.e. this is the Merton (1974) model. It is well-known that the value of equity is equal to the value of a call option while the value of debt is equal to the value of a risk-free bond minus the value of a put option. Consider the above model as one period in a discrete-time binomial tree version of the Merton model. We know that as the time period in the binomial model shrinks, the value of debt, equity, and deltas converge to the Black-Scholes values (Walsh (2003)). Therefore, the ratio between the relative bid-ask spreads converges to (KE A−KE B)/E0 (KD A−KD B)/D0→N(d1)/C(V0) 1−N(d1)/(D−P(V0)) (A.9) where C(V0) and P(V0) are Black-Scholes call and put option values, Dis the value of a risk-free zero-coupon bond with maturity date Tand face value equal to the face value of the risky debt, N(.) is the standard normal distribution function, and d1=1 σ√Tlog(V0/d)+(rt−δt−1 2σ2)T(A.10) where σis asset volatility, Tis the time-to-maturity of the bond, dis the default point, rtis the yield at time tfor a Treasury bond with maturity T, and δtis the payout rate at time t. We use data from several sources to estimate the model parameters. For a given bond on a given day, we use data from Mergent FISD to determine time-to-maturity Tand calculate rtas the interpolated maturity-matched Treasury rate using data from the Federal Reserve Bank. To estimate the remaining parameters, we combine annual accounting information from COMPUSTAT with daily stock market data from CRSP. We align each firm’s fiscal year with the calendar year and lag accounting data by six months when we merge the two datasets using the CRSP134 COMPUSTAT linking table. We only consider common stocks (SHRCD equal to 10 or 11 in CRSP) and calculate the daily market value of equity and the daily equity bid-ask spread from CRSP. If a firm has more than one share class, we compute a weighted bid-ask spread based on the market capitalization of each share class. We use the approach from Feldh¨utter and Schaefer (2018) to estimate firms’ asset volatilities as σt=R(Lt)(1 −Lt)σE,t (A.11) where σE,t is equity volatility and Ltis the market leverage ratio at time t, and Ris a stepfunction of Ltthat is 1 if Lt<0.25, 1.05 if 0.25 < Lt≤0.35, 1.10 if 0.35 < Lt≤0.45, 1.20 if 0.45 < Lt≤0.55, 1.40 if 0.55 < Lt≤0.75, and 1.80 if Lt>0.75. The firm’s daily market leverage is the ratio of total debt to the sum of total debt and the market value of equity. The equity volatility is the annualized standard deviation of daily stock returns from CRSP measured over the past three years. We require return observations on at least half the trading days in the three-year window before we compute the equity volatility. If a firm has more than one share class, we compute the weighted equity volatility based on the market capitalization of each share class. For a given firm, we calculate the average asset volatility over the entire sample period and use this constant asset volatility σfor every day in the sample period. We follow Feldh¨utter and Schaefer (2018) and calculate daily payout rates as the sum of interest payments to debt, dividend payments to equity, and net stock repurchases divided by the sum of total debt and the market value of equity. We also use the estimated default point d= 0.8944 ∗F from Feldh¨utter and Schaefer (2018) where Fis the total debt face value from COMPUSTAT. We use the linking table from Wharton Research Data Services (WRDS) to merge bond-level information with firm characteristics for bonds/firms with non-overlapping linking dates. Finally, we imply out firm value V0such that the value of the call option C(V0) equals the market value of equity at time tand subsequently we calculate the ratio in equation (A.9) and multiply the equity bid-ask spread with this ratio to derive a predicted bond bid-ask spread. Predicted bond bid-ask spreads are winsorized at the 1% and 99% level. 135 B Regression Results with Simulated Transaction Prices In this section, we analyze the relationship between bid-ask spreads and bond return volatility using simulated transaction prices. Let mit denote the mid-price for bond iat time t mit =mi,t−1+uit, uit ∼N(0, σ) (B.1) such that the transaction price pit for bond iat time tis pit =mit +qitci, ci∼unif(a, b) (B.2) where qit is the trade indicator (+1 for buys and -1 for sells) and ciis the half spread. We assume qit is independent of uit and P(qit = 1) = P(qit =−1) = 0.5. Let mi0= 100 for all i={1,...N} bonds and consider t={1,...T}months. The monthly bond return is rit =log(pit)−log(pi,t−1) (B.3) and the estimated monthly bond volatility for bond iis ˆσi=v u u t 1 T−1 T X t=1 (rit −ˆµi)2(B.4) where ˆµi=1 T T X t=1 rit (B.5) We calculate bid-ask spreads measured in bps as BAi= 2 ∗ci(B.6) and estimate the regression BAi=β0+β1ˆσi+i(B.7) For N= 10,000 bonds and T= 36 months, we only draw one set of random numbers and consider different combinations of underlying parameter values. In Table B.1, we present the regression results. Panel A shows that for institutional-sized bid-ask spreads (0-70 bps), it requires a small annualized bond volatility of 4% to generate a meaningful R2. For comparison, the average an136 nualized bond volatility is 8.3% in our sample. Panel B shows the results for retail-sized bid-ask spreads (0-220 bps). Both the magnitudes of the coefficient estimates ˆ β1and the R2’s are substantially higher for retail-sized transactions compared to institutional-sized transactions. These features are consistent with our findings in Table 16 and 17. Table B.1: Regressions Results Based on Simulated Transaction Prices This table presents regression results of the equation BAi=β0+β1ˆσi+ibased on simulated transaction prices. The bid-ask spread is measured in bps and annualized bond volatility is in percent. Panel A shows the results for (institutional-sized) bid-ask spreads between 0 og 70 bps while Panel B presents the results for (retail-sized) bid-ask spreads between 0-220 bps. Annualized σ 4% 8% 12% Panel A: Spreads from 0-70 BPS ˆ β015.23 29.1 31.85 (8.95) (16.95) (18.60) ˆ β1487.51 72.12 25.22 (11.62) (3.37) (1.77) Adj. R20.013 0.001 0.000 Panel B: Spreads from 0-220 BPS ˆ β0-161.11 -23.90 43.20 (-51.30) (-4.72) (8.14) ˆ β16006.51 1622.00 547.90 (87.21) (26.55) (12.59) Adj. R20.432 0.066 0.016 137