THREE ESSAYS IN CORPORATE BOND CONTRACT DESIGN AND VALUATION

Transcription

1 THREE ESSAYS IN CORPORATE BOND CONTRACT DESIGN AND VALUATION By JOHN C. BANKO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003

2 This document is dedicated to my parents, John and Sandy Banko; and to my wife, Khanh-Lien.

3 ACKNOWLEDGMENTS I thank the students and professors at the University of Florida and in the Department of Finance for seeing me through this endeavor. Joel Houston and M. Nimalendran provided support at many points during my education. I am fortunate to have Rich Romano from the Department of Economics serve on my committee. Chungrong Ai also provided keen insight at many points. I am especially thankful to Dave Brown and Mark Flannery for their counsel, support, and friendship over the years. iii

4 TABLE OF CONTENTS page ACKNOWLEDGMENTS... iii LIST OF TABLES... vi LIST OF FIGURES... viii ABSTRACT... ix CHAPTER 1 INTRODUCTION PUTABLE DEBT IN AGENCY THEORY Previous Research Agency Conflict Models: the Equivalence of the Call and Put Option Asymmetric Information Model setup Equilibrium strategies under asymmetric information Discussion Future Investment Opportunities Model setup Straight debt and callable debt-financing Putable debt-financing Discussion Risk-shifting Solution with callable and putable debt Discussion Summary of Theoretical Findings Empirical Summary Issues in Empirical Tests Data, Sample Selection, and Description Conclusions Findings Future Research DIRECTIONALITY OF CREDIT-SPREADS REVISITED Data and the Time Series of Credit Spread Volatility Regression Analysis of Credit Spreads and Rate Changes...57 iv

5 3.2.1 Choice of Interest Rate Variable Analysis of Full Sample Period Analysis of the Pre-1994 Sample Period Analysis of the Post-1991 Period Stock Market Evidence of Interest Rates and Issuer Prospects Directionality of Agency Spreads Conclusions SERIAL CORRELATION IN U.S. CORPORATE BOND EXCESS RETURNS Sources of Serial Correlation in Excess Bond Returns Zero-coupon Bond Example The Relation between Excess Returns and Past Excess Returns Data and Bond Excess Return Calculations Sample Selection Criteria Excess Returns Empirical Results Empirical Specification Results of the Empirical Analysis Implications for Risk Pricing Conclusions and Future Research CONCLUSION APPENDIX A PROOF OF PROPOSITION B PROOF OF EQUIVALENT SECURITY HYPOTHESIS C REGRESSIONS USING DIFFERENT BENCHMARK TREASURIES LIST OF REFERENCES BIOGRAPHICAL SKETCH v

6 LIST OF TABLES Table page 2-1. Debt financing with required rates Debt financing allowing firm separation State-dependent payoffs to the project State-dependent payoffs to putable bond investors Summary statistics: U.S. corporate debt issues, Summary Statistics by firm-type: U.S. corporate debt issues, S&P rating numerical conversion Credit-spread summary statistics for U.S. corporate debt Credit-spread summary statistics for U.S. agency debt Directionality of credit-spreads for the entire sample period Directionality of credit-spreads for the pre-1994 sample period, short-maturity Directionality of credit-spreads for the pre-1994 sample period, medium-maturity Directionality of credit-spreads for the pre-1994 sample period, long-maturity Directionality of credit-spreads for the post-1991 sample period, short-maturity Directionality of credit-spreads for the post-1991 sample period, medium-maturity Directionality of credit-spreads for the post-1991 sample period, long-maturity Relation between stock returns and interest-rate changes Directionality of credit-spreads for long-maturity agency bonds Regression results from simulated price paths vi

7 4-2. Summary statistics for U.S. corporate debt issues, Additional summary statistics for U.S. corporate debt issues, Regression results for investment-grade debt, Regression results for junk debt, Regression results by grade, S&P ratings for initial bond issuance C-1. Directionality of credit-spreads with different treasury yields vii

8 LIST OF FIGURES Figure page 2-1. Uncertainty about changes in project value Project with a future investment opportunity Changes in equity value from risk-shifting Changes in call option value from risk-shifting Changes in put option value from risk-shifting Debt covenant preferences with multiple agency conflicts Percentage of call options in corporate debt issues Percentage of put options in corporate debt issues Percentage of straight debt in corporate debt issues Initial debt yield in corporate debt issues Initial debt rating for corporate debt issues Yield spreads on U.S. corporate bonds Treasury bill yields Simulated bond price paths viii

9 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THREE ESSAYS IN CORPORATE BOND CONTRACT DESIGN AND VALUATION By John C. Banko May 2003 Chair: David T. Brown Major Department: Finance, Insurance, and Real Estate The chapters that comprise this dissertation examine three topics in corporate bond structure and pricing. Chapter 2 addresses why financial theory fails to explain the propensity of firms to include a call provision in long-term debt. I argue that this failure is possibly because the hypothesis is flawed. I offer theoretical support that a put option exists offering outcomes identical to a call option. I also describe a certain agency conflict that cannot be resolved with a call provision. These findings raise serious questions concerning previous investigations of the call option and suggest interesting future research. Chapter 3 provides an analysis of monthly credit-spread data on noncallable and nonputable investment-grade corporate bonds. In contrast to prior research, I find little evidence of a negative relation between credit-spreads and interest-rate changes in the 1990s. There is a positive relation between interest-rate changes and credit-spread changes for short-maturity, investment-grade portfolios. There is no significant relation between interest-rate changes and spread changes for medium-maturity portfolios. A ix

10 negative relation between interest-rate changes and spread changes occurs for top-rated short-term portfolios and for all credit-quality long-maturity portfolios. The chapter goes on to explore three additional areas: the relation between credit-spread changes and interest-rate changes over time, the relation between interest-rate changes and monthly returns on major stock indices, and the causes of credit-spread changes in long-maturity corporate bonds. Chapter 4 explores the time-varying structure of changes in corporate bond yields and yields on similar Treasury bonds. The difference between corporate bond yields and similar-maturity Treasury bond yields varies considerably over time. I show that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. Empirical analysis offers evidence that corporate bond excess returns are negatively related to lagged excess returns. Results suggest that the volatility in corporate bond excess returns is driven by time-varying risk premiums. The implications for the equilibrium pricing of credit risk are also discussed. x

11 CHAPTER 1 INTRODUCTION The structure of corporate debt offerings and their subsequent prices remain an important topic in financial economics. The chapters that comprise this dissertation examine three of these topics and offer new evidence supporting and challenging current views in the literature. Chapter 2 addresses an important disparity in the financial literature. Why does financial theory fail to explain the propensity of firms to include a call provision in long-term debt? Over the last 2 decades, significant contributions were made to our theoretical understanding of the call provision in corporate debt issues (Bodie and Taggart 1978; Barnea, Haugen, and Senbet 1980; and Robbins and Schatzberg 1986). These researchers show that callable debt consistently reduces or eliminates the agency cost of debt by allowing management to renegotiate the terms of the debt before maturity. Unfortunately, empirical evidence offers little support for theory. Kish and Livingston (1992) and Güntay, Prabhala, and Unal ( Callable Bonds and Hedging, Working Paper 1-1, University of Maryland) empirically test both the call provision hypothesis and the hypothesis that firms simply hedge future interest-rates (the hedging hypothesis ). These papers found limited support for agency explanations, favoring hedging arguments. Crabbe and Helwege (1994) found the agency hypothesis incapable of predicting the propensity of firms to issue callable debt. I argue that the failure to support the call provision hypothesis is possibly because the hypothesis is flawed. I develop the equivalent security hypothesis. I allow the put 1

12 2 provision to compete with the call provision in various agency settings. I offer theoretical support for the equivalent security hypothesis in several agency settings. I show that a put option exists offering outcomes identical to a call option, in terms of both ex ante expected and ex post actual outcomes. I also describe a certain agency conflict that cannot be resolved with a call provision. The equivalent security hypothesis fails; however, the put provision alone exhibits the ability to resolve the situation. Combined, these findings raise serious questions about previous empirical investigations of the call option and suggest an interesting avenue of future research. Chapter 3 provides an analysis of monthly credit-spread data on noncallable and nonputable investment-grade corporate bonds. Prior examinations of corporate bond yields by Longstaff and Schwartz (1995), Duffee (1998) and Collin-Dufresne, Goldstein and Martin (2003) found a negative relation between corporate bond yield spread changes and changes in Treasury bond yields: yield spreads tighten when interest-rates rise. An initial examination of credit-spreads and interest-rates reveals that credit-spreads are very volatile during the late 1980s and a dramatic credit-spread widening is associated with an increase in rates. After 1990 credit-spreads are much less volatile and it appears that credit-spread changes are positively related to rate changes. We used Duffee s (1998) approach (the same data source from 1985 through March 1995) to examine twelve portfolios of different credit quality and maturity. During the 1985 through 1991 period, the coefficients on the change in interest-rate variable are negative for all twelve portfolios. Further, when the model is estimated on progressively shorter sample periods, the explanatory power of the interest-rate variable increases and the coefficients become much more negative. The negative relation between

13 3 credit-spreads and interest-rate changes is very strong during the initial years of the sample period ( ). In contrast, estimating the relation between credit-spread changes and interest-rate changes for the period from finds very little evidence of a negative relation between credit-spreads and interest-rate changes. There is a positive and significant relation between interest-rate changes and credit-spread changes for AA, A and BBBrated short-maturity portfolios. There is no significant relation between interest-rate changes and spread changes for the medium-maturity portfolios. A negative and significant relation between interest-rate changes and spread changes occurs for AAA-rated short-term portfolios and for all credit quality long-maturity portfolios. Further, the coefficients are very similar across the four different credit quality portfolios. We go on to explore why the relation between credit-spread changes and interest-rate changes is different over the sample period. A simple analysis of the relation between stock returns and interest-rates suggests that the relationship between asset values supporting corporate bonds and interest-rates changed during the sample period. Chapter 3 further examines the relation between interest-rate changes and monthly returns on major stock indices over the sample period. The chapter concludes with an investigation of the causes of credit-spread changes in long-maturity corporate bonds. Some evidence is found that the negative relation between credit-spread changes and interest changes in long-maturity corporate bonds during the latter part of the sample is result of changes in the liquidity value of Treasuries rather than changes in credit quality. Chapter 4 explores the time-varying structure of changes in corporate bond yields and yields on similar Treasury bonds. The difference between corporate bond and

14 4 similar-maturity Treasury bond yields (yield spreads) exhibit considerable variation over time. There are two potential sources of this variation: changes in credit quality and changes in risk or liquidity premiums. Changes in credit quality represent changes in expected cash flows. Risk or liquidity premium changes are changes in the rate at which expected corporate bond cash flows are discounted (expected return premium) that result from changes in the market price of credit risk or changes in the liquidity premium in Treasury bond prices. There is reason to believe that time variation in the expected return premium on corporate bonds is significant. For example, Liu, Longstaff, and Mandell ( The Market Price of Credit Risk: An Empirical Analysis of Interest-rate Swap Spreads, Working Paper 1-2, UCLA) found that most of the time variation in LIBOR swap spreads is due to changes in the liquidity of Treasury bonds rather than changes in default risk. Casual observation of the quality spread suggests time variation in required corporate bond returns. Chapter 4 shows that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. The intuition is straightforward. An increase in the expected return premium reduces bond prices and results in a low holding-period return. However, after an increase in the expected return premium and a low realized holding-period return, the excess return is expected to be higher. In contrast, when excess returns are driven by changes in investor perceptions of default probabilities, excess returns are generally uncorrelated.

15 5 The empirical analysis examines the relation between excess corporate bond returns and lagged excess corporate bond returns over the period. Strong evidence is found that corporate bond excess returns are negatively related to lagged excess returns. Results suggest that much of the volatility in corporate bond excess returns is driven by time-varying risk or liquidity premiums. We also give limited evidence that below investment-grade (junk) bonds excess returns display negative serial correlation. This result is not surprising since innovations in expected default probabilities are probably a more important determinant of junk bond holding-period returns. Results of this analysis have important implications for the equilibrium pricing of credit risk. We argue that the structure of excess return premia offers investors the ability to insulate their holding-period returns from much of the monthly variation in the price of risk. In this framework, earlier research may overstate the true holding-period risk to a bond portfolio.

16 CHAPTER 2 PUTABLE DEBT IN AGENCY THEORY This chapter addresses an important disparity in the financial literature. Why does financial theory fail to explain the propensity of firms to include a call provision in long-term debt? Over the last 2 decades, several papers made significant contributions in our understanding of the call provision in corporate debt issues (Bodie and Taggart 1978; Barnea, Haugen, and Senbet 1980; and Robbins and Schatzberg 1986). Exploiting the seminal work of Jensen and Meckling (1976), these papers consider agency explanations to justify the call option in corporate debt. This call provision hypothesis argues that a firm financed with debt exhibits behavior potentially inconsistent with firm value maximization. Callable debt is consistently shown to reduce or eliminate this agency cost of debt by allowing management to renegotiate the terms of the debt before maturity. The hypothesis also shows that callable debt dominates a strategy of simply issuing short-maturity debt. Unfortunately, empirical evidence offers little support for this hypothesis. Kish and Livingston (1992) and Güntay, Prabhala, and Unal (Working Paper 1-1) empirically tested both the call provision hypothesis and the hypothesis that firms simply hedge future interest-rates (the hedging hypothesis ). They found limited support for agency explanations, favoring hedging arguments. Crabbe and Helwege (1994) found the agency hypothesis incapable of predicting the propensity of firms to issue callable debt. A recent trend in the use of the call option creates a further problem for the call provision hypothesis. Before 1990, over 50% of all new corporate debt included a call 6

17 7 provision, regardless of the initial credit risk. By 1990, a dramatic shift occurred (Figure 2-7). For several years around 1990, only 20% of all new issues incorporated a call provision. For the remainder of the 1990s, investment-grade debt issues maintained this low incidence of including a call provision. During the same period, newly issued junk bonds increased their use of the call provision, returning to a pre-1990 level by This dramatic change between investment-grade and below investment-grade issues remains difficult to explain with any existing hypothesis. I argue that the failure to support the call provision hypothesis is possibly because the hypothesis is flawed. I show that the call provision in corporate debt is not unique in its ability to reduce or eliminate certain agency conflicts. To show this, I develop the equivalent security hypothesis. I allow another debt covenant (the put provision) to compete with the call provision in various agency settings. Results are two-fold. First, I offer theoretical support for the equivalent security hypothesis in several agency settings. I show that a put option exists offering outcomes identical to a call option, in terms of both ex ante expected and ex post actual outcomes. Secondly, I describe a certain agency conflict that cannot be resolved with a call provision. The equivalent security hypothesis fails; however, the put provision alone exhibits the ability to resolve the situation. Combined, these findings raise serious questions about previous empirical investigations of the call option and suggest an interesting avenue of future research. 2.1 Previous Research The seminal work of Jensen and Meckling (1976) pioneered the exploration of the call provision in the context of agency problems. Earlier research sought to explain the high frequency of the call option via divergent interest-rate expectations (Bowlin 1966; Jen and Wert 1967; and Kidwell 1976), divergent risk preferences between bondholders

18 8 and shareholders (Barnea, Haugen, and Senbet 1985), and tax considerations (Boyce and Kalotay 1979). Bodie and Taggart (1978) [BT hereafter] were the first to exploit the agency story, exploring the ability of callable debt to restore the full value of future investment opportunities. In their model, a firm financed partly with debt bypasses some positive NPV projects when the bondholder benefits from reduced risk. Callable debt offers the firm s entrepreneur an opportunity to renegotiate the terms of the debt when favorable information arrives. With callable debt, the debt holder is compensated with an interest-rate consistent with her risk exposure, without compromising the firm s investment incentives. Barnea, Haugen, and Senbet (1980) [BHS hereafter] extend the work of BT, examining future investment opportunities along with modeling asymmetric information and risk-shifting. Both papers show that the inclusion of a call provision resolves the conflict between managers/owners and debt holders. A call provision offers the firm the ability to re-contract debt based on new, favorable information not available at the original debt issuance. These early papers fail to show a clear advantage of callable debt over a short-term debt policy. As constructed, the models rely on issuance costs to generate a separating equilibrium. To address this criticism, Robbins and Schatzberg (1986) found that risk-averse managers prefer callable debt to a short-term debt policy as a signaling mechanism when the value of the firm s investment quality is uncertain. Other papers, notably Flannery (1986), can show that callable debt dominates short-term debt, even absent transaction costs, when considered as a financing option. Kish and Livingston (1992) empirically tested both agency and nonagency hypotheses, examining callable and noncallable bonds issued from They ran

19 9 a series of logit regressions using firm characteristics such as leverage, growth, and book-to-market ratio to predict the presence of a call option in debt issued by the firm. They found mixed support for the call provision hypothesis. Growth firms are more likely to include a call provision. This is consistent with the predictions of BT. The findings of BT could not confirm any of the other agency theories. However, simple interest-rate hedging stories also gain support. The call feature is more prevalent during periods of high interest-rates and for longer maturity bonds. Crabbe and Helwege (1994) found the call provision hypothesis incapable of predicting the propensity of firms to issue callable bonds. Looking at industrial debt issues from 1987 through 1991, they found evidence against the call provision hypothesis. They conclude that the prevailing agency theories are not of first order importance in prompting firms to include a call provision in their debt issues. Güntay, Prabhala, and Unal (Working Paper 1-1) found strong support for the hedging hypothesis; and limited evidence favoring the call provision hypothesis. Put options received relatively little attention in the literature, perhaps consistent with their rare occurrence in debt covenants. No paper has examined the role of the put covenant in the general context of agency theory, or compared the relative merit of the put option versus the call option in resolving agency conflicts. Brick and Palmon (1993) proposed a bond contract that facilitates an alternative refunding policy. This bond contract gives each bondholder a put option as part of the bond covenants. Crabbe and Nikoulis (1997) examined the market for putable debt, looking at the historical features of these bonds. Although the article challenges the pricing of putable debt, it does not compare putable debt with its callable counterpart. Crabbe (1991) examined the advent

20 10 of the event-risk covenant (poison put) in corporate debt in response to the risk-shifting activities during the late 1980s. Cook and Easterwood (1994) examined the impact of the poison put on the outstanding securities of a firm. They conclude that a poison put benefits managers and bondholders, but at the expense of stockholders. Gibson and Singh ( Using Put Warrants to Reduce Corporate Financing Costs, Working Paper 2-1, Cornell University) examined put warrants in a situation with adverse selection costs. This paper is closest in spirit to the present work, but examines put options on equity instead of debt. 2.2 Agency Conflict Models: the Equivalence of the Call and Put Option In this section, I show that a variety of agency conflicts arising from debt-financing are resolved using either a call option or a put option in the debt covenants. I show that either option results in identical ex ante expected outcomes and identical ex post state-dependent outcomes for debt investors. An analogous result holds for the firm. I focus specifically on asymmetric information, future investment opportunities, and risk-shifting. Previous models, such at BT and BHS, have shown that a call option resolves these agency conflicts. I show here that a put option offers equivalent outcomes. I call this result the equivalent security hypothesis. By demonstrating that a specific put option is equivalent in these models, I show that the debate over the dominance of callable debt is incomplete. Essentially, the previous models explain why an embedded option is useful when questions of agency conflict arise. However, the dominance of the call option is not resolved. I consider the case of asymmetric information in a setting not previously explored in the literature. I exploit the model in Flannery (1986), which considered short-term and long-term financing (straight debt) in a 2-period model with asymmetric information. By

21 11 adding a call and a put option as financing opportunities, I derive scenarios where a call or a put option is preferred over other financing alternatives. I also show that equivalent contracts exist using either a call or a put option under some circumstances. With this evidence supporting the equivalent security hypothesis, I then turn to models of future investment opportunities and risk-shifting. In these cases, I extend the work previously completed by BT and BHS, respectively. In each scenario, I show that the equivalent security hypothesis holds. Lastly, I explore a situation where a call option and a put option are not comparable. This setting entails risk-shifting under conditions of asymmetric information. In this case, the equivalent security hypothesis fails, but not in favor of a call option. A put provision is favored Asymmetric Information Flannery s original model is cleverly designed to capture the pure signaling motivation for debt design by maintaining fixed future values for the firm. In the model, Good and Bad firms (described in Section ) enter the market for debt, issuing either short-term or long-term debt. If Good firms cannot successfully signal their true quality to investors, they pool with Bad firms, forced to accept a required rate on their debt that exceeds a fair rate of compensation based on their true risk. I modify the original model in two ways: I eliminate transaction costs from the model I allow firms to include either a call option or a put option in the debt offered As modified, the model offers several interesting insights. First, firms with favorable private information will issue debt including an embedded option. By using either a call option or a put option, Good firms separate in a situation where straight debt alone fails. Second, it is shown that the debt investor receives an equilibrium payout that exceeds the

22 12 market s required payout. The excess payout is the mechanism Good firms use to achieve a separating equilibrium. This proves less costly than suffering under a pooling equilibrium. Lastly, the equilibrium payout to the debt investor is shown to be identical using either a call or a put option. The same holds for the residual payout to the entrepreneur Model setup At time zero, an entrepreneur wishes to proceed with a positive NPV project. The project is indivisible and nontransferable. The project lasts for 2 periods, and all cash flows from the project are received at the end of the second-period. The value of the project, however, is uncertain through time (Figure 2-1). The value follows a binomial process where, during each period, the value of the project increases with probability p or decreases with probability (1-p). At time t=1 and t=2, the firm's value becomes public information. Throughout the project life, the individual firms in the market are impossible to tell apart. However, the market knows that θ% of the firms are Good firms, and (1-θ)% of the firms are Bad firms. Good firms differ from Bad firms in that their up probability, p G, is higher than that for Bad firms, p B. That is, p G > p B. Good firms cannot directly reveal their true type. To avoid pooling, Good firms must find some market mechanism to signal their true quality. Knowledge of θ, p G, and p B is public information. All market participants are risk-neutral wealth maximizers, and the risk-free rate of interest is zero for both periods. The cost of the project exceeds the entrepreneur s wealth, forcing her to borrow an exogenously determined amount D from the investor. The risk assumed by the investor is determined by both the debt maturity and the project value through time. The firm can

23 13 issue short-term debt, long-term debt, or long-term debt including either a call or put option. Short-term debt involves issuing one-period debt, both in the first-period and in the second-period. As constructed, the expected project value always exceeds the outstanding debt at t=1, suggesting that short-term debt at t=0 is default-free. The firm will pay exactly zero interest for this debt. Since the firm is solvent at t=1, I assume that it will reissue debt. The second-period interest-rate depends on the project value at time t=1. If the project value increases during the first-period, the subsequent one-period rate, F R S, is zero. When unfavorable information arrives, the investor charges an appropriate interest-rate, R R S probability of default. Investors charge a coupon rate. Long-term debt (2-period debt) always exhibits some, based on the equilibrium probability of default 1. Finally, the firm can issue callable or putable debt, promising to pay a rate of R C or R P, respectively, in 2 periods. With callable (putable) debt, the firm (investor) may buy (sell) the debt from (back to) the investor (firm) for the face value of the debt, D. If either option is exercised, the firm reissues the debt at a short-term rate consistent with the risk characteristics of the future cash flows. Liquidity is not a concern in this model. It is simple to show that the required rate for 2-period callable debt, R C, is a 2-period rate equivalent to R R S R L. In accepting callable debt, the investor assumes that the firm refrains from exercising the call option if first-period results are poor, and that the firm exercises the call option when first-period results are positive. With these assumptions, the debt exhibits risk characteristics consistent with a short-term debt 1 Both rate and are equivalent to the rates established in Flannery (1986), equations (4) and (5), respectively. R L R R S

24 14 rollover strategy. A rate consistent with this level of risk (a 2-period -equivalent rate) is required. This rate is consistent with actual firm behavior. When first-period results are positive, the firm exercises the call option and reissues the debt at the risk-free rate. Under poor first-period conditions, the firm finds the call option worthless and avoids calling the debt. The putable debt holder needs no assumptions since the option to redeem the debt is under her control. Accordingly, it can be shown that the firm offers a rate, RP, equal to the risk-free rate. With good first-period performance, the debt exhibits no risk. The debt holder is perfectly compensated for the actual risk of the investment. The put option has no value and is not exercised. If, however, the debt becomes risky, the investor exercises the put option, forcing the firm to reissue debt at a rate reflecting R the true risk ( R S ) Equilibrium strategies under asymmetric information Absent embedded options, Flannery found that a pooling equilibrium in short-term debt. All market rates reflect the average risk of the market participants. Good firms suffer, losing value from required market rates on debt that exceed rates consistent with their true risk characteristics. Bad firms benefit, paying a lower rate than they would under a separating equilibrium. Can either a call option or a put option resolve this? As constructed, a call strategy or a put strategy is equivalent to a short-term debt policy. Neither offers Good firms the ability to separate from Bad firms (Table 2-1). The required rates offer no explanation for the use of embedded options to reduce asymmetric information in this context. Robbins and Schatzberg (1986, page 935) discussed this problem: The theory of financial economics has failed to distinguish advantages of R R S

25 15 callable bonds from those of short-term debt. Absent transaction costs, embedded options in debt covenants simply mimic financing options available to the firm. To distinguish either option-based strategy from a short-term strategy, Good firms are forced to change the terms of the offering, diverging from the market s required rates. Any change must also benefit Good firms, allowing them to create a separating equilibrium with a cost lower then their loss in value under a pooling environment. I first show that this is possible with callable debt. I then focus on a solution including a put option. Although the required rate for callable debt is, equilibriums exist where Good firms issue callable debt including a call premium to separate from Bad firms. The call premium discourages Bad firms from mimicking the debt-financing choice of Good firms. Proposition 1. Under asymmetric information with zero transaction costs, a separating equilibrium exists where firms with favorable private information issue callable debt. Firms with poor prospects issue short-term debt, despite revealing 2 2 (1 pb ) M 5 + DR1 ( pb pb ) D their true condition. A call premium, R C =, is pb D included in the contact. If the firm exercises the call option, debt investors are repaid D C = D R C. Proof. See Appendix A. Good firms offer terms that exceed the market s demands. Bad firms avoid callable debt with a call premium 2 because of their higher probability of losing value in the R R S 2 Investors in a separating equilibrium are willing pay upfront for the expected call premium, or (p R C ), in addition to the contract amount D, partially offsetting the cost of signaling to Good firms. Assuming that firms act homogenously within a given type, the lower actual cost will maintain a separating equilibrium. This holds analogously for putable debt. However, as long as firms can issue debt with a face value of D, and also offer the premium, the separating equilibrium will result. Secondary market prices for the debt, however, will exceed the proceeds to the firm.

26 16 first-period. They cannot afford the call premium under good conditions and the short-term rate R R S under poor first-period performance. Given that a solution exists using callable debt, an equivalent strategy using putable debt is easily constructed. Putable debt is offered with the following terms: if the put option is exercised, the firm will pay debt holders D R P ; otherwise, if the debt is held for the full 2 periods, the firm will pay debt holders D. This strategy is equivalent to a callable debt strategy if RC = R P (Table 2-2). Existence, then, is a simple contractual R R S matter of setting R P = hypothesis: 2 1 p ) M + DR ( p ( B 5 1 p B D B p 2 B ) D. This leads to the following Equivalent security hypothesis 1. Conflicts between the debt holder and the firm arising from debt-financing under asymmetric information can be resolved using either a call option or a put option 3. Further, for a given debt contract including a call option, an equivalent contract including a put option can be written, despite shifting the option value from the firm to the investor Discussion This section offers several interesting outcomes concerning callable debt and agency conflicts. First, the call provision hypothesis holds. By showing that callable debt offers a mechanism to avoid the agency conflict arising from debt-financing under asymmetric information, I offer further support for the call provision hypothesis in a model not previously explored. Further, I show callable debt dominates short-term debt when a call premium is included. This offers support for firms issuing callable debt including a call premium. 3 Public information on firm condition is essential for this result. Results under uncertainty may lead to a different solution.

27 17 This section also shows that putable debt (including a put premium) offers the firm an equivalent financing option. Although putable debt shifts the option value to the debt holders, the equilibrium contract outcomes are identical to a callable debt strategy. Using either callable or putable debt, the firm faces the same expected costs ex ante and identical state-dependent residual payoffs ex post. This holds analogously for debt holders. The equivalent security hypothesis is established. This result suggests that the firm is indifferent between using a call option and a put option in the their debt covenants. If asymmetric information drives the firm to include a call option, an equal number of put options should also be observed in debt issues. Figure 2-7 shows this is not the case, with callable debt dominating putable debt significantly each year. Is the model here correct, suggesting that asymmetric information is not pushing firms to include a call option? Or, is asymmetric information important, but the model fails to capture an essential element in the decision? These questions are revisited later in the chapter Future Investment Opportunities When a firm s prospects include future investment opportunities, BT found the benefit of callable debt. Using their model, I show that callable debt or putable debt restores the full future investment incentives of the equity holders, garnering further support for the equivalent security hypothesis. I initially review the findings of BT for callable debt. I then extend the argument, considering putable debt. The putable debt contract maintains incentives consistent with callable debt. The full value of the investment attains with either option. Second, I alter the original model of BT, including asymmetric information regarding possible future projects. If the debt holder is unaware of (some) upcoming opportunities, either contract may include an unforeseen cost to the

28 18 firm. If this cost is high enough, the project may be bypassed, despite any potential benefit to the firm Model setup A firm invests $100 in a 2-period project (Figure 2-2). The condition of the economy is either good or bad in the first-period, with equal probability. If first-period conditions are good, the firm invests an additional $X at the beginning of the second-period, and that investment generates an additional revenue of $15.75 ln(x) for certain at the end of the second-period. Otherwise, first-period conditions are bad; consequently, no additional investment is made. Conditions and final payoffs during the second-period depend on first-period results (Table 2-3). For simplicity, the risk-free rate is 5% in both periods, and all participants are risk-neutral expected wealth maximizers. The firm has several investment choices. The project can be financed with all equity or 50% debt. If limited capital forces the use of debt-financing, the debt issuance options include 2-period (straight) debt and debt including an embedded option (call or put) Straight debt and callable debt-financing With all equity financing, it is simple to show that the firm will invest $15 at the end of the first-period, if conditions are good. Further, the project has an expected net present value of approximately $ For the remainder of this section, I assume that the firm s entrepreneur has limited capital, and partial debt-financing is required. I first consider straight 2-period debt, and then include a call option in the offering. By issuing straight debt, a portion of the future investment opportunity will be bypassed. The increase in firm value from the future investment accrues partly to the debt holders in the form of reduced risk. Unlike the case of all equity financing, the firm will only invest $9 at t=1. Based on the required rate on the debt, the expected residual

29 19 firm value falls to $36.12, a loss of roughly $0.80 due to agency issues. Callable debt resolves this under investment problem, allowing the equity holder to refinance the debt if favorable information arrives at t=1. In equilibrium, the debt holder expects to retain the debt if first-period results are bad, while forced to redeem the debt if the first-period results are good. The mean expected return 4 to the callable debt holder is 0.5[50(1.05) 2 ] + 0.3(25) + 0.2[50(1+r C ) 2 ]. (2-1) Since the risk-neutral investor requires, on average, the risk-free rate, setting Eq. 2-1 equal to 50(1.05) 2 allows us to derive r C. This results in a callable rate r C = 40.3%. This rate is consistent with debt holder expectations. The debt will be called if first-period results are good, but not when first-period results are bad 5. Further, when the debt is called, the firm will reissue debt at the risk-free rate of 5%. This restores the optimal investment at t=1 to $15. This, in turn, guarantees the debt holder repayment in full, consistent with the risk-free rate. From the firm s perspective, the optimal future investment of $15 also restores the full value of the firm under 100% equity financing Putable debt-financing The firms again issues $50 in debt. However, the bond contains a put provision allowing the investor to redeem the debt at t=1. If the option is exercised, the firm must pay the full principal amount plus accrued interest for one period, and then reissue the debt. The stated rate on the debt, r P, must fully reflect all expected losses to the bondholder. The firm s optimal future investment decision depends critically on the 4 This is a modification to BT. I assume that the debt is callable at par plus the risk-free rate. This adjusts the second-period rate on callable debt to reflect the risk of holding debt following poor first-period performance. 5 Indifference attains if first-period results are bad. The debt can be called for $52.50, but new debt will be issued with a coupon rate of 87.5%. Thus, the firm realizes no benefit from a call policy in this state.

30 20 required rate for putable debt, r P. Putable debt in this model is viewed as a full guarantee of principal to the debt holder. The firm expects the debt holder to retain the debt if the first-period is good, while she redeems the debt if first-period results are bad. The mean return to putable the debt holder is 0.5[50(1+r P ) 2 ]+0.3(25)+0.2[50(1+r P )(1.05)]. (2-2) Unlike callable debt, the putable debt investor sets the optimal put policy, considering her expected payoff. The corresponding payoff structure to the investor at t=1 is found in Table 2-4. With business in the first-period good, the debt is risk less, and the debt holder (ex ante) requires the risk-free rate of 5%. For any coupon rate greater than or equal to the risk-free rate, the debt holder does not redeem the debt. I assume, then, that r P =5%. With this rate, the optimal value of the future investment at t=1 is $15, and the expected value of the firm at t=1 is consistent with results from issuing callable debt. However, I must show that r P =5% is also the equilibrium rate with poor first-period performance. Assuming that r P = 5%, the putable debt holder redeems the debt if first-period performance is poor. By redeeming the debt, the investor forces the firm the finance the second-period at the required rate of 87.5%. This is consistent with our expectations. The putable debt holder retains the debt if first-period performance is good, but will redeem the debt is first-period performance is poor. Equivalent security hypothesis 2. Debt-financing can distort future investment opportunities when a portion of the value of the future investment accrues to the debt holder in the form of reduced risk. This appropriation of value from the shareholder to the debt investor is eliminated using either a call option or a put option in the debt covenants. With either debt covenant, the all-equity value of the firm is fully restored. Proof. See Appendix B.

31 Discussion This section confirms the call provision hypothesis and the equivalent security hypothesis. Callable debt with a rate r C = 40.3% restores the full value of the future project to the firm. Putable debt with a putable rate r P = 5% (the risk-free rate) achieves the same end. The equilibrium putable debt contract offers outcomes identical to a callable debt strategy. The agency conflict is resolved using either option contract. The firm is indifferent between using a call option and a put option. Asymmetric information or a future investment opportunity (when explored separately) theoretically results in an equal use of either option in corporate debt covenants. Results also hold in a model including asymmetric information and future investment opportunities. Consider a scenario where first-period results are bad, but the firm (somehow) creates the ability to pursue the identical future investment opportunity. To introduce asymmetric information, the debt investor (for some reason) is unaware of this opportunity, and it is costly for the firm to credibly educate them. Neither callable debt nor putable debt offers a superior solution. Callable debt is called, new investors are educated, and new debt is issued at the risk-free rate. With putable debt, the firm educates the investor. Since the investment retains its risk-free characteristics, none of the debt is redeemed. In either scenario, the investment opportunity remains viable as long as the cost to educate is low enough. If the cost exceeds the benefit of the project, the firm may forego (part of) the project, despite its benefit to the firm Risk-shifting Risk incentives may induce a debt-financed firm to shift away from a high value project (A) to a low value project (B). The value of the firm under project B is lower than the alternative project A (Figure 2-3). Although both projects require the same

32 22 initial outlay, project B is riskier than project A [i.e., σ(b) > σ(a)]. This creates the incentive for the firm to raise debt in the amount of V D (A), claiming that project A will be undertaken. Once debt-financing is secured, the firm shifts to project B. Although the value of the firm falls, by V = V(B) V(A) < 0, the firm s equity increases in value, by S = S(B) S(A) > 0. A transfer of wealth occurs from the debt holder to the firm s equity holder because the value of the debt falls by more than the value of the firm. Without a credible mechanism signaling that project A will be pursued, the debt holder must assume that project B is undertaken. Debt-financing only in the amount of D(B) is made available to the firm. Consequently, the firm s equity holder suffers from the additional capital requirements Solution with callable and putable debt BHS found that a call option can be constructed as a credible mechanism to indicate that project A is pursued. The value of a call option on debt 6 will fall (by C) as the value of the underlying debt diminishes, as in the case of shifting to project B (Figure 2-4). Recall that the value of a call option on debt fully accrues to the firm s shareholder. The shareholder solves the risk-shifting incentive problem by constructing the call option (i.e., setting the strike price) such that any gains from shifting to project B result in an equal or greater offsetting loss in the value of the call option. That is, set the strike price such that C S holds. Putable debt also achieves the same goal. The value of a put option on debt will rise (by V P ) as the value of the underlying debt diminishes (Figure 2-5). Unlike the call option, the value of a put option on debt fully accrues to the debt holder. The risk-shifting incentive problem in this scenario is solved by constructing the 6 This assumes that option pricing follows the Black-Scholes (1973) pricing model.

33 23 put option such that any loss to debt holders as the firm shifts to project B results in an equal or greater gain in the value of the put option. Set the strike price such that P D holds Discussion Clearly, callable debt resolves this class of agency problems, and is often sited as strong theoretical support for the existence of the call option in corporate debt. As shown, however, a put option achieves the same end. Further, a put option provides additional protection that a call option cannot. Consider a scenario where a third project (C) exists, but the debt holder is unaware of the project (asymmetric information). Project C is riskier than project B [i.e., σ(c) > σ(b)], and by shifting to project C, the shareholder gains additional value from risk-shifting. Is the debt holder protected? Under callable debt, if the strike price is set such that C = S assuming only the existence of project B, the answer may be no. Beyond a limit, a loss in debt value cannot correspond to an offsetting decrease in call value (Figure 2-4). The shareholder, once the strike price is set, may have an incentive to undertake a project risky enough such that debt holder wealth is expropriated in her favor. In the limit, the debt holder requires a strike price on the call option of zero. Of course, the debt holder pays nothing for such debt (since it can be called at zero), and the firm is forced to issue new equity. Putable debt avoids the problem of unknown, riskier projects. Figure 2-5 shows that any incremental loss in value of the underlying debt is exactly offset by a corresponding increase in put value. By setting the strike price such that P D for any known, possible shift in risk, the debt holder is fully protected from any incremental shift to unknown riskier projects. The shareholder has nothing to gain from risk-shifting alone.