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... known as the convertible bonds information content puzzle (Datta, Iskandar-Datta, and Raman, 2003), have mainly relied on information asymmetries between managers and market participants in the. .. These figures are similar to those in Datta, Iskandar-Datta, and Raman (2003) and Spies and Affleck-Graves (1995) Panel A of Table reports summary statistics of firm’s characteristics as of the. .. negative abnormal returns In the former case managers will use cash to pay out bondholders, reducing the available resources at their disposal In the latter case managers can eliminate debt (and
Graduate Schoo, E TD F e n * 9 PURDUE UNIVERSITY GRADUATE SCHOOL Thesis Acceptance This is to certify that the thesis prepared By Fernando R. Diaz Entitled Convertible Bonds Under Asymmetric Information and Agency Problems: A Solution to the Convertible Debt Puzzle Complies with University regulations and meets the standards of the Graduate School for originality and quality Doctor of Philosophy For the degree o f _____________________ Final examining committee members David J. Denis Co- . _____________________________________________________ , C h a ir Rodolfo Martell Co-Chair P. Raghavendra Rau John J. McConnell Approved by Major Professor(s): Dav*d J- Denis Approved by Head o f Graduate Program: Jack Barron______________ Date of Graduate Program Head's Approval: 02/19/2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C O N V E R T IB L E D E B T U N D E R A S Y M M E T R IC IN F O R M A T IO N A N D A G E N C Y P R O B LE M S : A S O L U T IO N T O T H E C O N V E R T IB L E D E B T PU ZZLE A Thesis Submitted to the Faculty of Purdue University by Fernando Diaz In Partial Fulfillment of the Requirem ents for the Degree of Doctor of Philosophy M ay 20 0 7 Purdue University W est Lafayette, Indiana r ~ " ' V . . - ' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3278668 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3278668 Copyright 2007 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS The author would like to thank Sonya Lim and John Barron who read early versions of this thesis and made important suggestions to improve it. This work has also benefited from conversations with Sandipan Mullick and M atthew Cain. I am particularly grateful to Jason Abrevaya, Mike Cooper, David Denis, Rodolfo Martell, John McConnell, and Raghu Rau for their valuable comments and feedback. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS P age LIST O F T A B L E S ........................................................................................................................v LIST O F F IG U R E S ................................................................................................................... vi A B S T R A C T .................................................................................................................................vii C H A P T E R 1. Introduction........................................................................................................1 C H A P T E R 2. Literature R eview .............................................................................................7 2.1. Use of Convertible D e b t............................................................................................... 7 2.2. Stock price reactions to announcements of convertible issues.....................11 2.3. Stock price reactions to announcements of redem ption .................................13 2.4. Relation to Prior Literature........................................................................................ 16 C H A P T E R 3. A Non technical overview of the M o d e l.................................................20 C H A P T E R 4. A Bayesian Model of Asymmetric Inform ation.................................... 2 4 4.1. The Basic M o d e l.......................................................................................................... 2 4 4.2. The Model Augmented with Agency P ro b le m s..................................................2 7 C H A P T E R 5. Data description and M eth odology......................................................... 41 C H A P T E R 6. Empirical R esults.......................................................................................... 48 6.1. M arket Reaction at the Issuance D a te ..................................................................48 6.2. Market Reaction at the Redemption D a te ............................................................57 6.3. Relation between the first and second dates of the m odel............................. 66 6.4. Liquidity........................................................................................................................... 70 C H A P T E R 7. Conclusions.................................................................................................... 72 R E F E R E N C E S .........................................................................................................................74 A P P E N D IX ............................................................................................................................... 103 V IT A ............................................................................................................................................112 c Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V LIST O F TABLES Table P age Table 1. Descriptive Statistics............................................................................................. 77 Table 2. M arket Reaction at Issuance Announcement D a y........................................79 Table 3. Relation between CARs at Issuance Announcem ent Day and proxy variables for Agency Problems and Firms’ V a lu e ...................................................80 Table 4. Relation between CARs at Issuance Announcem ent Day, Agency Problems and Insiders’ Ownership..............................................................................83 Table 5. Industry Adjusted Capital Expenditures to Assets and Industry Adjusted q-R atio..................................................................................................................................8 4 Table 6. Regression for Below and Above Sam ple Median Industry Adjusted qRatio...................................................................................................................................... 85 Table 7. M arket Reaction at the Issuance Announcem ent Day versus Market Reactions at the Call Announcement Day for Bonds which Conversion Options is In the M oney.................................................................................................. 86 Table 8. Relation between CA Rs at Call Announcem ent Day and proxy variables for Firms’ T yp e................................................................................................................... 87 Table 9. Relation between CARs at Call Announcem ent Day and proxy variables for Firms’ Type and Agency Problem s.......................................................................89 Table 10. In and Out of the M oney Conversion Option at the Call Announcem ent D a y .........................................................................................................................................93 Table 11 Logistic Regression: Relation between proxy variables for Agency Problems and the Probability of calling In the M oney Convertible Bonds 94 Table 12. Logistic Regression: Relation between M arket Reactions at the Issuance Date and the Probability of calling In the M oney Convertible Bonds. ................................................................................................................................................ 95 Table 13. Relation between Agency Conflicts at the Issuance Announcem ent Day and Frequency of Conversion Forcing Calls. ..................................................96 Table 14. Relation between Agency Conflicts at the Issuance Announcem ent Day and M arket Reactions to Conversion C alls......................................................97 Table 15. Liquidity Analysis...................................................................................................98 Table 16. Joint Distribution of B and y............................................................................... 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST O F FIG U R E S Figure Page Figure 1. Timing of the Model: W ho knows w hat and w h en................................... 100 Figure 2. Values of y and a for which Truthful Revelation holds under the C S 1 contract.............................................................................................................................. 101 Figure 3. Informational Structure of the M o d el............................................................. 102 r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vii ABSTRACT Diaz, Fernando. Ph.D., Purdue University, M ay, 200 7. Convertible Debt Under Asymmetric Information and Agency Costs: A Solution to the Convertible Debt Puzzle. M ajor Professors: David J. Denis and Rodolfo Martell. I develop a model with asymmetric information and agency problems that explains the negative stock price reactions observed when convertible bonds are issued and w hen they are subsequently called. This model constitutes an improvement over previous theories of convertible debt that consider these stock price reactions separately and neglect the possibility of agency conflicts. The empirical analysis supports the model, with firms that have a higher probability of agency conflicts experiencing significantly m ore negative price reactions at the offering announcem ent day. These firms also experience more adverse price reactions when the calling of these bonds is announced. Finally, consistent with the unified model, I docum ent a positive relation between abnormal returns at issuance and the time elapsed between issuance and calling of convertible bonds. f \ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 CHAPTER 1. INTRODUCTION A convertible bond is a corporate debt instrument, usually a junior debenture, which can be exchanged, at the option of the holder, for a specific number of shares of the issuing company's common stock. The amount of equity covered by each bond is determined by the conversion ratio, which is obtained by dividing the face value of the bond by the conversion price. Convertible bonds are usually callable bonds. This means that the issuer has the right to redeem the debt (for its cash value or equity equivalent) at a pre specified price (the call or redemption price) before the redemption date. A large academic literature has explored the reasons for the use of convertible securities, the type of firms that issue convertible securities, and the effects of their issuance on the issuer’s stock price. Even though there seems to be agreement on which types of firms issue convertible securities and on the effects on stock price of the use of such instruments, the underlying factors that explain these effects remain to be identified. Understanding the consequences of the use of convertible debt becomes more important as its relevance in the fixed income security market increases. In 2002, new issues of convertible bonds represented the same proportion of the US corporate bond market as the high yield sector, with an aggregate issuance value close to 15% ($92 billion) of all new corporate issues. Extant research has documented two different effects of these instruments on stock price. First, there is a negative stock price reaction (around 2% ) when ( it is announced that convertible bonds will be issued (Stein, 1992; Kim and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 Stulz, 1992). Second, there is a negative stock market reaction to the announcement of forced conversion of callable securities (Mikkelson, 1981; Oferand Natarajan 1987; Asquith and Mullins, 1991). Regarding the negative market reactions observed when firms announce their intentions to issue convertible debt, the theoretical literature provides no clear prediction about this reaction because of the ambiguous effects of the trade-off between the tax and agency benefits of convertible instruments and the potential for dilution shareholders might experience if the bonds are converted into stock. Explanations for the negative stock market reaction to the announcement of forced conversion of callable securities, known as the “convertible bonds information content puzzle”, have relied mainly on information asymmetries between managers and market participants in the context of signaling models. The puzzle arises from the fact that these negative stock market reactions are inconsistent with the arguments put forward by Ingersoll (1977) and Brennan and Schwartz (1977) in which conversion allows stock holders to capture the value of the option, thus predicting a positive price reaction. I develop and test a model with asymmetric information and agency problems that is capable of explaining the above described phenomena within a unified framework. The development of such theoretical framework constitutes an improvement over existing theories of convertible debt that consider these phenomena separately. In the model, it is assumed that the issuers of convertible bonds -which have empirically been shown to be high growth firms with low ratios of tangible to total assets-, are likely to suffer from informational asymmetries. The informational asymmetry is introduced by assuming that there are two types of firms in the economy, low value and high value firms. In order / to allow for agency conflicts between insiders of the firm and outside investors, it Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 is assumed that there are two types of managers, one that always behave in the interest of current stockholders -good managers-, and one that not only cares about the wealth of the stockholders, but also values private benefits of control bad managers. It is shown that under a set of reasonable investors’ beliefs, the issuance of a convertible bond generates changes in the market valuation of the stock of the issuing company that is related to the market perceptions about firm value and the likelihood of agency problems. Specifically, the model predicts that at the announcement of a convertible debt offering firms more likely to have agency conflicts and less valuable investment opportunities will experience more negative returns. Furthermore, the model predicts that a convertible debt contract will induce an equilibrium in which only firms that suffer from agency problems call their bonds after the realization of bad news about firms’ value. In this way, the model rationalizes the negative market reaction associated with conversion-forcing calls and takes a first step towards the resolution of the convertible debt puzzle. To test the model, I analyze a sample of 340 bonds issued between December, 1986 and March, 2004. For the issuance announcement day, I find strong evidence that the in the cross-section of bond-firm observations, firms more likely to suffer from an agency problem or more likely to be low value firms, experience more negative stock price reactions. In the empirical specifications, the cumulative abnormal returns centered at the issuance announcement day are regressed against common proxies for agency problems: the expense ratio, which exhibits negative and significant coefficients, the sales to asset ratio, which has positive and significant coefficients, and insiders’ ownership, which shows positive, though insignificant coefficients. Furthermore, the specifications also control for the most likely used of the raised Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 funds by including the capital expenditures to assets ratio and its interaction with a proxy variable for agency problems - a dummy variable that distinguishes between firms with high and low growth opportunities, which are proxied by Tobin’s q. I find that convertible issuers that have a history of high levels of capital expenditures and have few growth opportunities suffer significantly more negative stock price reactions upon the issuance announcement of convertible bonds. These results are consistent with the prediction of the model that at the issuance announcement day stockholders of firms more likely to have agency conflicts and/or less valuable investment opportunities will experience more negative impacts on their shares. The analysis of the abnormal returns at the redemption announcement reveals that stock price reactions are consistent with the predictions of the model. First, when firms are sorted by proxies of agency problems, I find a significant difference of 2.35% between good (0.84% ) and bad (-1.51% ) managers when firms call their in-the-money bonds. Second, proxying for firm’s type by the return on equity, I find that low value firms that call their in-themoney bonds experience significantly more negative returns than do high value firms do. Finally, when abnormal returns are sorted on the moneyness of the call embedded in the bonds I find a significant difference of almost 2% between bonds that are out-of-the-money and those that are in-the-money, with the former having a mean abnormal return of 0.78% and the latter o f -1.16%. These findings are consistent with the existence of a Bayesian Separating Equilibrium in which good managers separate from bad managers in low value states of nature. Incorporating agency problems into a model of asymmetric information is essential to developing a comprehensive model. Models based only on asymmetric information can not explain the negative market reactions observed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 at the issuance announcement day. Stein’s (1992) model, for instance, predicts a separating equilibrium in which low value firms have no incentive to issue convertible bonds, and these securities are issued only by firms which are optimistic about the future. Mayers (1998, 2000) argues that convertible bonds are the most efficient way for firms with high growth opportunities to fund a sequence of investments of uncertain timing and value. Also, and more importantly, these models, which neglect the possibility of having agency problems, have not been successful in explaining the negative market reactions associated with the redemption announcement.1 Furthermore, Brick, Palmon, and Patro (2004) find that the cumulative abnormal returns at the redemption announcement day are not related to common measures of asymmetric information. In this sense, the no-agency problems case can be considered a particular case of my model. Specifically, if the probability of having a self serving manager is set to zero, or the value of the private benefits of control are set to zero, then the model predicts no changes in market valuation upon the announcement that bonds will be converted. This situation is consistent with the lack of explanatory power of models that neglect the possibility of agency problems. I contribute to the literature in this area in several ways. First, my model is the first to provide a unified explanation for the stock returns associated to the announcement of a new offering of convertible bonds and to their subsequent calling and conversion. Second, and in accord with the model, I show that these stock responses are more negative for firms with a higher ex-ante likelihood of facing agency problems and having poor growth prospects. Third, and related to the second point, I show that incorporating agency conflicts into a model with 1 An exception is the model by Harris and Raviv (1985), who are able to rationalize the negative market reaction to forced conversion of calls in a pure informational asymmetry framework. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 asymmetric information helps to solve the apparent inconsistency between the predictions of these types of models and the empirical regularities associated with convertible debt financing. This thesis is organized as follows. Chapter 2 presents the literature review and the place of this work in the literature. Chapter 3 provides a non technical summary of the model. Chapter 4 presents the formal theoretical framework. Chapter 5 presents data description and methodology. Chapter 6 presents the empirical results. Chapter 7 concludes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 CHAPTER 2. LITERATURE REVIEW In this chapter, I briefly review the academic literature related to use of convertible securities and their impact on stockholders’ interest in the firm. The current explanations of the effects of the use of these instruments on stock prices - the negative stock price reaction observed at the issuance announcement day and the subsequent negative stock price reaction at the redemption announcement day - are analyzed from the perspective of considering them as two separated and distinct phenomena. I argue that these theories, even when considered as explanations of a single phenomenon, lack power to explain the observed stock price reactions. I also discuss the relation of my model to the existing literature, emphasizing the importance of having a unified theory able to explain the effects of the issuance and conversion of convertible securities. 2.1. Use of Convertible Debt In the presence of a potential risk shifting problem, a levered firm might find it costly to raise funds to finance new investment projects.2 Additional debt might be too expensive or even unavailable given investors’ rational anticipation of a risk shifting problem. Furthermore, in the context of informational asymmetries, a stock issue might also be costly if it is considered bad news by the market 2 Black and Scholes (1973) were the first to note that the shares of a levered firm correspond to a call option written over the value of the firm. A risk shifting problem may arise when the manager of a levered firm, acting on behalf of her current stockholders, faces different investment projects. The convex shape of the payoffs of levered equity provides the manager with the incentives to take excessive risks and therefore, to invest in projects that do not maximize net present value. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 (Myers and Majluf, 1984). Green (1984) argues that convertible debt and warrants can mitigate the incentive to take excessive risks, reversing the convex shape of levered equity and restoring net present value maximizing incentives. In this sense, the rationale for the use of convertible bonds is that they are less sensitive to ex-post risk shifting than common debt. Stein (1992) argues that convertible bonds might be used as an indirect method for moving to a less levered capital structure when adverse selection problems make a stock issue unattractive -i.e., the back door equity motive for the use of convertibles. His model, an adaptation of the model in Myers and Majluf (1984), explains two key features of the issuance of convertible bonds: first, almost all convertible bonds are also callable bonds, which implies that companies can force conversion. Since convertible bonds are ultimately a portfolio of straight debt and an option to convert, it might be in the interest of the holders of these instruments to keep their option alive as long as possible, since if they don’t convert, they receive interest payments on the debt and keep the value of their option. The only way for the issuing company to force investors to exercise their conversion option early is to include a call feature in the convertible debt contract. Second, excessive debt can lead to financial distress. Given that financial distress is costly, a company that is already levered and issues convertible bonds should be signaling to the market that it is optimistic about the future. The outcome of Stein’s model is a separating equilibrium in which low value firms do not have the incentive to issue convertible bonds and, therefore, do not try to mimic high value firms. Since debt holders will convert only when this action is in their own interest, the issuing company must be expecting an increase in its stock price, otherwise, conversion would not take place, leaving the firm with an even larger debt burden to service. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 Stein also documents the results of surveys carried out by Pilcher (1955), Brigham (1966) and Hoffmeister (1977) regarding the reasons firms choose to use convertible securities. In Pilcher (1955), 82% of the surveyed managers answered that the desire to raise common equity on a sort of delayed action basis played the most important role in the decision to issue convertible debt. In Brigham (1966), 73% of the surveyed managers answered that their primary intent in issuing a convertible was to obtain equity financing. Finally, in Hoffmeister (1977), the delayed equity motive emerged again as the single most important. Chakraborty and Yilmaz (2003) investigate the underinvestment problem that arises when insiders have an informational advantage over outsiders regarding the investment opportunity set of their firms. In the spirit of Myers and Majluf (1984) they argue that when firm types are not observable, this will lead to a pooling equilibrium in which securities issued by firms will be competitively priced at their expected value, leading to dilution in the claims of firms that are better than the average firm. Accordingly, managers behaving in the interest of their current stockholders may choose not to invest in positive NPV projects. However, the authors show that when the initial informational asymmetry is solved over time, a callable convertible security solves the adverse selection problem costlessly; i.e., there is no dilution in the claims of existing equity holders and managers invest regardless of their private information, achieving the symmetric information outcome. Furthermore, the bond will be called (and converted by debt holders) after good news about the value of the firm is received. The rationale for the use of convertible debt in this model is that the value of callable convertible bonds is independent of the private information of the manager and, therefore, mitigates the adverse selection problem. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Mayers (1998, 2000) argues that convertible debt is the most cost-effective way for corporations with large growth opportunities to finance a sequence of investments of uncertain timing and value. The logic is the following. When a firm has a sequence of valuable investment opportunities over time, it faces a fundamental trade-off: if it raises the entire amount needed for the whole sequence at once, investors might fear that their money will be misspent in the future, regardless of the profitability of available investment opportunities. Accordingly, they might demand terms that compensate them for bearing this risk, which in turn increase the cost of external funds for the firm. On the other hand, if the firm raised money only when it was needed, the issuing costs for the entire sequence would be too high. Mayers claims that convertible bonds are ideal for funding sequential investments in that they minimize the sum of overinvestment and issue costs. Bondholders have the choice of converting their bonds into equity in the future, if profitable investment opportunities do materialize. This leaves the funds inside the company as equity, which can be used to finance growth. On the contrary, if investment opportunities appear to be unprofitable when the time comes to make them, bondholders will not convert (or be forced to convert), and they will redeem their bonds instead. This mechanism ensures that future investment options are made only if profitable, thus controlling the over-investment problem. Mayers analyzes nearly 300 callable convertible debt issues between 1971 and 1990. He finds that convertible issuers have higher R&D to sales ratios, higher market to book ratios, and more volatile cash flows than their industry counterparts. These characteristics are typical of firms with high growth options and likely to face informational asymmetries. Korkeamaki and Moore (2004) find strong empirical support for the Mayers’ Sequential Financing motive for convertible debt financing and provide a satisfactory explanation to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 differences observed in the level of call protections offered by different firms. In particular, they find evidence that firms design the call provisions on convertible bonds according to their need for short term financing flexibility. Moreover, they find that the length and strength of the call protections are inversely related to the capital expenditures of the firms in the years following the bond issuance. In summary, the use of convertible securities has been rationalized in the academic literature as a solution to a risk shifting or asset substitution problem (Green, 1984), as a way to modify the capital structure of the firm in the context of strong informational asymmetries (Stein, 1992), as a solution to an underinvestment problem, given the low sensitivity of the value of these instruments to the private information of firm’s insiders (Chakraborty and Yilmaz, 2003), and as the most efficient way to finance a sequence of investments of uncertain timing and value (Mayers, 1998, 2000). 2.2. Stock price reactions to announcements of convertible issues The theoretical literature predicts ambiguous effects of convertible debt issuances on stock prices, since there is a trade-off between the tax and agency benefits of debt and the dilution effect that occurs when the bonds are converted into stock. The empirical literature, however, consistently finds negative abnormal returns to the announcement of convertible bond issuances, which suggests that the dilution effect outweighs the debt benefits of these instruments.3 Dann and Mikkelson (1984), Mikkelson and Partch (1986) and Eckbo (1986) are among the first to document a significant negative abnormal return at the 3 Note that, given informational asymmetries, an adverse selection problem might also be part of the explanation for dilution. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 initial announcement of a convertible debt offering. Stein (1992) summarizes some results from the empirical literature documenting market reactions between -1.3% and -2.3%. Kim and Stulz (1992) report an average abnormal return of -1.7% for a sample of 280 convertible bond issues between 1965 and 1987. Some studies document not only a negative reaction to the announcement of convertible bond issuances, but also report heterogeneity in the market reactions in the cross section of firms. Dann and Mikkelson (1984) find that the abnormal returns are less negative when the new convertible bonds have an important impact on the increase in leverage compared to those that have a small impact on firm leverage. More recently, Arshanapalli, Fabozzi, Switzer, and Gosselin (2004) find that abnormal returns at the announcement of convertible bond issuances are related to firm specific characteristics, including market value, price to book ratio, and the size of the issue. Specifically, they find that bigger convertible bond issues, which have a larger impact on firm’s leverage, lead to more negative abnormal returns on the announcement days. Their evidence supports the conjecture that that the dilution effects of future conversion outweigh the tax benefits of short term increase in leverage. They also find that price to book is negatively related to abnormal returns, meaning that growth firms are more likely to be negatively affected by the announcement of convertible debt issue. Finally, they find that larger firms experience less negative abnormal returns. This can be interpreted as a smaller impact on the firm’s capital structure when conversion occurs, but it is also consistent with the view that smaller informational asymmetries are associated with less negative market reactions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 2.3. Stock price reactions to announcements of redemption I Mikkelson (1981), Ofer and Natarajan (1987), and Asquith and Mullins (1991) are among the first papers to document significant adverse stock price reactions to calling announcements. This phenomenon is inconsistent with the fact that conversion transfers the value of the option from bondholders to stockholders (Ingersoll, 1977; Brennan and Schwartz, 1977). The efforts to explain the negative market reaction observed when firms announce their intentions to redeem their in-the-money convertible securities, which has become to be known as the “convertible bonds information content puzzle” (Datta, Iskandar-Datta, and Raman, 2003), have mainly relied on information asymmetries between managers and market participants in the context of signaling models. Most notably, Harris and Raviv (1985) develop a model that rationalizes the negative market reaction to conversion forcing calls. They show that there exists an equilibrium in which managers truthfully signal their private information by calling their convertibles if they receive unfavorable information. In this sense, their model predicts that managers that receive favorable information will tend to delay conversion. The authors argue that firms that receive favorable information have lower costs of delaying conversion since for such firms it is more likely that conversion will take place anyway. Even though Harris and Raviv’s model rationalizes the negative abnormal stock return associated with call announcements, it has two important limitations. First, and with respect to the logic for delaying conversion, it is not clear that bondholders will have the incentives to voluntarily convert.4 In fact, there are situations in which voluntary conversion will not take place until the last possible chance bondholders have to convert. Taking the extreme case in 4 Stein (1992) argues that a call feature is the only way companies have to force bondholders to exercise their conversion option early. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 which the firm does not pay dividends, a bond holder that decides to wait until next period to convert will get the interest payments (if any) corresponding to the current period and benefits from the value of the option. Since the stock does not pay dividends, she bears no costs from not converting. Accordingly, she has no incentives to convert today, being optimal to wait until next period. Since the same argument applies every period, bond holders will convert at their last chance to do so. If the company pay dividends, bond holders’ optimal strategy is to wait one period to convert if the expected interest payments for the next period are higher that the expected dividend payment during that period. If the dividend payments are uncertain and the interest payments are not, the same will be true under risk neutrality. If risk aversion is assumed, an expected interest payment lower than the expected dividend payment might make bondholders unwilling to convert their debt, as long as dividend payments are sufficiently more risky than interest payments. With respect to the delayed conversion issue, Harris and Raviv predict that managers that receive favorable information will tend to delay conversion. Ingersoll (1976), Mikkelson (1981) and Constantinides and Grundy (1987) find that it is not always the case that firms call convertibles as soon as the conversion value exceeds the call price. However, Asquith (1995) demonstrates that there is no call delay phenomenon related to convertible bonds. For a sample of 199 bonds, issued between January 1, 1980 and December 31, 1982, Asquith finds that most bonds, given their call protections, are called as soon as possible. Furthermore, the median call delay for all convertible bonds is less than four months, and if firms require a safety premium to call their bonds - i.e., they wait for the conversion value to exceed the call price by 20% to safely assure it will still exceed the call price at the end of the normal 30 day call notice period - the median delay period is less than one month. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 Chakraborty and Yilmaz (2003) investigate the reason for the use of convertible bonds in the context of a model with asymmetric information, where insiders of the firm are better informed about firm value than outside investors. Assuming that the asymmetry of information is resolved over time, they show that the value of convertible bonds is independent of manager’s private information and that, consequently, such instruments can mitigate the adverse selection problem and achieve the symmetric information outcome. In their model, the convertibility and callability features of convertible debt play a central role. Convertibility allows bondholders to choose which kind of security (debt or equity) they will end up holding after information about firm type is disclosed, and callability allows managers to force conversion. In the model developed by Chakraborty and Yilmaz there is no dilution in the claims of the existing equity holders, so managers invest regardless of their private information. Furthermore, the bond will be called (and converted by debt holders) only after good news about the firm is received. It is therefore difficult to reconcile this prediction with the negative price reactions observed when firms announce their intentions to redeem their convertible instruments. Some studies find that the negative stock price reaction to a forced conversion is only a transitory effect caused by selling pressure rather than a negative signaling effect. Campbell, Ederington and Vankudre (1991) challenge the results in Ofer and Natarajan (1987), arguing that their sample is biased. Correcting for this bias they find that post-call cumulative abnormal returns are not significantly negative. Mazzeo and Moore (1992), Byrd and Moore (1996) and Ederington and Goh (2001) find that the negative stock price reaction to a forced conversion is only a transitory effect consistent with the price pressure hypothesis. Furthermore, and also against the signaling hypothesis, Brick, et al. (2004) find that cumulative abnormal returns (CARs) at the redemption Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 announcement day are not related to common measures of asymmetric information. 2.4. Relation to Prior Literature The negative market reaction observed when firms announce their intention to issue convertible securities and the subsequent negative reaction to the early redemption of these instruments have been treated in the existing literature as two distinct phenomena. Furthermore, even though the convertible bonds puzzle refers only to the observed price reaction associated with redemption announcements, when considered together, the above described phenomena is perhaps a more challenging puzzle for proponents of market efficiency and investor rationality. Arshanapalli, et al. (2004) examine a zero investment strategy aimed at taking advantage of price variations that follow convertible debt issues. Through simulations, they show that a strategy that takes a long position in the firm’s convertibles bonds and a short position in the firms’ stock yields significant profits up to 36 months after the issuance date. According to the authors, the profitability of such strategy constitutes evidence against market efficiency. Furthermore, since the median time elapsed between issuance and redemption of convertible bonds is close to 3 years, it is likely that the strategy considered by the authors covers both event dates for a large proportion of the bonds they consider.5 This situation emphasizes the importance of considering both phenomena under a unified analysis. If a unified theoretical framework is able to explain the market reactions at the issuance announcement day and at the 5 For my sample of bonds, the median time elapsed between issuance announcement and redemption announcement for bonds called in-the-money is 3.3 years. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 redemption announcement day in the context of rational investors, then it is not easy to claim that the profitability of such strategy constitute evidence against market efficiency. Instead, it might be the case that these profits are just a risk reward to investors for holding these instruments in their portfolios. When considered as an isolated phenomenon, the negative market reaction associated with the issuance announcement of convertible securities does not constitute a problematic issue for market efficiency. Given the potential for dilution of existing shareholders’ interest in the firm, the negative market reaction can be justified as a rational anticipation of such effect by investors. However, it can be argued that rationality should not leave enough room to the existence of negative abnormal returns around the redemption announcement of the bonds, given the price impact induced by the issuance announcement. First, and given that convertible issuers tend to be strongly levered firms with high degrees of informational asymmetries and profitable growth opportunities, inveslois shouldnol be willing to provide funds if they do not believe that the distinctive features of a convertible debt contract can properly mitigate the risk shifting (Green, 1984), overinvestment (Mayers, 1998), or adverse selection (Stein, 1992) problems. Since firms’ characteristics are observable when the decision to provide funds is taken, it should be the case that the market valuation of firms’ debt and equity includes all relevant risks, including the odds that the issue will be converted in the future. Furthermore, given that the protection period is stated in the bond indenture, together with the fact that firms generally call convertible debt as soon as they can (Asquith, 1995), then it must be the case that investors can also anticipate the most likely date of a call announcement. If the announcement then systematically generates a surprise in the market, leading to a correction in stock prices, then there is a case against rationality and market efficiency. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 The above discussion highlights the shortcomings that the existing literature faces when attempting to separately explain the price reactions observed at the issuance announcement and redemption announcement of convertible bonds. However, when agency problems are included, together with informational asymmetries in the context of a unified theoretical framework that covers both event dates, the puzzle disappears. The model that I propose is able to explain the negative market reactions associated with the issuance and early redemption of convertible bonds in the context of rational investors and market efficiency. To the best of my knowledge, this is the first attempt to explain both phenomena under a unified theoretical framework. Rationality follows from the participation constraints of bondholders who are willing to provide the required funds for investment only if they are compensated for the additional risk induced by not being able to observe manager and firm types. Managers are utility maximizers and base their actions (issuance and redemption of their convertible instruments) on standard preferences. Market efficiency holds because firm securities are priced by market participants at their expected value, conditional on the information set available to them at every point in time. Since the model attempts to explain both the market reactions at the issuance announcement day and at the redemption announcement day, it also offers an explanation for the relative size of the stock price changes observed at these events. In general, the market reaction observed at the former date is considerable larger than the one observed at the latter date. The informational structure of the model rationalizes this situation. This is a unique feature of the model that cannot be obtained by considering these phenomena separately. The model developed in this work also highlights the importance of including agency problems in a theoretical framework aimed at explaining the wealth Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 consequences of the use of convertible instruments. As previously discussed, in models based solely on informational asymmetries, it is difficult to reconcile the negative market reaction observed when managers take certain actions if these actions are always intended at benefiting shareholders. In addition, since the model covers both event dates and relates the market reactions to the probability and extent of agency problems, it provides a risk based explanation for the apparent arbitrage opportunities derived from the strategies proposed in Arshanapalli, et al. (2004). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 CHAPTER 3. A NON TECHNICAL O VERVIEW OF THE MODEL The basic assumptions of the model are as follows. In line with previous literature, there are three points in time. At date 0 firms issue convertible debt to fund a new project and investors decide whether to include these instruments in their portfolios. At this point, there are two sources of uncertainty about the firm. First, firms can be low value or high value, depending on the value of their assets in place and on the profitability of their investment opportunities. Assets in place and the new investment combined generate a random cash flow, whose probability density function depends on firm type. The manager privately knows the type of her firm. Investors do not know the type of a firm, but the distribution of firm types is common knowledge. Second, it is assumed that there are two types of managers. Type A managers always behave in favor of their current stockholders. Type B managers care for the wealth of their current stockholders, but they also care about their own private benefits of control. Accordingly, the latter type of managers face a trade-off when they evaluate corporate actions that hurt stockholders but favor themselves. A key assumption of the model is that debt restricts managerial access to private benefits and, consequently, type B managers dislike debt. Managers privately know their type and the distribution of manager types is assumed to be common knowledge. In the model, it is assumed that the decision to issue convertible debt has already been made and is therefore exogenous. Consequently, I do not attempt to explain the choice of instrument made by firms. I assume a pecking order that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 leads certain type of firms to choose convertibles over other types of instruments. The existing literature provides sound arguments for certain type of firms choosing convertible debt financing, particularly in the context of informational asymmetries between insiders and outsiders. Chakraborty and Yilmaz (2003) show that the value of callable convertible bonds is independent of the private information of the manager and, therefore, mitigates the adverse selection problem. Stein (1992) develops a model in which convertible bonds serve as a signal to the market about the quality of the firm. In his model, managers of high value firms will not issue equity because their stock would be underpriced, and thus they prefer to issue straight debt. As long as financial distress is costly, managers of low value firms will find it impossible to mimic this behavior and, consequently, will issue equity. Managers of medium value firms will issue convertibles only if they are optimistic about the future. The logic of Stein’s model provides a rationale for high growth, levered firms to rely on convertible bonds for their financing needs. Good managers, behaving in favor of their current stockholders, issue convertible securities to fund their investment projects. Since neither managers’ types nor firms’ types are observable at this point in time, type B managers can hide behind type A managers and also issue convertible bonds. Note that if agency problems are not introduced in the model, managers of firms who are not optimistic about the future would not issue convertible securities, making it difficult to explain the documented negative market reaction at the issuance announcement day. Managers’ possibility of hiding both their own type and their firm type creates the required tension in the model to give rise to a signaling game in which investors have an incentive to try to infer manager type from their observable actions, and type B managers may have an incentive to mislead Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 investors. All this makes market reactions to convertible bond issuances particularly informative about investor priors. At the beginning of date 1, firm type is announced and investors update their beliefs and valuation of firms. Manager type is still private information, and firms are priced at their expected value, but at this time expectations are only taken over manager types. At the end of date 1 managers decide whether to redeem their debt. This last decision provides the market with a signal about the type of manager in charge. Finally, at date 2, cash flows are realized and distributed. The model predicts that at the issuance announcement day (date 0) the stock price reaction will be more negative for firms that are more likely to experience agency conflicts and that have less valuable investment opportunities. The model also predicts that at the redemption announcement day (date 1), firms in low value states should exhibit more negative returns than do high value firms when they call their in-the-money convertibles. This result, a direct consequence of the signaling mechanism and its corresponding separating equilibrium, derives from the fact that only managers that are more concerned about the consumption of private perquisites than the wealth of their stockholders call their firms’ convertibles after the market receives bad news about the firms’ values. These two predictions constitute the basis for the empirical verification of the model. Another implication of the agency story behind the model, based on a free cash flow type of story, is that firms that call out-of-the money bonds should experience positive abnormal returns while those that call in-the-money ones should experience negative abnormal returns. In the former case managers will use cash to pay out bondholders, reducing the available resources at their disposal. In the latter case managers can eliminate debt (and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 thus get rid of the disciplinary constraints it imposes) without paying its value in cash. Even though this is an indirect implication of the model, it is empirically tested as further support for the agency conflict story upon which the theoretical foundation of the model rests. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 CHAPTER 4. A BAYESIAN MODEL OF ASYM METRIC INFORMATION 4.1. The Basic Model I start from the basic setup in Chakraborty and Yilmaz (2003) which closely follows the structure in Myers and Majluf (1984). For tractability and ease of comparison between my results and theirs, I adopt their notation and basic definitions.6 Consider an economy with two types of firms. Let 0 denote the type of firm, with 9 e {61 , 62}- Each firm in the economy has an asset in place - A, and an investment opportunity which requires an investment I = 1. There is type dependent uncertainty about the value of the assets in place, in the sense that the cash flows associated with them are dependent on the firms’ type. Let A\Gj stand for the expected value of the cash flows from the assets in place given Q,. 6 = The manager privately knows 0 and always behaves in favor of current stockholders. All agents are risk neutral and the risk free rate of the economy is zero. These last two assumptions imply no discounting. The assets in place and the new investment combined generate a random cash flow X, with cumulative density function G ( ) dependent on firms’ types: (4.1) P r [ jr < x ] = (7 (x |0 ) 6 I consider the simplest case in Chakraborty and Yilmaz (2003), in which the optimality of convertible debt is analyzed under perfect resolution of the information asymmetries between managers and market participants. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 The project cash flows for type Dominate those for type (4.2) 6 6 = 0 2 firms First Order Stochastically = 0i firms. Then, G ( x |02) < G ( x |0.) Given risk neutrality, First Order Stochastic Dominance is sufficient to characterize the difference in risk between the two types of firms. Regardless of the type of firm, projects have positive net present value.7 Then, (4.3) E [X \d i] - A i >\ It will be assumed that it is not possible for firms in the economy to issue riskless debt; i.e., it will be assumed that G (1\6i) > 0. The value of a type / firm V, - is given by the expected value of its cash flows: (4.4) V , = E [ X \ 0 t] From (4.2), V2 > Vi. economy and let (p(x) e 0 Let 0 be the set of admissible securities in the be the payoff from security o o CO * T*> o> CO T— d d CO *“ o o o d CM hhCO O CM _ S § « O o o o o IP § CO iq o o CO ho CM o> CM d o d CO CM o> CO hd CO Table 8, continued. s CO m CM 5? CO o o h. O TJ $ g" O o CO 2- CM CO d © o> CO O d d CM h- o CM CO T- CO O O CM CM C O O O O CM TCM d d C O C M h- o o s T- 0> o> CM _ § 2 O CO CM CO 00 CO O o: uj o q: < o (X O) c 0> < D o> a> a if) > CM o o o> o o o o o o> C M o> o o o o o 0 3) Z o o o d 5 5 on Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 Table 9. Relation between CARs at Call Announcement Day and proxy variables for Firms’ Type and Agency Problems This table presents results from different specifications of CARs as dependent variable on proxy variables for firms’ types, for the probability of agency conflicts and for the degree of informational asymmetries. Panel A presents weighted least squares regression, where the weights correspond to the relative redemption ratio, defined as the ratio of the redemption amount of the convertible bond to the corresponding firm’s long term debt. Columns (1) and (2) of Panel B presents weighted least squares regressions, where the weights correspond to the relative redemption ratio, while columns (3) and (4) presents the results of un-weighted ordinary least squares. Panel C presents the results of un-weighted ordinary least squares estimated separately for firms above and below, respectively, of the sample median relative redemption ratio. Panel D presents the results of un-weighted ordinary least squares. The dependent variable is CARs, computed at the call announcement day, using Market Adjusted Returns. The equally weighted CRSP index is used as the market benchmark. (-1,0) corresponds to a two day window, with day 0 being the event day. (-1.+1) corresponds to a three day window centered at the event day. The independent variables are Tobin’s q, defined as the product of the price at the third month of the corresponding quarter and the number of common shares outstanding, plus total assets, minus the book value of common equity, divided by total assets, the ratio of capital expenditures to assets, the expense ratio, defined as selling, general, and administrative expenses over total sales, the ratio of sales to assets, and a dummy variable for the return on common equity -R O E - , defined as income before extraordinary items divided by common equity. The dummy variable takes a value of one for firms which ROE is above its industry average, and zero otherwise. The spell length, defined as the time elapsed between the issuance announcement day and the redemption announcement day, and firms’ leverage, defined as long term debt to total assets, are included as controls. In Panel D, the explanatory variables are interacted with the relative redemption ratio, which is also included as a control All explanatory variables are measured at the quarter ending immediately before the call announcement day. The capital expenditures to assets ratio, the expense ratio, the sales to assets ratio, leverage, and Tobin’s q are industry adjusted at the 4 digit level SIC codes, p-values are shown below parameters' estimates. Panel A 1 intercept ROE Spell Length 2 3 4 5 6 (-1.0) (-1.+1) (-1.0) (-1.+ 1) (-1.0) (-1,+1) -0.1006 -0.1307 -0.0104 -0.0199 -0.1014 -0.1084 (0.0001) (0.0001) (0.2904) (0.0337) (0.0007) (0.0001) 0.0579 0.0638 0.0767 0.0681 (0.0001) (0.0001) (0.0002) (0.0004) 0.00003 0.00005 0.00002 0.00003 (0.0001) (0.0001) (0.1105) (0.0552) capex/assets exp. ratio sales to assets 0.3910 0.3729 0.1475 0.1425 (0.0435) (0.0396) (0.4179) (0.406) -0.0006 -0.0002 0.0005 0.0009 (0.9043) (0.9707) (0.9012) (0.8218) 0.0309 -0.0119 0.0452 0.0045 (0.6210) (0.8386) (0.4243) (0.9327) 0.0013 0.0008 0.0019 0.0015 leverage 0.0042 (0.1183) (0.0263) (0.7590) (0.8284) (0.6057) (0.6656) Tobin's q -0.0002 -0.0002 -0.0031 -0.0041 -0.0056 -0.0064 (0.6515) (0.5725) (0.5618) (0.4003) (0.2463) (0.1607) 91 91 62 62 62 62 5.7 N 0.0059 F value 12.96 19.96 2.1 3.94 4.24 p-value 0.0001 0.0001 0.0785 0.0039 0.0009 0.0001 R2 0.3762 0.1581 0.2604 0.3545 0.4249 0.4814 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 9, continued. Panel B WLS- Relative Redemption Size 1 Un-weighted OLS 2 3 (-1.0) (-1.+1) (-1.0) (-1.+1) -0.1014 -0.1084 -0.0380 -0.0682 (0.0007) (0.0001) (0.0944) (0.0025) 0.0767 0.0681 0.0247 0.02619 (0.0002) (0.0004) (0.1879) (0.1461) 0.00002 0.00003 0.00001 0.0002 (0.1105) (0.0552) (0.1876) (0.0097) capex/assets 0.1475 0.1425 -0.0703 -0.0341 (0.4179) (0.406) (0.7544) (0.8743) exp. ratio 0.0005 0.0009 0.00132 -0.0007 (0.9012) (0.8218) (0.6887) (0.9818) sales to assets 0.0452 0.0045 0.0345 0.0251 (0.4243) (0.9327) (0.4602) (0.5751) leverage 0.0019 0.0015 0.0005 0.0012 (0.6057) (0.6656) (0.5930) (0.1752) -0.0056 -0.0064 -0.00133 -0.0026 (0.2463) (0.1607) (0.4492) (0.1322) intercept ROE Spell Length Tobin's q 4 N 62 62 63 63 F value 4.24 5.7 0.55 1.43 p-value 0.0009 0.0001 0.7906 0.2117 R2 0.3545 0.4249 0.0657 0.1541 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 9, continued. Panel C Below median Relative Above median Relative Redemption Redemption 1 2 3 4 (-1.0) (-1.+1) (-1.0) (-1.+1) 0.0100 -0.0345 -0.08654 -0.0725 (0.6759) (0.2143) (0.0922) (0.1191) ROE -0.0221 -0.0101 0.0660 0.0587 (0.3173) (0.6854) (0.0757) (0.0817) Spell Length 0.00001 0.00002 0.00001 0.00001 (0.5188) (0.0427) (0.6388) (0.7229) capex/assets 0.0504 0.06104 -0.3856 -0.3937 (0.8014) (0.7905) (0.5145) (0.4654) exp. ratio -0.0015 -0.0058 -0.00655 0.0087 (0.7985) (0.3787) (0.7266) (0.6094) 0.0461 0.05336 0.0400 0.0156 (0.3064) (0.3020) (0.7395) (0.8863) -0.0003 0.0006 0.0117 -0.01588 (0.7181) (0.4571) (0.7577) (0.6466) 0.0001 -0.00156 -0.014 -0.0107 (0.9293) (0.3437) (0.4744) (0.5324) intercept sales to assets leverage Tobin's q N 33 33 29 29 F value 0.42 1.32 1.00 0.64 p-value 0.8781 0.2841 0.4610 0.7156 R2 0.1061 0.2692 0.2493 0.1766 ( Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 9, continued. Panel D 1 intercept ROE*Rel.Redemp Spell Length*Rel.Redemp (capex/assets) * Rel.Redemp 2 3 4 (-1.0) (-1.+1) (-1.0) (-1.+1) 0.0008 -0.0091 0.0085 -0.00338 (0.9381) (0.4047) (0.1621) (0.5857) 0.0935 0.0831 0.0666 0.0635 (0.0021) (0.0073) (0.0015) (0.0032) 0.00003 0.00001 0.00003 0.00003 (0.2594) (0.2061) (0.0514) (0.0324) 0.0032 -0.1390 0.00747 0.0124 (0.9920) (0.6981) exp. ratio*Rel.Redemp -0.0013 0.0024 (0.9286) (0.8735) sales to assets*Rel.Redemp 0.1073 0.0487 (0.3315) (0.6690) leverage*Rel.Redemp 0.0054 -0.0018 (0.8422) (0.9444) (0.2800) (0.0841) Tobin's q *Rel.Redemp -0.0201 -0.0242 -0.0005 -0.00121 (0.1530) (0.0931) (0.8082) (0.5871) -0.1274 -0.1222 -0.11709 -0.1226 (0.0071) (0.0117) (0.0002) (0.0001) Rel. Redemption N 62 62 91 91 F value 1.82 1.50 3.87 4.58 p-value 0.0946 0.1806 0.0033 0.0010 R2 0.2151 0.1843 0.1856 0.2123 AIC -357.85 -354.27 -547.68 -542.41 BIC -352.85 -349.27 -544.84 -539.58 F value for H° 0.58 0.34 p-value 0.6330 0.7971 H° corresponds to the hypothesis that the coefficients of (capex/assets) * Rel.Redemp, exp. ratio*Rel.Redemp, and sales to assets*Rel.Redemp are all zero. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 Table 10. In and Out of the Money Conversion Option at the Call Announcement Day. This table presents results for market reactions at the redemption announcement day for convertible bonds divided in two groups according to the status of their conversion option at the even date. Panel A reports CARs computed using Market Adjusted Returns, with the equally weighted CRSP index used as the market benchmark. (-1,0) corresponds to a two day window, with day 0 being the event day. (-1 ,+1) corresponds to a three day window centered at the event day. The Kruskal-Wallis test and the Wilcoxon Two Sample Test are shown in Panel B. The symbols $,*,**, and *** denote statistical significance at the 0.10, 0.05, 0.01 and 0.001 levels, respectively, using a 1-tail test. Panel A Out of the Money N= 100 In the Money Patell Z tstat Mean CAR Patell Z tstat N = 112 Mean CAR (-1,0) 0.57% 1.572$ 1.348$ (-1.0) -0.14% -0.637 -0.328 (-1.+1) 0.78% 1.662* 1.495$ (-1.+ 1) -1.16% -2.590** -2.160* Panel B Kruskal-Wallis Test and Test for Equality of Means between groups. Wilcoxon 2 Sample Test Kruskal-Wallis Test Normal Approx p value (1 tail) x2 P value (-1,0) 1.099 0.1359 1.2102 0.2713 (-1.+ 1) 2.5972 0.0047 6.7511 0.0094 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 Table 11 Logistic Regression: Relation between proxy variables for Agency Problems and the Probability of calling In the Money Convertible Bonds. This table presents results from a weighted logistic regression. The logistic model computes the probability that the bonds are called for redemption when their conversion options are in the money. Weights correspond to the ratio of the offering amount for each bond to the value of the corresponding firm’s common equity. Panel A presents the analysis of the maximum likelihood estimates. The independent variables are the ratio of capital expenditure to total assets, the expense ratio, defined as selling, general, and administrative expenses over total sales, and the asset utilization ratio, defines as sales to total assets ratio. All independent variables are measured at the issuance announcement day and adjusted according to their industry averages, where industry is defined by the 4 digit SIC code. Column (1) presents the estimated coefficients for each variable. The p-value of the Wald Chi-Squared individual significance test is presented below the coefficient estimates. Column (2) presents the Odds Ratio Point Estimates for each of the slopes of the logistic regression. The limits of the 95% Wald Confidence Intervals are presented in squared brackets below point estimates. Panel B presents the Hosmer and Lemeshow Goodness-of-Fit Test. The null hypothesis is that there is no difference between the observed and predicted values of the response variable. Panel C presents Maximum Likelihood Tests for the null hypothesis that all slopes are zero. Panel A 1 2 Odds Ratio Point coefficient Estimate intercept -0.1048 capex/assets 1.8756 6.525 (0.0001) [4.917 8.658] expense ratio 0.0123 1.012 (0.0001) [1.009 1.016] (0.0001) sales to assets 0.039 1.04 (0.3317) [0.961 1.125] N 127 in the money / out of the money 6 4 /6 3 Panel B Hosmer and Lemeshow Goodness-of-Fit Test Hosmer & Lemeshow Statisti.c( x2) 6.7048 p-value 0.5688 Panel C Joint Significance Tests LR Test Score Test Wald Test Statistic 234.4541 234.3010 233.2290 p-value 0.0001 0.0001 0.0001 r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 Table 12. Logistic Regression: Relation between Market Reactions at the Issuance Date and the Probability of calling In the Money Convertible Bonds. This table presents results from a weighted logistic regression. The logistic model computes the probability that the bonds are called for redemption when their conversion options are in the money. Weights correspond to the ratio of the offering amount for each bond to the value of the corresponding firm's common equity. Panel A presents the analysis of the maximum likelihood estimates. The independent variables are the cumulative abnormal returns for the (-1, 0) and (-1 ,+1) windows, centered at the issuance announcement day and computed using Market Adjusted Returns. The equally weighted CRSP index is used as the market benchmark. Columns (1) and (3) present the estimated coefficients for each window. The p-values of the Wald Chi-Squared individual significance tests are presented below the coefficient estimates. Columns (2) and (4) present the Odds Ratio Point Estimates for each of the slopes of the logistic regression. The limits of the 95% Wald Confidence Intervals are presented in squared brackets below point estimates. Panel B presents the Hosmer and Lemeshow Goodness-of-Fit Test. The null hypothesis is that there is no difference between the observed and predicted values of the response variable. Panel A 1 2 coefficient Point Estimate intercept -0.1274 (-1.0) -1.5716 0.208 (0.0001) [0.164 0.262] 4 3 Odds Ratio Odds Ratio coefficient Point Estimate -0.123 (0.0001) (0.0001) (-1.+1) -0.961 0.383 (0.0001) [0.293 0.500] N 193 193 in the money / out of the money 9 8 /9 5 9 8 /9 5 Panel B Hosmer and Lemeshow Goodness-of-Fit Test Hosmer & Lemeshow Statistic.fx2) p-value 12.6793 8.8594 0.1234 0.3543 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 Table 13. Relation between Agency Conflicts at the Issuance Announcement Day and Frequency of Conversion Forcing Calls. This table presents results for frequency of conversion forcing calls for convertible bonds divided in two groups according to the likelihood of having agency problems at the issuance announcement day. In Panel A bond firm observations are sorted according to the expense ratio, defined as selling, general, and administrative expenses over total sales, measured as the issuance announcement day. Firms in the bottom (top) quartile are classified as firms with a low (high) probability of having agency problems. In Panel B bond firm observations are sorted according to the asset utilization ratio, defined as sales to total assets, measured as the issuance announcement day. Firms in the bottom (top) quartile are classified as firms with a high (low) probability of having agency problems. A Wilcoxon Two Sample Test for the differences in means between the two groups is presented. Panel A: Expense Ratio Low Agency High Agency Wilcoxon Two- Problems Problems Sample Test Frequency 45.71% 66.66% N 35 36 Z p-value 1.76 0.0783 Panel B: Sales to Assets Low Agency High Agency Wilcoxon Two- Problems Problems Sample Test Frequency 38.29% 57.44% N 47 47 Z p-value 1.84 0.0652 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 Table 14. Relation between Agency Conflicts at the Issuance Announcement Day and Market Reactions to Conversion Calls. This table presents results for market reactions at the redemption announcement day for convertible bonds divided in two groups according to the likelihood of having agency problems at the issuance announcement day. In Panel A bond firm observations are sorted according to the expense ratio, defined as selling, general, and administrative expenses over total sales, measured as the issuance announcement day. Firms in the bottom (top) quartile are classified as firms with a low (high) probability of having agency problems. In Panel B bond firm observations are sorted according to the asset utilization ratio, defined as sales to total assets, measured as the issuance announcement day. Firms in the bottom (top) quartile are classified as firms with a high (low) probability of having agency problems. CARs are computed using market adjusted returns. The equally weighted CRSP index is used as the market benchmark. (-1,0) corresponds to a two day window, with day 0 being the event day. (-1.+1) corresponds to a three day window centered at the event day. A Wilcoxon Two Sample Test for the differences in means between the two groups is also shown. The symbols $,*,**, and *** denote statistical significance at the 0.10, 0.05, 0.01 and 0.001 levels, respectively, using a 1-tail test. Panel A: Expense Ratio Low Agency High Agency Wilcoxon Two-Sample Problems Problems Test Z p-value (-1.0) 0.87% -0.71% 1.7871 0.0785 (-1 .-1 ) 0.84% -1.51% 2.1132 0.0346 N 33 34 Panel B: Sales to Assets Low Agency High Agency Wilcoxon Two-Sample Problems Problems Test Z p-value (-1.0) 0.50% -0.33% 0.113 0.91 (-1.+1) -0.38% -1.16% 0.0888 0.9293 N 45 45 ( Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 Table 15. Liquidity Analysis. This table presents results for weighted and un-weighted OLS regressions. The dependent variables are the cumulative abnormal returns for the (-1, 0) and (-1 ,+1) windows, centered at the issuance announcement day. CARs are computed using Market Adjusted Returns. The equally weighted CRSP index is used as the market benchmark. The independent variable is industry liquidity, where industry is defined at the two digit level SIC code. In Panel A, liquidity is measured at the event date. In Panel B, liquidity is measured at the event month. Weights correspond to the reciprocal of the variance of the cumulative abnormal returns, p-values are shown below parameters' estimates. Panel A: Liquidity at Redemption Panel B: Liquidity at Redemption Announcement Day Announcement Month 1 2 Weighted 3 4 Un-weighted 5 6 Weighted 7 8 Un-weighted (-1,0) (-1.+1) (-1,0) (-1.+1) (-1,0) (-1,+1) (-1,0) (-1.+1) -0.0101 -0.0320 -0.0191 -0.0406 -0.0289 -0.0447 -0.0338 -0.0507 (0.7202) (0.2670) (0.5785) (0.2573) (0.4084) (0.2105) (0.3909) (0.2086) 0.0010 0.0024 0.0020 0.0029 0.0035 0.0037 0.0035 0.0040 (0.7180) (0.4069) (0.5701) (0.4145) (0.3986) (0.2961) (0.3775) (0.3224) N 41 41 41 41 38 38 38 38 F value 0.13 0.7 0.33 0.68 0.73 1.12 0.8 1.01 p-value 0.7180 0.4090 0.5701 0.4145 0.3986 0.2961 0.3775 0.3224 Ra 0.0034 0.0175 0.0083 0.0171 0.0199 0.0303 0.0217 0.0272 intercept liquidity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 Table 16. Joint Distribution of 6 and YThis table presents the joint distribution of 9 and y assuming that they are Bernoulli independent random variables. e Y 9i e2 Yl pA p(1-A) Yh (1-p)A (1-p)(1-A) c Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 Nature reveals firms’ types. t=0 Manager Market Some managers call and reveal their type t= 1 t= 2 Knows his type of firm, 0, and his own Knows 0 and his own Type.- Type. Can call. Project cash flows are realized and distributed. Doesn’t know 0 At the beginning of t =1 learns firms’ types. and competitively values the securities issued by the firms. Knows the distribution of managers and firms types. At the end of t =1 learns managers’ types. Can convert. Figure 1. Timing of the Model: Who knows what and when. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 0.5 1 alpha Figure 2. Values of y and or for which Truthful Revelation holds under the C S 1 contract. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 Nature Chooses Firms Type High Value Firm Type A manager calls Low Value Firm Type B manager calls The market reacts and price the securities of the firm based on the probability of observing each type of manager. Type B manager calls Type A manager does not call For this node there is no event data. Type B managers reveal their type and the market values its securities accordingly, Figure 3. Informational Structure of the Model Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D IX f I \ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 APPENDIX Proof o f Proposition 2. Case 1 (0 = d2) Let’s assume that at time t = 1 nature reveals 6 = 92 and that the manager of the firm does not call the bond. If bondholders convert, they will get a of the value of the firm. Since bondholders cannot infer what kind of manager is in charge of the firm in this case, they base their actions upon the unconditional value of the firm. It follows that the payoffs to bondholders from converting and not converting are given by: (1.1) Bondholders' Payoff from Converting = a (p (V 2- + p ) V 2^ (1.2) Bondholders' Payoff from Not - Converting = D2(F ) In the spirit of the work of Stein (1992), I assume that there are no incentives for bondholders to voluntarily convert when the nature reveals the high payoff state. Therefore, it must be the case that: (1.3) D1( F ) > a ( p ( r J- B ) + ( l - p ) V 2) = a ( r 1- p B ) ( Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 Let’s assume now that at time t = 1 nature reveals 9 = 62 and the manager of the firm does call the bond. The payoff to bondholders from converting is again given by (1.1); however, their payoff from not converting is now k, the call price. In order for bondholders to convert, it must be the case that: (1.4) a ( V 2 - PB ) > k Case 2 ( 9 = 9i) Let’s assume that at time t = 1 nature reveals 9 = 61 and the manager of the firm does not call the bond. Given {SB}, investors infer that a type A manager is in control of the firm. The expected payoffs to bondholders from their different conversion decisions are given by: (1.5) Bondholders' Payoff from Converting =aV x (1.6) Bondholders' Payoff from Not - Converting = D, ( F ) In this case, bondholders will not want to convert if they are not forced to do so, since the low cash flows state of nature was revealed. Then, (1.7) D x{ F ) > a V x Suppose now that at time t = 1 nature reveals 9 = 9i and the manager of the firm calls the bond. In this case, bondholders infer that a type B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 manager is in control of the firm and their payoffs from converting and not converting are given by: (1.8) Bondholders' Payoff from Converting = a (V, - B ) (1.9) Bondholders' Payoff from Not - Converting = k Bondholders will be forced to convert as long as the value from converting is higher than the call price k. Accordingly, for bondholders to convert, the following restriction must hold: (1.10) a ( V j - B ) > k The restrictions arising from case 1 and case 2 can be summarized as: (1.11) D 2( F ) > a ( V 2 - p B ) > c c ( V l - p B ) > a ( V l - B ) > k The first inequality in (1.11) follows directly from (1.3). The second inequality is a consequence of the Stochastic Dominance assumption about firms’ types. The third inequality derives from the fact that p, the probability of having a manager of type /W6, must be less than one.26 The last inequality follows from (1.10). Proof of Proposition 3. 26 p < 1 a p B < a B o -a p B > -a B aV} - a p B > aVl - a B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 Case 1 (9 = 9i) Let’s consider first the set of beliefs corresponding to decision faced by a type A manager. If he calls, given that 6 6 = 61 and the = Q1 and {SB}, the market will infer he is of type B; if he doesn’t call, investors will infer he is of type A. So, the payoffs from the decision of whether to call or not, given the market beliefs and the revealed state of nature 9 = 6 X, are: (1-12) U \ , ^ = r ( l - a ) ( r , - B ) 0-13) U A^ _ allt,t = r ( v , - D , ( F ) ) A type A manager will have incentives not to call as long as: (1-14) = r(V, - D , ( F ) ) > -B) It follows that (1.14) will hold if and only if: (1.15 ) a * D^ - B Vt - B Equation (1.15) will hold for a variety of values of Di(F), B, and Vi. Similarly, if 6=9-) and a type B manager calls, the market will recognize him as a type B manager and bondholders will convert. If he tries to mimic a type A Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 manager by not converting, the market will infer he is an A type of manager, and bondholders will not convert.27 Therefore; (1.17) U ‘ N ot-C a ll ~= r ( y , - D , ( F ) ) Accordingly, type B managers will call if and only if: (1.18) U B{'Calling > ^ U u B,N ot-C alling a y +1 - 2 y > y ( a V 1- D l ( F ) ) B Case 2 (6= 62) Consider now the equilibrium when G = 9 2 and investors believe that both types of manager will call. In this case, given {SB}, the market does not obtain any further information about managers’ types from their calling decisions. Remember also that when G = G2, bondholders will convert only when forced to do so. The question here is whether either type of manager has incentives to deviate from the proposed equilibrium by not calling. Let’s consider first a type A manager. Whether he calls or not, the market assigns him a probability p of being of type B. The payoffs for a type A manager from calling and not calling are given, respectively, by: 0-19) U “c ~ , = r < ! - a ) [ p { y 2- B ) + ( i - p ) V 2'] Calling ( 27 Note that he does not get 6, since bondholders don’t convert. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 (1.20) U AN^ Camng= r {p(V2- B - D 1{F ) ) + { \ - p ) ( V 2--D2(F))) Type A managers will have incentives to call whenever: d -21) > U AH^ a U v o A ( F ) > aV2- a p B The above condition holds directly from equation (1.11). Therefore, A type managers do not have incentives to deviate, and they call. By the same reasoning, the payoffs for a type B manager from calling and not calling are given, respectively, by: (1.22) U , c,m^ r ( l - a ) [ p ( V 1 - B ) + ( l - p ) V 2] + ( l - r ) B (1.23) = y [ p ( V 2- B - D , (F ))+ (1 - p)(V2 - D2(F ))] A type B manager will call as long as the payoff from calling are higher than the payoffs from not calling. It is easy to show that: (1 -24) u ’ c ^ > £/v * O r A (*■) > roc (v2- p B ) + B ( r - 1) Given that 0 < y < 1 and B(y-1) < 0, condition (1.24) holds directly from (1.3). Then, from (1.21) and (1.24) no manager type has incentives to deviate. r Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 Proof of Proposition 4 Given the equilibrium characterized in Proposition 1, the expected payoff to bondholders at time t = 0 is given by: E [Bondholders' Payoff] = /I (a (F, - Z?)) + (l - y?)Z), (.F)J + (1 -X)[p( cc {V2- B ) ) + ( \ - p ) a V 2] Simplifying (1.25): (1.26) ^[Bondholders' Payoff] = XpaV,+XDl ( F ) ( \ - p ) + aV2 [ l - X \ - p a B Bondholder will be willing to provide funds as long as their expected payoff is greater or equal to 1, the amount invested. Relative Size o f Market Reactions at the Issuance and Conversion Announcement Dates with a Continuum of Firms and Manager Types. The analysis can be easily extended to the case when both the type of firm and the type of manager are assumed to be normally distributed continuous random variables rather than discrete random variables. Let’s assume that: ( Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 (1.27) 6 ~ N ( p g,og) (1.28) y ~ N ( j u y,crr ) It will again be assumed that V = 9 + y. Consequently, the higher the value of 9, the higher the value of the firm, and the lower the value of y. the higher the agency problems, and the lower the value of the firm. For the market reaction at t = 0, the unconditional variance of V is given by: (1.29) Var[v] = a 2 g + a 2 - 2p aga y where At the beginning of time t = 1, the market forms its expectations regarding firms’ values based on a new piece of information, the firm’s types. Accordingly, (1.30) E [ v \ e ] = e + E [ y \ e ] and (1.31) Var[V\0] = E \ y 2 \ e \ - E 2[V\G] A standard result of the bivariate normal distribution establishes that: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 111 (1.32) E [ r \ e ) = Mr + p — [ 6 - V e ) ae Since I am mainly concerned with the second moment of the distribution of cash flows, it will be assumed that the means of both 0 and y are zero. In this case, equation (1.32) can be written as: (1.33) E [ y \ e ] = p ^ e ae Using (1.30) and (1.33) in (1.31), it is easy to show that: (1.34) Var[V\e] = a 2 r - p 2a 2 r The market reaction at time t = 0 will be stronger that the one at t = 1 as long as: (1.35) Var[v] = a 2e + a 2- 2 p o gcry > Var[V \ 6\ = a 2- p 2a 2 Or, (1.36) a ] - 2p aga r + p 2a 2 = (a g - p a r f > 0 which is always true. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VITA Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 VITA Fernando Diaz was born in Santiago, Chile, on September 30th, 1968. He obtained his B.S. in Economics in 1995 from Universidad Catolica de Chile. He obtained his M.A. in Economics in 1997 from the same University. In 1998, he was awarded with the Fundacion Andes Scholarship for graduate studies in the United Kingdom. In 1999 he obtained his M.S. in Financial Economics from the London School of Economics. He joined the Ph.D. program at Purdue University in 2003 and obtained his Ph.D. in Finance in 2007. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [...]... rather than a negative signaling effect Campbell, Ederington and Vankudre (1991) challenge the results in Ofer and Natarajan (1987), arguing that their sample is biased Correcting for this bias they find that post-call cumulative abnormal returns are not significantly negative Mazzeo and Moore (1992), Byrd and Moore (1996) and Ederington and Goh (2001) find that the negative stock price reaction to. .. is assumed that there are two types of managers, one that always behave in the interest of current stockholders -good managers-, and one that not only cares about the wealth of the stockholders, but also values private benefits of control bad managers It is shown that under a set of reasonable investors’ beliefs, the issuance of a convertible bond generates changes in the market valuation of the stock... at the issuance announcement day and at the redemption announcement day, it also offers an explanation for the relative size of the stock price changes observed at these events In general, the market reaction observed at the former date is considerable larger than the one observed at the latter date The informational structure of the model rationalizes this situation This is a unique feature of the. .. based solely on informational asymmetries, it is difficult to reconcile the negative market reaction observed when managers take certain actions if these actions are always intended at benefiting shareholders In addition, since the model covers both event dates and relates the market reactions to the probability and extent of agency problems, it provides a risk based explanation for the apparent arbitrage... to convertible bond issuances particularly informative about investor priors At the beginning of date 1, firm type is announced and investors update their beliefs and valuation of firms Manager type is still private information, and firms are priced at their expected value, but at this time expectations are only taken over manager types At the end of date 1 managers decide whether to redeem their debt. .. manager and firm types Managers are utility maximizers and base their actions (issuance and redemption of their convertible instruments) on standard preferences Market efficiency holds because firm securities are priced by market participants at their expected value, conditional on the information set available to them at every point in time Since the model attempts to explain both the market reactions at... efforts to explain the negative market reaction observed when firms announce their intentions to redeem their in -the- money convertible securities, which has become to be known as the convertible bonds information content puzzle (Datta, Iskandar-Datta, and Raman, 2003), have mainly relied on information asymmetries between managers and market participants in the context of signaling models Most notably,... requires an investment I = 1 There is type dependent uncertainty about the value of the assets in place, in the sense that the cash flows associated with them are dependent on the firms’ type Let A\ Gj stand for the expected value of the cash flows from the assets in place given Q, 6 = The manager privately knows 0 and always behaves in favor of current stockholders All agents are risk neutral and the risk... control Accordingly, the latter type of managers face a trade-off when they evaluate corporate actions that hurt stockholders but favor themselves A key assumption of the model is that debt restricts managerial access to private benefits and, consequently, type B managers dislike debt Managers privately know their type and the distribution of manager types is assumed to be common knowledge In the model,... observed at the issuance announcement and redemption announcement of convertible bonds However, when agency problems are included, together with informational asymmetries in the context of a unified theoretical framework that covers both event dates, the puzzle disappears The model that I propose is able to explain the negative market reactions associated with the issuance and early redemption of convertible