CONVERTIBLE DEBT

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Convertible Debt under Asymmetric Information and Agency Problems: A Solution to the Convertible Debt Puzzle

Fernando Díaz* Rodolfo Martell** Gabriel G. Ramírez*** March 2008

Abstract We develop a model with asymmetric information and agency problems that is able to explain simultaneously three empirical regularities associated with the issuance and conversion of convertible bonds. First, the model predicts that the negative stock price reactions observed when convertible bonds are issued are related to agency conflicts between firm management and stockholders, and to the type of firm that is issuing convertible debt. Second, the negative returns observed when bonds are subsequently called are explained in an equilibrium in which only ”bad” managers call their in-the-money convertibles in low value states of nature. Third, the model explains the less negative returns seen at the redemption announcement day (compared to those observed at the issuance announcement day). We also provide empirical evidence in support of the model propositions. In short, we find that firms with a higher probability of agency conflicts exhibit significantly more negative stock price reactions at the offering announcement day and are more likely to force conversion of their in-the-money convertible bonds. Finally, we also find that firms that call out-of-the-money convertibles do not experience negative returns at the redemption announcement day.
* Assistant professor of finance, Facultad de Ciencias Económicas y Empresariales, Universidad de los Andes. ** Assistant professor of finance, Krannert School of Management, Purdue University, and Barclays Global Investors. *** Professor of finance, Coles College of Business, Kennesaw State University. We thank Jason Abrevaya, John Barron, Matthew Cain, Mike Cooper, David Denis, Sonya Lim, John McConnell, Sandipan Mullick, and Raghu Rau for comments and feedback. All errors are ours. Address correspondence to [email protected].

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Introduction Convertible bonds are increasingly becoming a popular source of financing in

the U.S. and around the world. In 2002, new issues of convertible bonds represented the same proportion of the U.S. corporate bond market as the high yield sector, with an aggregate issuance value close to 15% ($92 billion) of all new corporate issues. Academic interest in convertible securities has focused on their use, the type of firms that issue them, and the effects of their issuance on firm value. In particular, extant research documents two different effects of these instruments on firm value: a negative stock price reaction when issuance of convertible bonds is announced and a negative stock market reaction to the announcement of the call for convertibles. Except for Nyborg (1995), asymmetric information models of convertible debt are not able to explain this symmetry of stock price reactions and thus this phenomenon is called the “convertible bonds information content puzzle.” Furthermore, as concluded by Brick, Palmon, and Patro (2007) information asymmetry can not be the only explanation for this puzzle. They also test the price pressure hypothesis and reach similar conclusion that the convertible puzzle is still unresolved. In this paper, we provide a more general and flexible model for convertible debt, one that incorporates asymmetric information and agency problems and empirically test its predictions. More specifically, we show that under a set of reasonable beliefs, the offering of a convertible bond generates changes in the market valuation of the stock of the issuing company that are related to market perceptions of firm value as well as to the likelihood and extend of agency problems. In particular, the model predicts that at the announcement of a convertible debt offering, firms more likely to have agency conflicts and face less valuable investment opportunities will experience more negative returns. This is because in the presence of agency problems, bondholders require a higher stake of the shares of the company (i.e., the conversion premium) to provide funds. This higher share of the value of the company compensates them for the likelihood of agency

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problems and causes more negative stock returns when convertibles are issued. The model also predicts that when management forces conversion of convertible bonds, there will be larger losses in value for firms with higher ex-ante measures of agency problems, particularly when they turn to be low value firms. In our model, the decision of a manger to call conveys information about her type allowing a convertible debt contract to induce an equilibrium in which only firms that suffer from agency problems convert after the realization of a negative state of the world. We find support for the predictions of the model. In particular, we find strong evidence that the variability in the cross section of stock price reactions at the issuance announcement day is related to prior beliefs of investors regarding the probability and size of agency conflicts between firm management and stockholders, and to the type of firm that is issuing convertible debt (i.e., low or high value firm). In our analysis of abnormal returns at the call announcement, we consider the moneyness of the call embedded in the bonds. The assumption is that managers convert in-the-money bonds to obtain “back door” equity as argued by Stein (1992). When convertible bonds are in-themoney, firms with low probability of agency problems experience a 3-day cumulative abnormal return (CAR) of 0.84% while firms with high probability of agency problems exhibit a 3-day CAR of -1.51% . 1 These percentages are statistically different from each other at conventional significance levels. Though, our model does not have specific predictions for forced conversions of out-of-the-money convertibles, it is interesting to note that we find a significant difference of almost 2% between called 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 of -1.16%. 2 We contribute to the literature in the following ways. First, we develop a model that depicts the dynamics of information asymmetry and agency problems likely to exist

A bond is considered “in-the-money” when the value of converting the bond into equity is higher than the value of redeeming it for cash. 2 Datta, Iskandar-Datta and Raman (2003) indeed find that firms that force conversion of in-the-money convertible bonds underperform their peers by a median of 64% over the five years after the conversion.

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in convertible bonds and thus provide an explanation for the symmetry of stock returns at the announcement of a new offering of convertible bonds and their subsequent calling and conversion. Second, we show that stock price reactions are directly related to the exante likelihood of agency problems and firm value. Third, we show that incorporating agency conflicts to a model of asymmetric information helps solve the apparent inconsistency between the predictions of previous models and empirical regularities. Finally, we provide a flexible model that is able to incorporate two competing reasons for issuing convertible and subsequent forced conversion: (1) overvalued low quality firms have an incentive to eliminate debt and (2) entrenched managers have an incentive to eliminate debt in order to estinguish the disciplinary effects of debt. The remainder of this paper is organized as follows. Section 2 presents institutional framework for convertible issuance, conversion and the existence of the convertible bond information content puzzle. In section 3 we provide a non technical summary of the model. Section 4 presents the formal theoretical framework. Section 5 presents empirical implications and estimation results. Section 6 concludes the paper.

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Convertible debt issuance and conversion A convertible bond is a corporate debt instrument, usually a junior debenture that

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 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 body of literature has explored the reasons for the use of convertible securities, the type of firms that issue them, and the effects of their issuance on firm value. Even though there seems to be agreement on which types of firms issue convertible securities and on

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the stock price effects at announcement of the use of convertibles and their calls, the underlying factors that explain these effects remain to be identified. Extant research documents two different effects of convertibles on firm value. First, there is an average negative stock price reaction (around 2%) at the announcement of a convertible bond issuance (Stein, 1992; Kim and Stulz, 1992). 3 Second, there is an average negative stock market reaction to the announcement of a forced conversion of callable convertibles (Mikkelson, 1981; Ofer and Natarajan, 1987; Asquith and Mullins, 1991). 4 This is the so-called convertible bonds puzzle. 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) where conversion allows stock holders to capture the value of the option, thus predicting a positive price reaction. While signaling models based on information asymmetries between managers and market participants are able to explain either the first or the second negative stock price reaction separately, they are not able to explain the symmetry of the stock price reaction. An exception is Nyborg (1995)’s model in which conversation (“delayed equity) always lead to a drop in share price, condition that allows the existence of an equilibrium that supports the empirically observed symmetry of average negative stock price. In his model, forced conversions signal even worse prospectus than originally anticipated at the time convertibles were issued which explains why a forced conversion results in a negative stock price reaction. This should result in forced conversion being associated with poor performing firms and thus a bad signal. However, there appears to be at least three empirical issues that seem at odds with this model: (1) an increasingly growing percentage of convertible issues are callable, (2) a majority of the firms calling

Dann and Mikkelson (1984), Mikkelson and Partch (1986) and Eckbo (1986) were among the first to document a significant negative abnormal return at the 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. 4 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. 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.

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convertible bonds are not low performing firms as it would be implied by the model, and (3) it takes on average of about three years for a convertible issue to be called, a long enough period for information about firm’s quality to be revealed prior to the call. Thus, a richer model of convertible debt that better explains these stylized facts is warranted. Incorporating agency problems to a model of asymmetric information is essential to developing a comprehensive model consistent with the empirical literature. Models based on asymmetric information only have limited explanatory power over the negative market reactions observed at the issuance and at the forced conversion. In some cases, the predictions from these models are inconsistent with empirical facts that previous research has documented. For instance, Mayers (1998) 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. It is difficult to reconcile this proposition with the observed negative stock price reactions of issuers when they announce their intention to issue convertibles. Another example is Stein’s (1992) model, which predicts a separating equilibrium in which low value firms have no incentive to issue convertible bonds, and thus these securities are issued only by firms which are optimistic about the future. Other models presented by Harris and Raviv (1985) and Nyborg (1995) propose that firms should delay the conversion of their outstanding convertibles rather than forcing conversion at the earliest opportunity. Asquith (1995) finds that there is no call delay phenomenon related to convertible bonds. Further, Brick, Palmon, and Patro (2007) find that convertible bond issuers’ cumulative abnormal returns (CARs) at the call announcement day are not related to common measures of asymmetric information. This evidence, together with the fact that convertibles are not called late, cast some doubts on models that rely exclusively on informational asymmetries to explain the empirical regularities associated with convertible bonds. 5
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It should be noted that our model achieves the no-agency problems case by setting the value of the private benefits of control and/or the probability of agency problems equal to zero. In this case, the model predicts that there should be no market reactions at the time firms announce their intention to redeem their debt early. This is consistent with the lack of explanatory power of proxies for informational asymmetries in CAR regressions reported by Brick et.al. (2004). In our model, when informational asymmetries are resolved over time, agency conflicts are required to

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Summary of the model The basic assumptions of the model are as follows. 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: firm type and manager type). The manager privately knows her type and the type of her firm. Investors do not know the manager’s type or the type of firm, but the distribution of firm and manager types is common knowledge. 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 combine to generate a random cash flow, whose probability density function depends on firm type. Type A managers always behave in favor of their current stockholders. Type B managers in addition to caring for the wealth of their current stockholders value and exploit private benefits of control. Accordingly, the latter type of managers face a tradeoff 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. In our model, the decision to issue convertible debt has already been made and is exogenous. 6 Good managers, behaving in favor of their current stockholders, issue
generate price corrections at the issuance announcement day.
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We assume the decision to issue convertible debt as exogenous and do not attempt to explain the choice of instrument made by firms. We assume a pecking order that 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.

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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 mimic type A managers and issue convertible bonds. 7 The possibility of managers 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 investors. Therefore, market reactions to convertible bond issuances are 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 or not to redeem their debt. This 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), low value firms should exhibit more negative returns than high value firms when they call their in-the-money convertibles. This result 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 convertibles after the firm has been shown to be of the low value type. These two predictions constitute the basis for the empirical verification of the model. Another implication of the agency story behind the model 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
Note that without agency problems in the model, managers of firms who are not optimistic about the future would not issue convertible securities, making it impossible to explain the documented negative market reaction at the issuance announcement day.
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managers will use cash to pay out bondholders, reducing the available resources at their disposal. In the latter case managers can eliminate debt (and 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, we test it as further support for the agency conflict story upon which the theoretical foundation of the model rests.

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A Bayesian Model of Asymmetric Information The Basic Model We start following the basic setup in Chakraborty and Yilmaz (2003) and in

Myers and Majluf (1984). For tractability, we adopt the notation and basic definitions of the former. 8 Consider an economy with two types of firms. Let θ denote the type of firm, with θ є {θ1,θ2}. Each firm in the economy has an asset in place – Ai - 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 firm type. Let Ai|θi stand for the expected value of the cash flows from the assets in place given θ = θi. The manager privately knows θ 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 combine to generate a random cash flow X, with cumulative density function G(ּ) dependent on firm type: (4.1)
Pr [X ≤ x ] = G ( x | θ )

The project cash flows for firms type θ = θ2 first order stochastically dominate those for type θ = θ1 firms. Given risk neutrality, first order stochastic dominance is sufficient to characterize the difference in risk between the two types of firms. Then, (4.2)
G ( x | θ 2 ) ≤ G ( x | θ1 )

8 We 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.

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Regardless of firm type, projects have positive expected net present value, i.e., E[X|θi] -Ai > 1. 9 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|θ1) > 0. The value of a type i firm – Vi - is given by the expected value of its cash flows: (4.3)
Vi = E [X | θ i ]

From (4.2), V2 > V1. Let Φ be the set of admissible securities in the economy and let φ(x) є Φ be the payoff from security φ when cash flows are x. Admissible securities are assumed to be non decreasing in x and satisfy limited liability. Accordingly, E[φ(x)|θ2] ≥ E[φ(x)|θ1] and 0 ≤ φ(x) ≤ x. The set of admissible securities includes equity, debt and convertible securities. Equity share is denoted by α є [0,1]. The expected value of the cash flows from equity, given θ = θi , is given by αVi. Debt is assumed to be a bond with face value F. The bond is a standard debt contract with payoffs given by Di(F) =E [min(X,F)|θi]. Since securities are assumed to be non decreasing in x, it follows that D2(F) > D1(F). A callable convertible security is specified in the model by a tuple (F, α, k, T1, T2), where T1 is the maturity date of the call option and the convertibility option, T2 is the maturity of the bond, k is the call or redemption price, α is the percentage share of the firm the bondholders will get, if they decide to convert into common stock, and F denotes the face value of the bond. There are three dates in the model. At date 0, the manager privately knows θ and makes her investment and financing decisions. The market is uninformed about θ and prices securities at their expected value. At date 1, nature reveals firm type, managers are allowed to redeem the debt, and bond holders can choose to convert their bonds into common equity. At date 2, cash flows are realized and distributed. 10 Using this framework, Chakraborty and Yilmaz (2003) show that there exists a callable convertible
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Note that date 2 is included for completeness. There is no new information flowing into the market between the end of period t =1 and t = 2. Clearly, bond holders are allowed to convert on time t =1 or at any later date. However, since there is no discounting and there is no information innovation after t = 1, there is no reason for bondholders to wait until t = 2. Alternatively, t = 2 can be thought as occurring immediately after t =1.

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This positive expected net present value assumption does not preclude overinvestment because, ex-post, once firm type is revealed, projects can have a realized negative net present value.

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security that is issued by both types of firms in a pooling equilibrium that solves the adverse selection problem costlessly. There is no dilution in the claims of the existing equity holders, so managers invest regardless of their private information, achieving the symmetric information outcome. Furthermore, the bond will be called (and converted by debt holders) only when θ = θ2. We proceed to ask two questions. First, why is a negative stock price reaction observed at time t = 1 when the convertibles are called, if, according to the model, calling (and conversion) occurs only when the good state of nature is revealed? Second, if there is no reduction in the value of the claims of the existing equity holders, how can the negative stock market reactions to the announcement of convertible debt issuance be justified? We conjecture that one of the key assumptions in the model is violated: managers do not always behave in favor of their current stockholders. In the following section, we propose a modification of the basic setup in order to take into account a possible agency problem between stock holders and management. 4.2 The Model Augmented with Agency Problems Consider the existence of two types of managers; one type of manager, MA, always behaves in favor of his current stockholders. The other type of manager, MB, cares for the wealth of his current stockholders, and also cares about the private benefits of control that arise from her position as manager of the firm. We assume that debt restricts her access to these benefits and, consequently, that she dislikes having debt in the firm’s capital structure. Each type of manager privately knows his own type. Manager MB will always try to move to a less levered capital structure, even though this action might affect negatively the wealth of the current stockholders of the firm. We also assume that the distribution of firm types is independent from the distribution of manager types. For each type of firm θ there is a probability p of having a manager of type MB. The ex-ante probability of a firm being of type θi is λi. The timing and informational structure of the model is presented in Figure 1.

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Let’s define B as the private benefits from control. We assume that in the presence of agency problems, the value of the firm for its shareholders is reduced by the total value of the private benefits of control. The utility functions of each type of managers are: (4.4) (4.5)
U A ( SH , B ) = γ V SH V U B ( SH , B ) = γ V SH + (1 − γ ) B V with with 0 < γ <1 0 < γ <1

where VSH is the true value of the firm accruing to its shareholders. 11 We claim that there exists a Bayesian separating equilibrium at time t = 1 in which type A and type B managers reveal their own type when their firms turn out to be low value firms ( θ1 ). In contrast, there exists a pooling equilibrium at time t = 1 when nature reveals that the firms are high value firms (θ2).

Proposition 1 (Existence of a Bayesian equilibrium) For the game defined above, there exists a convertible security that induces a Bayesian Nash equilibrium such that: i. At time 0, bondholders are willing to provide the necessary funds for investment to take place and both types of managers issue convertible debt; ii. At time 1, when the high cash flows state is revealed (θ = θ2) both types of managers call and bondholders convert; iii. At time 1, when the low cash flows state is revealed (θ = θ1) only managers of type B call and bondholders convert, but type A managers do not call and bondholders

In equation (4.4) the utility function of the type A managers can just be defined as VSH. However, the γ is included for tractability. It should be noted that a manager’s utility function as defined in (4.4) is consistent with an optimal fee schedule for management under unobservable actions, as in Ross (1977). Under the risk neutrality assumption, the utilities of managers and shareholders will be linearly related and any optimal fee schedule with which (4.4) was consistent will satisfy the similarity condition in Ross’ model. Henceforth, managers will always choose the actions most favorable for her stockholders. The inclusion of private benefits of control, B, in the utility function of type B managers in equation (4.5) breaks the optimality of such fee schedule, and allows managers to rationally choose actions that do not maximize the wealth of their shareholders. Also, the fact that the private benefits of control are modeled as a fixed amount rather than as a fraction of firm value considerably simplifies the development of the model. This assumption is not restrictive, since type B managers will still have incentives to increase the amount of assets under their control as long as the value for shareholders is monotonically weakly related to the value of the assets of the firm.

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do not convert. 12

We next specify time t = 1 beliefs of the investors regarding the type of manager that is in control of the firm.

Set of Beliefs {SB} i. If θ = θ2 , investors believe that both types of manager will call. ii. If θ = θ1 , and a manager calls, investors believe that her type is B; if θ = θ1, and a manager does not call, investors believe that his type is A.

For these beliefs to induce an equilibrium, it must be the case that managers truthfully reveal their own type, given the optimal conversion policy for bondholders and the value of the firm revealed. Similarly, the optimal conversion policy for bondholders depends on the value of the firm revealed and on their beliefs about type dependent manager actions. The optimal bondholder decision is given by Proposition 2. Managers’ truthful revelation constraints are given in Proposition 3.

Proposition 2 (Bond Holders Optimal Decision) If the condition: (4.6)
D2 (F ) ≥ α (V2 − pB ) > α (V1 − pB ) > α (V1 − B ) > k

holds, then, whatever state of nature is revealed, given {SB}, bondholders will convert if managers call, and they will not convert if managers do not call. Proof: (See Appendix 1).

For the first inequality of condition (4.6) to hold, we assume that there are no

Note that at this point the assumption that firms that issue convertible bonds have restricted access to the equity or straight debt market becomes crucial. Given the informational structure of the model, type A managers, privately knowing their firm types, would have issued straight debt at time t = 0, separating themselves from type B managers earlier.

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incentives for bondholders to voluntarily convert when nature reveals the high payoff state. This is a reasonable assumption, since if bondholders decide to wait until the maturity of their conversion option, they will receive interest payments, if any, and still benefit from the conversion option embedded in their instrument. 13 The second inequality is a direct consequence of the stochastic dominance assumption about firm types. The third inequality derives from the fact that p, the probability of having a manager of type MB, must be less than one. The last inequality follows from the fact that bondholders will be forced to convert in the low value states of nature only if the value from converting is higher than the call price k.

Proposition 3 (Truthful Revelation Constraints) If θ = θ1, managers will truthfully reveal their types if and only if: D (F ) − B (4.7) α ≥ 1 V1 − B and γ (αV1 − D1 (F )) (4.8) αγ + 1 − 2γ > B If θ = θ2, managers will truthfully reveal their types if and only if: (4.9) and (4.10) γ D2 (F ) > γα (V2 − pB ) + B (γ − 1) Proof (See Appendix 1).
D2 (F ) > αV2 − α pB

Equations (4.7) and (4.8) impose restrictions on the values of the parameters of the model such that, under the realization of the low value state of nature and given investors’ beliefs, type A and type B managers, respectively, obtain a higher utility from
13 This is one reason why Stein (1992) argues that if firms issue convertibles to move to a less levered capital structure in the future, a call feature is the only way to force bondholders to exercise their conversion option early. It should be clear that for bond holders it is an optimal strategy to wait one period to convert if the expected interest payments for the next period are higher than 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 considered riskier than interest payments .

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revealing their own type rather than by mimicking the other type. Equations (4.9) and (4.10) have an analogous interpretation for the realization of the high value state of nature. Finally, investors must be willing to provide funds for investments. The required participation constraints are given by Proposition 4.

Proposition 4 (Participation Constraints) In the equilibrium given by Proposition 1, investors will be willing to hold the convertible securities as long as: (4.11) λ pα V1 + λ D1 (F )(1 − p ) + αV2 [1 − λ ]− pα B ≥ 1 Proof (See Appendix 1).

The left hand side of equation (4.11) corresponds to the expected payoff to bondholders, given the parameters of the model. If the amount required for investment is $1, bondholders, which are risk neutral, will be willing to provide such amount as long as their expected payoff is at least $1. There exists a callable convertible security for the model presented in section 2.1 that is issued by both types of firms in a pooling equilibrium and that investors are willing to hold. Chakraborty and Yilmaz (2003) show that a convertible security defined by (4.12) below solves the adverse selection problem costlessly: ⎧ D1 ( F ) = 1 ⎪ (4.12) CS 0 (F , α , k , T1 , T2 ) = ⎨ αV2 = 1 ⎪ k =1 ⎩ However, their model does not incorporate agency problems. In fact, it is easy to show that convertible debt contracts characterized by (4.12) will not work in the presence of agency problems, because investors will not be willing to provide the required funds for the investment. 14 As an alternative, we propose the following
From (4.11), bondholders will be willing to buy the convertible securities as long as their expected return is equal to or greater than one, the amount of funds provided for investment. Replacing (4.12) in (4.11), it is easy to show that bondholders will invest as long as λ(αV1 -1) ≥ αB. Since αV2=1 > αV1, it is clear that λ(αV1 -1) < αB, regardless of the value of p, as long as there are positive benefits from control.
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convertible security:
⎧ ⎪ (4.13) CS (F , α , k , T1 , T2 ) = ⎨ ⎪ ⎩
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αV1 = D1 ( F ) = 1 αV2 = 1 + δ k < 1−αB

where δ > 0 is a direct measure of the value reduction in stockholders’ wealth at time t = 0, induced by agency conflicts. 15 It is straightforward to verify that CS1 satisfies (4.6) and (4.7). Regarding (4.8), it is clear that replacing CS1 in the right hand side of the inequality yields: (4.14) αγ + 1 − 2γ > 0 There are many values of α and γ for which (4.14) holds, and correspond to the area between the curve and the horizontal axis in Figure 2. 16 Equation (4.9) and (2.10) holds directly from (4.6). Finally, replacing (4.13) in equation (4.11): (4.15) E [Bondholders' Payoff ] = λ p + λ (1 − p ) + (1 + δ )(1 − λ ) − pα B ≥ 1 Solving for δ : pα B (4.16) δ ≥ >0 1− λ Corollary 1 Given the value of the parameters p, γ, λ, B, V1, and V2, it is always possible to design a convertible bond characterized by CS1 such that Proposition 1 holds.

Equation (4.16) establishes the minimum conversion premium, defined as the minimum rate required by bondholders in good states of nature to hold the bonds. Remember that in this case, bondholders are willing to provide funds despite the potential agency problems of the firm. This equation has a strong intuitive appeal and

Note that the condition k < 1 – αB is consistent with the fact that, empirically, many of the bonds that are converted on call have redemption prices below their principal. 16 Note that as α→ 0, the values of γ for which a manager will choose to call become more and more restricted. In the limit, a type B manager will only call when γ < 0.5. Since the preferences of a type B manager are given by equation (4.5) above, it is clear that these managers will have incentives to call in the low cash flows state of nature only if they obtain a higher marginal utility from the private benefits of control (B) than from looking after the wealth of their shareholders.
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represents one of the central results of the model for empirical validation. Comparing (4.12) with (4.13), it can be seen that when agency problems are present, bondholders require a higher stake of the shares of the company (represented by δ > 0) when good states are revealed in order to provide funds for investment. In other words, they are not willing to break even, even though they are risk neutral investors. This higher share of the value of the company compensates them for the odds of having an agency problem and induces a reduction in the wealth of current stockholders when convertibles are issued. Furthermore, note that δ, a direct measure of the value reduction in current stockholders’ wealth, increases with p, the probability of having an agency problem, increases with B, the private benefits of control, and increases with λ, the probability of having a low value firm. Finally, our model is able to explain the different magnitudes in market reactions when it is announced that convertible bonds will be issued and when it is announced that bonds will be called for early redemption. 17 Given that θ and γ are distributed Bernoulli (λ) and Bernoulli (p), respectively, and assuming that the value of the firm is linearly related to these variables, it is easy to verify that the variability of the value of the firm at time t = 0 will always be larger than the variability of its value at time t = 1. Furthermore, if the probability of having agency problems is zero, then the model predicts no market reaction when firms announce their intentions to redeem their bonds early. This result stresses the importance of incorporating agency problems to models of asymmetric information to properly account for the observed empirical regularities. Our model is able to explain two key features of convertible debt financing: the negative stock market reaction to the issuance announcement of such instruments, and the negative stock market reaction to the forced conversion, or calling. The former phenomenon is explained in the model as a reduction of current stock holders’ interest in the firm. Also, bondholders require a higher conversion rate than in the case when the

17

These results are formally derived in the appendix.

17

agency problem does not exist. This comes at the expense of current stock holders, who find that the expected value of their future wealth is reduced. The second phenomenon, the negative stock market reaction to the forced conversion, is a direct consequence of the fact that when the type of firm is revealed in the second period, only managers that seek the private benefits of control will force conversion in the bad states of the world. These managers signal to the market their type by forcing conversion.18 When the good states of the world are revealed, conversion does not signal to the market the type of manager running the firm, since in this case both types of managers will convert. Figure 3 plots these relations.

5 5.1

Empirical Analysis Data Description Our sample of convertible bonds comes from the FISD (Fixed Income Security

Database) and covers the period from December 1986 to March 2004. The database contains 2,300 convertible bonds. We select a subsample of convertible bonds that satisfy the following criteria. We require that the issuance announcement day coincides between the FISD database and the information collected from Bloomberg. Convertible bonds must be classified as redeemable or callable, and it must be possible to uniquely match the CUSIP number of the issuer with the PERMNO variable in the Center for Research in Security Prices (CRSP) database. Exchangeable bonds are excluded from the sample. Our final sample is comprised of 340 bonds. Individual (quarterly) information for the issuing firms is obtained from COMPUSTAT. The mean and median notional values in our sample are $368 million and $175 million, respectively. 19 The median value of assets for the firms in the sample is $1,239 million, while the median value of equity is $441 million. These figures are similar to those in Datta, Iskandar-Datta, and Raman (2003) and Spies and Affleck-Graves (1995).
18 19

In our model the conversion announcement is an information event that conveys a signal to the market. The mean and median notional values for the complete FISD are $294 million and $150 million, respectively.

18

Table 1report summary statistics adjusted by their respective industry medians, where industries are defined at the 4 digit SIC level. Panel A of Table 1 reports Tobin’s q, defined as the product of the price at the third month of the corresponding quarter (data 14) times the number of common shares outstanding (data 15), plus total assets (data 44), minus the book value of common equity (data 59), all divided by total assets (data 44). It also reports the ratio of intangibles (data 235) to total assets (data 44), the ratio of research and development expenses (data 4) to sales (data 2), the value of assets (data 44), and leverage, which is defined as long term debt (data 51) over the book value of common equity (data 59). The firms in our sample have higher growth opportunities than their industry peers, as proxied by either Tobin’s q or research and development expenses. They are also bigger; more levered, and have a higher proportion of intangible assets. Thus, the use of convertible securities seems to be an attractive alternative for high growth firms that are more likely to suffer from informational asymmetries.

5.1.2 Market Reactions at Issuance and Calling Dates Changes in market valuation are measured by three-day market adjusted cumulative abnormal returns (CARs). Results of CARs (-1,+1) computed using the equally weighted CRSP index as benchmark are presented in Table 2. There is a negative market reaction on the day the issuance of convertible bonds is announced, in line with the results of Dann and Mikkelson (1984), Stein (1992), and Kim and Stulz (1992). The 3-day CAR at issuance of convertible bonds is -2.09% which is significantly different from zero at conventional levels (Z-statistic of 6.61 and a tstatistic of 5.36). We construct a sample of bonds that have been called and converted. The Fixed Income Security Database only includes information about the bonds at the time they

19

were issued, so to find out their call and conversion status we use Bloomberg and LexisNexis. Bloomberg provides information on whether the bond has been called or not, but does not always specify if bond was converted or redeemed. To find out the latter, we check in LexisNexis for information regarding conversion and redemption. Out of the 228 bonds that we were able to identify, 42% have information on LexisNexis. For the rest of the bonds, we check (using data from CRSP) if the conversion option was deep-in-the-money during the conversion period, where we define deep-in-the-money as having a conversion value at least 10% higher than the redemption value. If a bond is deep-in-the-money, we consider that the bond was completely converted. 20 There are 112 such bonds. The 3-day CAR at the call announcement date is -1.16% and is significantly different from zero at conventional levels (Z-statistic of 2.59 and a t-statistic of 2.16). These results are consistent with previous studies and further document the symmetry of negative stock price reactions to the issuance and redemption of convertible bonds.

5.2

Testable Implications In this section, we investigate the model predictions and implications at the two

key dates of the model: the issuance date and the call announcement date. One implication of our model, as explained in Figure 1, is that the market reaction at the issuance announcement day should be larger (in absolute value) than the market reaction observed at the call announcement day. At the beginning of t = 1 firm type is revealed and, consequently, the only uncertainty to the market about the firm is the manager type. At the end of t = 1, when firms decide whether to call their debt, uncertainty is resolved but only for those firms that are in the low value state, since for firms in the high value state both types of managers will convert. Because the only information revealed to the market at the end of this period is manager type, we expect a

20 We applied this rule to the bonds that have specific information regarding the conversion/redemption outcome, and found that for all but one of the bonds the rule works correctly.

20

smaller price reaction than the one observed at the issuance announcement day (t =0), when both firm and manager type are unknown. A formal derivation of this result is presented in the appendix, section A2. As seen in table 2, the mean CARs at the time bonds are issued is -2.09%. On the other hand, when the in-the-money bonds are called, the mean CAR is -1.16%. These percentages are statistically different from each other (Kruskal-Wallis test with a pvalue=1.3%). Since CARs are basically changes in valuation, these results are consistent with a reduced amount of uncertainty at calling announcement date compared to the issuance announcement date. Perhaps a more important testable implication of the model refers to the relation between firm value and the extent and the probability of agency conflicts, given firm type and the value of private benefits of control. More specifically, at the announcement date of convertibles, low value firms and firms likely to face agency conflicts should experience more negative returns. Thus, we conduct this analysis using a multivariate regression in which the dependent variable is the 3-day CARs, centered at the issuance announcement day, and the independent variables are a set of proxies for agency problems and firm value. 21 We collect data on several variables that have been used in the literature as proxies for the likelihood and extent of agency problems, and for the probability of being a low or high value firm. We measure all proxy variables at the end of the quarter immediately before the issuance announcement day. We use the expense ratio to proxy for the extent of agency problems. As defined by Ang, Cole, and Lin (2000), the expense ratio is computed as selling, general, and administrative expenses (data 1) over net sales (data 2). The expense ratio captures how well the manager controls operating expenses, including perquisite consumption and non monetary benefits. We hypothesize that it will be positively related to the probability of agency problems, p, and/or to the
21 For most of the analysis, results using 2-day windows (-1, 0) yield qualitatively similar results as using 3-day windows (-1, +1). For brevity, all remaining tables present results only for 3-day windows.

21

magnitude of the private benefits of control, B. For completeness, we also use Asset Utilization Ratio (Sales to assets) as an alternative measure of the extent of agency problems. As in Ang, Cole, and Lin (2000), we define this variable as net sales (data 2) divided by total assets (data 44). The asset utilization ratio is likely to capture if the manager makes poor investment decisions, exerts low levels of effort or buys unproductive assets. The higher the asset utilization ratio, the lower the agency costs. We use two proxy variables to capture the distribution of firm value: Tobins´ q (captures growth opportunities) and the ratio of capital expenditures to total assets, capex, which represents the attractiveness of the set of investment opportunities faced by the firm. Table 1 presents descriptive statistics for these variables. The empirical testing of the model requires that the variables used capture the dynamics between the extent of agency problems, firm value, and management incentives. One example of the need to account for these interactions in the empirical implementation of the model is capital expenditures. Even though the level of capital expenditures might proxy for the value of investment opportunities of the firm, in the presence of agency conflicts between managers and stockholders, capital expenditures may not necessarily indicate that the firm is experiencing valuable investment opportunities. For example, when a firm faces high growth (as captured by a high Tobin’s Q) and a high level of capital expenditures, issuing convertible debt should be good news. In this scenario, it is likely that the funds raised will be used in efficient investments (the result of good management decisions) reflecting either an absence or a reduced level of agency problems. However, for firms with little or no growth potential (low Tobin’s Q), a high level of capital expenditures might be associated with agency problems; e.g. over-investing by a self interested manager to increase benefits of private control. In analysis not reported here, the CARs for the sample of firms representing the former type is more than twice as negative as the CARs for the latter (these differences

22

are significant at the 1% level). 22 These results suggest that market reactions at the time convertible instruments are issued depend, at least partially, on investors´ perceptions about the likely use of the funds raised and a function of agency problems. This requires the use of a set of dummy variables to capture the interactions between low and high levels of capex and low and high Tobin’s Q. Alternatively, we can include both capex and an interaction term between capex and a dummy variable, qDummy, that takes the value of one (zero) if the firm’s Tobin’s q is above (below) the corresponding industry average of our sample of firms. We expect that for high growth opportunity firms (qDummy = 1), an additional dollar in capital expenditures should be associated with a milder adverse market reaction than an additional dollar in capital expenditures for low growth opportunity firms (qDummy = 0). Consequently, we expect a positive coefficient for the interaction variable and a negative coefficient for capex to reflect the negative impact of agency problems. Another variable, prevalent in the extant empirical literature that captures the interaction between the benefits of private control and firm value is leverage. The argument is that self-indulgent managers dislike the disciplinary role of debt, and therefore it is likely that they will try to keep low levels of leverage or eliminate leverage opportunistically. As shown by McConnell and Servaes (1995), leverage has a different impact on value depending on firms’ growth opportunity characteristics. In a regression analysis not reported here (but available upon request), we find that leverage has a significantly positive (negative) coefficient for firms below (above) the median Tobin’s q-ratio. This result is consistent with the idea that leverage has a different impact on value depending on firms’ growth opportunity characteristics: firms with low growth opportunities experience a disciplinary role of debt, where more leverage is perceived to be good and reduce the abnormal reaction to the announcement of
22

In the analysis not reported here, we constructed four portfolios depending on whether each firm is above or below its industry adjusted Tobin’s q and above or below its industry adjusted capex ratio. Firms a high q and low capex are likely to be firms that have not been able to take full advantage of their growth opportunities. Firms with low q and high capex are likely candidates for over-investing.

23

convertibles. In contrast, firms with high Tobin’s q ratios might experience a debt overhang problem which would explain the negative and significant coefficient between leverage and CARs. 23,24 Accordingly, we include an interaction term between leverage and qDummy in our regression analysis. Leverage is measured as long term debt over total assets. Results of the regression analysis are presented in Table 3. The expense ratio coefficient is negative and significant at conventional levels. We interpret this as evidence that firms more likely to suffer from agency problems – i.e., those with higher expense ratios, exhibit more negative market reactions when they announce their plans to issue convertible securities. The effect of the expense ratio on market valuations is also economically significant 25 . The alternative measure of agency problems, the sales to assets ratio, is not significantly different from zero. We include the Tobin’s Q and leverage to check the stability of the interaction terms between the qDummy and capex and between qDummy and leverage. Neither coefficient is statistically significant. The coefficient for the capex ratio is a significant -0.317 while the coefficient of the interaction between capital expenditures and q is a positive and significant value of 0.602. This is consistent with the view that the issuance of convertible securities by firms with low with a high level of capital expenditures is perceived negatively by the market if they face low growth opportunities (qDummy = 0) and positively if they face high growth opportunities (qDummy = 1). These results are in line with the predictions of the model that firms more likely to use funds that will be raised efficiently experiencing less adverse market reactions at the issuance announcement day. The coefficient for the interaction between leverage and qDummy is negative and
We split our sample at the median Tobin’s q-ratio and regress, for each of these two subsamples, CARs on capex, expense ratio, sales to assets ratio, and leverage. 24 Consequently, our results for leverage not only support the agency story of the model, but they are also consistent with the previous empirical literature on firm value, growth and leverage (Myers, 1977; Jensen, 1986; McConnell and Servaes, 1995). 25 A one standard deviation increase in the industry adjusted expense ratio increases the negative market reaction by 0.15% (-0.54% * 0.2833). This means that for the average bond-firm CAR in the sample, such a change in the level of expenses to total assets would increase the negative market reaction from -2.09% to -2.24%.
23

24

significant at the 1% level. Therefore, for low growth firms (qDummy = 0), leverage does not seem to significantly affect the change in firm value induced by the issuance announcement. On the contrary and consistent with the arguments of McConnell and Servaes (1995), for high growth firms (qDummy = 1), leverage increases adversely affect firm value as reflected in negative CARs at the convertible issuance announcement. In summary, the predictions of our model are supported by these results. Particularly, the results for the interaction of capex and Tobin’s q suggest that the market perception regarding the issuance of convertible securities is influenced by the plausible use the firm will make of the funds raised. The more likely funds will be used for efficient investment, the less negative the abnormal returns; the most likely funds will be used to increase the number of assets under mangers’ control in low growth firms, the more negative the abnormal returns. Finally, the significantly negative estimated coefficient for the expense ratio provides additional support for the theoretical model. We next proceed to the analysis of the stock price reaction at the calling of the convertible bonds. As a direct test of the influence of agency problems on market reactions upon redemption, we split our sample between bonds whose convertible option was out-of-the-money and those that were in-the-money at the time of the redemption announcement and compute, for each subsample, cumulative abnormal returns. CARs for each subsample are presented in Table 4. If a bond is called when the convertible option was out-of-the-money, the market reaction is positive and significant. This result is consistent to those found by Cowan, Nayar, and Singh (1993). On the other hand, stock reactions to bonds called when the option was in-the–money are negative and significant. Albeit our model does not explicitly account for this phenomenon, this result provides support for the agency story. When an out-of-the-money convertible is called, management uses cash to pay the debt. This is perceived favorably by the market, since less discretionary funds will be

25

available to the managers. On the other hand, if the bond is called when the conversion option is in the money, management eliminates the burden of debt and cash holdings remain at their disposal. This is perceived negatively by the market. Furthermore, this result is also consistent with the results in Datta, Iskandar-Datta, and Raman (2003) where they find that common stock of firms who call their in-the-money convertible bonds underperforms by a median of 64% their peers over the five years following forced conversion. The negative and significant market reaction observed for our sub sample of firms that call their in-the-money convertible bonds might be an anticipation by the market to such future underperformance. Since one of the advantages of our model over other theories is its ability to explain both the negative market reactions observed when firms announce the issuance of convertible bonds and when they call their bonds for early redemption, we next investigate the relation between market reactions at the two key dates of the model. We proceed in the following way: at the second date, when firms call their debt for early redemption, we investigate if firms associated with a higher probability of having agency conflicts at the issuance date are also more likely to call their convertible bonds at the call announcement day when their conversion options are in-the-money. If so, this result would provide support for both the existence of the predicted Bayesian equilibrium of the model and its informational structure, since as depicted in Figure 3, self indulgent managers call regardless of the realization of firm value. Table 5 presents the results of the logistic regression we use to analyze this issue. The dependent variable takes a value of one when the bonds are called in-themoney at the redemption announcement day, and zero otherwise. In column (1) the independent variables are capex, the expense ratio, the sales to assets ratio, and leverage, all industry adjusted and measured at the issuance announcement day. The expense ratio, which is directly related to the probability of having an agency conflict, has a positive and significant coefficient. This suggests that the market is able, on average, to

26

identify at the issuance day which firms are more likely to have an agency problem. The coefficient for capex is positive and significant, suggesting that firms that invest more than their industry peers before the issuance of convertibles are more likely to force conversion. These results are in accord with Mayers (1998) and his sequential financing motive. Leverage has a positive and significant coefficient: the higher the leverage of firm before it issues convertibles, the more likely is that it will force conversion. In column (2), the independent variable corresponds to the 3-day CARs. A more negative market reaction at the announcement day is associated with a higher likelihood of having agency problems at that date, and is related with a higher probability of forcing conversion, in line with the predictions of our model. Finally, in Table 6, we form quartiles of our firm-bond observations according to their expense ratio at the issuance announcement date. Firms in the bottom (top) quartile are classified as firms with a low (high) probability of having agency problems. We then compute CARs for the extreme quartiles at the redemption announcement date. As expected, firms more likely to experience agency problems at the issuance announcement day have a negative reaction at the redemption announcement date, while those with a low ex-ante probability of agency problems experience a positive stock return to the announcement of conversion. The difference between these groups is statistically significant, with a p-value of 3%. Given that at the issuance date, market reactions are related to the likelihood of agency problems and that at the redemption date all uncertainty is likely to be resolved, our results suggest that investors tend to be right when assessing the type of managers they are dealing with.

6

Conclusions Financial researchers have devoted a large amount of effort to explain the

negative market reaction to forced conversion of convertible securities. Until today, the negative stock market reaction when convertibles are issued has generally been treated

27

as a separate phenomenon from the stock price reaction to announcements of convertible calls (redemptions). In this paper, we present a model with asymmetric information and agency problems in which both market reactions are explained in the context of efficient capital markets and rational investors. The empirical tests provide support for the implications derived from our model. We find that firms that are more likely to suffer from agency problems experience larger negative returns when they announce the issuance of convertible bonds. We also find, at the call announcement day, evidence that supports the existence of a Bayesian separating equilibrium implied by the model. There is a significant difference in price reactions at the issuance announcement date and at call announcement date, consistent with the informational structure and timing of the model. We find evidence showing that firm characteristics at the issuance date are related to the presence and extend of agency problems at the call date. This result provides evidence on the ability of the market to recognize agency problems and, more importantly, stresses the importance of modeling both events together.

28

References Ang, J., Cole, R. A., and Lin, J. W.; 2000; Agency Costs and Ownership Structure. Journal of Finance; 50: 81-106. Asquith, P.; 1995; Convertible bonds are not called late; Journal of Finance; 50: 12751289. Asquith, P. and Mullins, D.; 1991; Convertible debt: Corporate call policy; Journal of Finance; 46: 1273-90. Brennan, E.J. and E. Schwartz; 1977; Convertible Bonds: Valuation and optimal strategies for call and conversion; Journal of Finance 32: 1699-1715. Brick, I., Palmon, O., and Patro; 2007; Stock Price Response to Calls of Convertible Bonds: Still a Puzzle; Finalcial Management, 65-85. Byrd, A. K. and Moore, W. T.; 1996; On the information content of calls of convertible securities; Journal of Business; 69: 89-101. Campbell, C. J.; Ederington, L.; and Vankudre, P.; 1991; Tax shields, sample selection bias, and the information content of convertible bond calls; Journal of Finance; 46 : 1291-1324. Chakraborty, A. and Yilmaz, B.; 2003; Asymmetric Information and Financing with Convertibles; Working Paper, The Rodney L. White Center for Financial Research, University of Pennsylvania. Constantinides, G. and B. Grundy; 1987; Call and Conversion of Convertible Corporate Bonds: Theory and Evidence; Working Paper, Graduate School of Business, University of Chicago. Cowan, A. R., Nandkumar Nyar, Ajai K. Singh; 1993; Calls of Out-of-the-Money Convertible Bonds; Financial Management, 22 (4):106-116 Dann, L. and Mikkelson, W.; 1984; Convertible Debt Issuance, Capital Structure Change and Financing-Related Information: Some New Evidence; Journal of Financial Economics; 13: 157-186. Datta, S., Iskandar-Datta, M., and Raman, K.; 2003; Convertible Bond Calls: Resolution of the Information Content Puzzle; Journal of Financial Intermediation;12:255276. Eckbo, B.; 1986; Valuation Effects of Corporate Debt Offerings; Journal of Financial Economics; 15: 119-151. Ederington, L. H. and Goh, C.; 2001; Is a convertible bond call really bad news? Journal of Business; 74: 459-476.

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Harris, M. and Raviv, A.; 1985; A sequential signaling model of convertible debt call policy; Journal of Finance; 40: 1263-1281. Ingersoll, J.; 1977; A contingent-claims valuation of convertible securities; Journal of Financial Economics; 4: 289-321. Ingersoll, J.; 1977; An examination of corporate call policies on convertible securities; Journal of Finance; 32: 463-478. Jensen, M.; 1986; Agency Cost of Free Cash Flow, Corporate Finance, and Takeovers; The American Economic Review; 76: 323-329. Kim, Y. and Stulz, R.; 1992; Is there a global market for convertible bonds; Journal of Business; 65: 75-91. Mayers, D.; 1998; Why firms issue convertible bonds: the matching of financial and real investment options; Journal of Financial Economics; 47: 83-102. Myers, S.; 1977; Determinants of Corporate Borrowing, Journal of Financial Economics; 5: 147-175. Myers, S. and Majluf, N.; 1984; Corporate Financing and Investment Decisions when Firms have Information that Investors do not have; Journal of Financial Economics; 13: 187 - 221. McConnell, J. and Servaes, H.; 1995; Equity ownership and the two faces of debt, Journal of Financial Economics; 39: 131-157. Mikkelson, W.; 1981; Convertible calls and security returns; Journal of Financial Economics; 9 (September): 237-264. Mikkelson, W. and M. Partch; 1986; Valuation Effects of Security Offerings and the Issuance Process; Journal of Financial Economics; 15: 31-60. Nyborg, K.; 1994; Convertible Debt as Delayed Equity: Foreced versus Voluntary Conversion and the Information Role of Call Policy; Journal of Financial Intermediation; 4: 358-395. Ofer, A. and Natarajan, A.; 1987; Convertible call policies: An empirical analysis of an information-signaling hypothesis; Journal of Financial Economics; 19: 91-108. Ross, S.; 1977; The Determination of Financial Structure: The Incentive-Signalling Approach; Bell Journal of Economics; 8: 23-40. Spies, D. and Affleck-Graves, J.; 1995; The long run performance of stock returns following debt offerings; Journal of Financial Economics 54: 45-73. Stein, J.; 1992; Convertible Bonds as "Back Door" Equity Financing; NBER, W.P. No. 4028.

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Table 1. Descriptive Statistics. Panel A presents descriptive statistics for the sample of firms used for analysis at the issuance announcement day. Tobin's q is 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. Intangibles correspond to the ratio of intangibles to total assets. R&D is research and development expenses over sales. Assets correspond to the value of total assets, and leverage is long term debt over total assets. Panel B presents descriptive statistics of additional variables included in the regression analysis at the issuance announcement day. The capital expenditures ratio is defined as the ratio of capital expenditures to total assets. The expense ratio is defined as selling, general, and administrative expenses over total sales. The asset utilization ratios is defined as the ratio of sales to total assets, Each variable is adjusted subtracting its industry median, where industry is defined at the 4 digit SIC level. A t test for the null hypothesis that the mean of each variable is equal to zero, and a sign and Wilcoxon tests for the null hypothesis that the median of each variable is equal to zero are also presented. p-values are reported under their respective statistics. Panel C presents the correlation matrix (Pearson correlation coefficients) for the variables included as regressors in the regression analysis at the issuance announcement day. p-values are reported under their respective statistics. Panel A Raw data Mean Tobin's q Intangibles R&D Assets (billions) Leverage Panel B: Descriptive Statistics Raw data Mean Expense Ratio Capital Expenditures Ratio Asset Utilization Ratio 0.31 0.03 0.19 Median 0.24 0.02 0.14 Std. Dev. 0.32 0.06 0.18 Mean 0.02 0.01 -0.01 Industry adjusted Median -0.01 0.00 -0.03 Std. Dev. 0.28 0.05 0.13 2.28 0.06 0.94 12.63 1.32 Median 1.55 0.006 0.13 1.24 0.71 Std. Dev. 2.54 0.13 2.81 51.96 4.50 Mean 0.72 0.05 0.78 11.57 1.07 Industry adjusted Median 0.08 0.004 0.00 0.91 0.48 Std. Dev. 2.42 0.12 2.75 51.91 4.49

Panel C: Correlation Matrix Capex ratio Capex ratio
-

exp. ratio

sales to assets

leverage

exp. ratio

0.047
0.49

sales to assets

-0.058
0.32

-0.23
0.0006

leverage

-0.119
0.04

-0.079
0.24

-0.13
0.03

Tobin's q

0.009
0.87

0.09
0.16

-0.06
0.32

0.01
0.83

31

Table 2 This table presents Cumulative Abnormal Returns (CARs) are computed using market adjusted returns, with the equally weighted CRSP index used as the market benchmark. (-1,+1) corresponds to a three day window centered at the event day. 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. Market Reaction at Issuance Announcement Day. Issuance Announcement Day

N = 319 (-1,+1)

Mean CAR -2.09%

Patell Z -6.61***

t stat -5.36***

Panel B. Market Reaction at the Call Announcement Day for Bonds which Conversion Option is In the Money.

Call Announcement Day

N = 112 (-1,+1)

Mean CAR -1.16%

Patell Z -2.59**

t stat -2.16*

32

Table 3. Relation between CARs at Issuance Announcement Day and Proxy Variables for Agency Problems and Firm Value. This table presents results from a weighted least squares regression. The dependent variable is 3-days CARs centered at the issuance announcement day computed using market adjusted returns. The equally weighted CRSP index is used as the market benchmark. Weights in the least squares specifications correspond to the ratio of the offering amount for each bond to the value of the corresponding firm's common equity. The independent variables are the ratio of capital expenditures to total assets, the expense ratio, defined as selling, general, and administrative expenses over total sales, the ratio of sales to assets, leverage, defined as long term debt over total assets, 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, and the interaction between capital expenditures and a dummy variable for Tobin's q, qDummy, which takes the value of one if a firm’s q is above the corresponding industry average. Variables are industry adjusted at the 4 digit level SIC codes. All explanatory variables are measured at the quarter ending immediately before the announcement day. p-values are shown below parameters' estimates.

intercept exp. ratio sales to assets Tobin's q capex ratio q
Dummy

-0.028
0.0001

-0.005
0.0001

0.098
0.733

0.0005
0.459

-0.317
0.066

*(capex ratio)

0.602
0.007

leverage q
Dummy

0.001
0.326

* leverage

-0.006
0.0001

N F value p-value R2

208 12.84
0.0001

0.31

33

Table 4. 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 Cumulative Abnormal Returns (CARs) computed using market adjusted returns, with the equally weighted CRSP index used as the market benchmark. (-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 (-1,+1) Mean CAR 0.78% Patell Z 1.66* t stat 1.50$ N = 112 (-1,+1)

In the Money Mean CAR -1.16% Patell Z -2.59** t stat -2.16*

Panel B

Kruskal-Wallis Test and Test for Equality of Means between groups. Wilcoxon 2 Sample Test Normal Approx 2.56 p value (1 tail) 0.0047 Kruskal-Wallis Test χ2 6.75 p value 0.01

34

Table 5. 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. In column (1) 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 sales to 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. In column (2) the independent variables are the cumulative abnormal returns for (-1,+1) windows centered at the issuance announcement day computed using market adjusted returns. The equally weighted CRSP index is used as the market benchmark. Weights in the logistic regression correspond to the reciprocal of the variance of the cumulative abnormal returns. p-values are shown below parameters' estimates. The table also reports 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.

1

2

intercept

-0.087
0.0001

-0.12
0.0001

Capex ratio

1.76
0.0001

expense ratio

0.015
0.0001

sales to assets

0.06
0.1374

leverage

0.006
0.0013

CAR (-1,+1)

-0.96
0.0001

N in / out of the money

125 64 / 61

193 98 / 95

Hosmer and Lemeshow Goodness-of-Fit Test χ2 p-value 8.08 0.43 8.86 0.35

35

Table 6. 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. Bond firm observations are sorted according to the expense ratio, defined as selling, general, and administrative expenses over total sales, measured at the issuance announcement day. Firms in the bottom (top) quartile are classified as firms with a low (high) probability of having agency problems. Cumulative Abnormal Returns (CARs) are computed using market adjusted returns. The equally weighted CRSP index is used as the market benchmark (-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.

Low Agency Problems

High Agency Problems

Wilcoxon Two-Sample Test Z p-value 0.035

CAR (-1, +1)

0.84% 33

-1.51% 34

2.11

N

36

Figure 1 Timing of the Model: Who knows what and when Some managers call and reveal their type. t=2

Nature reveals firm type. t=0

t=1

Manager

Knows θ and his own Knows θ and his own type. type. Can call. Doesn’t know θ and competitively values the securities issued by the firms. Knows p and λ. At the beginning of t =1 learns firm type. At the end of t =1 learns manager type. Can convert.

Project cash flows are realized and distributed.

Market

Figure 2 Values of γ and α for which Truthful Revelation holds under the CS1 contract

αγ + 1 − 2γ > 0, 0 < α < 1, 0 < γ < 1

gamma

1

0.5

CS 1 holds

0 0 0.5 alpha 1

37

Figure 3 Informational Structure of the Model
Nature Chooses Firms Type

High Value Firm

Low Value Firm

Type A manager calls

Type B manager calls

Type A manager does not call

Type B manager calls

The market reacts and price the securities of the firm based on the probability of observing each type of manager.

No event to test.

Type B managers reveal their type and the market values its securities accordingly.

38

APPENDIX

A1. Proofs of Proposition 1 to Proposition 4. To show that the equilibrium in Proposition 1 exists we proceed backwards in time and analyze the optimality of the decision of the manager to call the bonds and the optimality of the decision of the bondholders to convert, given market beliefs. It is necessary to specify the time t = 1 beliefs of the investors regarding the type of manager that is in control of the firm, conditional on which θ is revealed by nature and on the decision of the manager regarding whether calling or not calling the convertibles. The set of beliefs proposed is given by {SB}.

Proof of Proposition 2. Case 1 (θ = θ2) Let’s assume that at time t = 1 nature reveals θ = θ2 and that the manager of the firm does not call the bond. If bondholders convert, they will get α 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) (1.2)
Bondholders' Payoff from Converting = α ( p (V2 − B ) + (1 − p ) V2 ) Bondholders' Payoff from Not - Converting = D2 ( F )

In the spirit of the work of Stein (1992), we 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)
D2 ( F ) ≥ α ( p (V2 − B ) + (1 − p ) V2 ) = α (V2 − pB )

Let’s assume now that at time t = 1 nature reveals θ = θ2 and the manager of 39

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)

α (V2 − pB ) > k

Case 2 (θ = θ1) Let’s assume that at time t = 1 nature reveals θ = θ1 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) (1.6) Bondholders' Payoff from Converting =αV1
Bondholders' Payoff from Not - Converting = D1 ( 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)
D1 ( F ) ≥ αV1

Suppose now that at time t = 1 nature reveals θ = θ1 and the manager of the firm calls the bond. In this case, bondholders infer that a type B manager is in control of the firm and their payoffs from converting and not converting are given by:

(1.8) (1.9)

Bondholders' Payoff from Converting =α (V1 − B )

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:

40

(1.10) α (V1 − B ) > k The restrictions arising from case 1 and case 2 can be summarized as: (1.11) D2 ( F ) ≥ α (V2 − pB ) > α (V1 − pB ) > α (V1 − B ) > k

Proof of Proposition 3. Case 1 (θ = θ1) Let’s consider first the set of beliefs corresponding to θ = θ1 and the decision faced by a type A manager. If he calls, given that θ = θ1 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 θ = θ1 , are: (1.12) U ACalling = γ (1 − α )(V1 − B ) (1.13) U A Not −Calling = γ (V1 − D1 ( F ) ) A type A manager will have incentives not to call as long as: (1.14) U A Not −Calling = γ (V1 − D1 ( F ) ) > U ACalling = γ (1 − α )(V1 − B ) It follows that (1.14) will hold if and only if: (1.15) α ≥ D1 ( F ) − B V1 − B

Equation (1.15) will hold for a variety of values of D1(F), B, and V1. Similarly, if θ=θ1 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 manager by not converting, the market will infer he is an A type of manager, and bondholders will not convert 26 . Therefore;

26

Note that he does not get B, since bondholders don’t convert.

41

(1.16) U B Calling = γ (1 − α )(V1 − B ) + (1 − γ ) B (1.17) U B Not −Call = γ (V1 − D1 ( F ) ) Accordingly, type B managers will call if and only if: (1.18) U B Calling > U B Not −Calling ⇔ αγ + 1 − 2γ >

γ (αV1 − D1 ( F ) )
B

Case 2 (θ=θ2) Consider now the equilibrium when θ = θ2 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 θ = θ2, 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: (1.19) U ACalling = γ (1 − α ) ⎡ p (V2 − B ) + (1 − p ) V2 ⎤ ⎣ ⎦ (1.20) U A Not −Calling = γ p (V2 − B − D2 ( F ) ) + (1 − p ) (V2 − D2 ( F ) ) Type A managers will have incentives to call whenever: (1.21) U ACalling > U A Not −Calling ⇔ D2 ( F ) > αV2 − α pB 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 B Calling = γ (1 − α ) ⎡ p (V2 − B ) + (1 − p ) V2 ⎤ + (1 − γ ) B ⎣ ⎦

(

)

42

(1.23) U B Not −Calling = γ ⎡ p (V2 − B − D2 ( 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 B Calling > U B Not −Calling ⇔ γ D2 ( F ) > γα (V2 − pB ) + B ( γ − 1) Given that 0 < γ < 1 and B(γ-1) < 0, condition (1.24) holds directly from (1.3). Then, from (1.21) and (1.24) no manager type has incentives to deviate.

Proof of Proposition 4 Given the equilibrium characterized in Proposition 1, the expected payoff to bondholders at time t = 0 is given by: (1.25)
E [ Bondholders' Payoff ] = λ ⎡ p (α (V1 − B ) ) + (1 − p ) D1 ( F ) ⎤ + ⎣ ⎦

(1 − λ ) ⎡ p (α (V2 − B ) ) + (1 − p ) αV2 ⎤ ⎣ ⎦

Simplifying (1.25): (1.26) E [ Bondholders' Payoff ] = λ pαV1 + λ D1 ( F )(1 − p ) + αV2 [1 − λ ] − pα B Bondholder will be willing to provide funds as long as their expected payoff is greater or equal to 1, the amount invested.

43

A2. Relative Size of Market Reactions at the Issuance Announcement Date and at the Redemption Announcement Day

Let’s assume that the value of the firm, V, is linearly related to θ and γ: (1.27) V = θ + γ Note that θ and γ are distributed Bernoulli (λ) and Bernoulli (p), respectively. Assuming independence between firms’ types and managers’ types, their joint distribution will just be the product of their marginal distributions. Their joint distribution is presented in Table A1 below. Table A1: Joint Distribution of θ and γ. Θ θ1 γ γL γH pλ (1-p)λ θ2 p(1-λ) (1-p)(1-λ)

The unconditional first and second moments of θ and γ are: (1.28) Et = 0 [θ ] = λθ1 + (1 − λ ) θ 2 (1.29) Vart = 0 [θ ] = λ (θ1 − E (θ ) ) + (1 − λ ) (θ 2 − E (θ ) ) = (θ 2 − θ1 ) (λ − λ 2 )
2 2 2

(1.30) Et = 0 [γ ] = pγ L + (1 − p ) γ h (1.31) Vart =0 [γ ] = (γ H − γ L ) 2 ( p − p 2 ) Since V =θ + γ, and given the assumption that θ and γ are independent, the unconditional variance of the value of the firm at time t = 0 is given by: (1.32) Vart = 0 [V ] = (θ 2 − θ1 ) (λ − λ 2 ) + (γ H − γ L ) 2 ( p − p 2 )
2

At time t = 1 nature reveals the types of firms and investors update their expectations about the value of the firm. Accordingly;

44

(1.33) Et =1 [V ] = E [V | θ ] = θ + E [γ | θ ] (1.34) Vart =1 [V ] = Var [V | θ ] = E ⎡V 2 | θ ⎤ − E 2 [V | θ ] ⎣ ⎦ It is easy to see that E[V2 |θ] = θ2 + 2θE[γ|θ] + E[γ2 |θ]. Given the independence assumption, E[γ|θ] = E[γ] and E[γ2 |θ] = E[γ 2]. Then, the conditional variance of the value of the firm at t = 1 is given by: (1.35) Vart =1 [V ] = Var [V | θ ] = ( γ H − γ L )
2

(p− p )
2

Accordingly, the variance of the value of the firm at time t = 0 is always larger than the variance of the value of the firm at time t = 1, regardless of the values of the parameters of the model. 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: (1.36) θ ~ N ( μθ , σ θ ) (1.37) γ ~ N ( μγ , σ γ ) It will again be assumed that V =θ + γ. Consequently, the higher the value of θ, the higher the value of the firm, and the lower the value of γ, 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: (1.38) Var [V ] = σ θ2 + σ γ2 − 2 ρσ θ σ γ where ρ =
Cov [θ , γ ]

σθσ γ

.

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,

45

(1.39) E [V | θ ] = θ + E [γ | θ ] and (1.40) Var [V | θ ] = E ⎡V 2 | θ ⎤ − E 2 [V | θ ] ⎣ ⎦ A standard result of the bivariate normal distribution is that: (1.41) E [γ | θ ] = μγ + ρ

σγ (θ − μθ ) σθ

Since we are mainly concerned with the second moment of the distribution of cash flow, it will be assumed that the means of both θ and γ are zero. In this case, equation (1.41) can be written as: (1.42) E [γ | θ ] = ρ

σγ θ σθ

Using (1.39) and (1.42) in (1.40), it is easy to show that: (1.43) Var [V | θ ] = σ γ2 − ρ 2σ γ2 The market reaction at time t = 0 will be stronger than the one at t = 1 as long as: (1.44) Var [V ] = σ θ2 + σ γ2 − 2 ρσ θ σ γ > Var [V | θ ] = σ γ2 − ρ 2σ γ2 Or, (1.45) σ θ2 − 2 ρσ θ σ γ + ρ 2σ γ2 = (σ θ − ρσ γ ) > 0
2

which is always true.

46

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