Convertible debt under asymmetric information and agency problems, a solution to the convertible debt puzzle

... 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

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 o f the Graduate School for originality and quality

Doctor of Philosophy

For the degree o f _

Final examining committee members

_ , 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 o f Graduate Program Head's Approval: 02/19/2007

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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 2 0 0 7 Purdue University

W est Lafayette, Indiana

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-V - '

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The author would like to thank Sonya Lim and John Barron who read early versions of this thesis and m ade 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 com m ents and feedback.

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P ag e

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 e v ie w 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 red em p tio n 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 Info rm atio n 2 4 4.1 T h e Basic M o d e l 2 4 4.2 T h e Model Augmented with Agency P ro b le m s 2 7 C H A P T E R 5 Data description and M e th o d o lo g y 41

C H A P T E R 6 Empirical R e su lts 4 8 6.1 M arket Reaction at the Issuance D a te 48

6.2 M arket 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 7 4 A P P E N D IX 103

V IT A 112

c

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LIST O F TA BLES

Table 1 Descriptive Statistics 7 7 Table 2 M arket Reaction at Issuance Announcem ent D a y 79 Table 3 Relation between CA Rs at Issuance Announcem ent Day and proxy variables for Agency Problems and Firms’ V a lu e 80 Table 4 Relation between CA Rs at Issuance Announcem ent Day, Agency

Problems and Insiders’ Ownership 8 3 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 M edian Industry Adjusted q-

R atio 85 Table 7 M arket Reaction at the Issuance Announcem ent Day versus M arket Reactions at the Call Announcem ent Day for Bonds which Conversion Options is In the M oney 8 6 Table 8 Relation between C A R s at Call Announcem ent D ay and proxy variables for Firms’ T y p e 87 Table 9 Relation between CA Rs at Call Announcem ent D ay and proxy variables for Firms’ Typ e 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

Table 12 Logistic Regression: Relation between M arket Reactions at the Issuance D ate and the Probability of calling In the M oney Convertible Bonds 95 Table 13 Relation between Agency Conflicts at the Issuance Announcem ent

D ay 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

T ab le 15 Liquidity Analysis 98

Table 16 Joint Distribution of B and y 99

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Figure Page Figure 1 Timing of the Model: W h o knows w hat and w h e n 10 0

Figure 2 V alues 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 e l 102

r

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A B S T R A C T

Diaz, Fernando Ph.D , Purdue University, M ay, 2 0 0 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 asym metric information and agency problems that explains the negative stock price reactions observed w hen 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 T hese firms also experience more adverse price reactions w hen the calling of these bonds is announced Finally, consistent with the unified model, I docum ent a positive relation betw een abnormal returns at issuance and the tim e elapsed between issuance and calling of convertible bonds.

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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

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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

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is assumed that there are two types of managers, one that always behave in the

interest of current stockholders -g ood 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

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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-the- money 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

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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.

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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.

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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.

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(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.

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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.

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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

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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.

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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

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.

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2.3 Stock price reactions to announcements of redemption

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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.

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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.

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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

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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

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.

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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.

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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

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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).

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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

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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

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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

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

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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.

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CHAPTER 4 A BAYESIAN MODEL OF ASYM M ETRIC 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

Q, 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.

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The project cash flows for type 6 = 0 2 firms First Order Stochastically

(4.2) 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]

The payoffs of admissible securities are assumed to be non-decreasing in x and satisfy limited liability Accordingly,

(4.6) 0 < < p ( x ) < x

The set of admissible securities includes equity, debt and convertible

securities Equity share is denoted by a e [0,1] The expected value of the cash flows from equity, given 0 = 0,, is given by aV, Debt is assumed to take the

form of a bond with face value F The bond is a standard debt contract with payoffs given by:

(4.7) Dt ( F ) = E\_ m in (X ,F )|3 ]

Since the payoffs from securities are assumed to be non decreasing in x,

it follows that D 2 (F) > Di(F) A callable convertible security is specified in the

model by a tuple (F, a, k, T1t T 2 ), where 7"* is the maturity date of the call option

redemption price, a 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 0 and makes his investment and financing decisions The market is uninformed about 0 and prices securities at their expected value At date 1,

nature reveals the firm’s 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.

Using the above framework, Chakraborty and Yilmaz (2003) show that there exists a callable convertible 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

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outcome Furthermore, the bond will be called (and converted by debt holders)

only when 9 =

02-Even though the pooling equilibrium at time t = 0 can be used as an

argument to explain the empirically observed negative market reaction to the issuance of convertible securities, two questions arise 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 can be justified? I conjecture that one of the key assumptions in the model is likely to be violated: managers do not always behave in favor of their current stock holders In the following section, I 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

I implicitly assume that a company that issues convertible debt has chosen this instrument based on its relative issuing cost to equity and straight debt Given the arguments put forward by Stein (1992), it is likely that for high- growth levered firms, with low ratios of tangibles to total assets, convertibles are the least costly instruments.8

8 Convertible bonds are typically unsecured instruments that are attractive to companies with few tangible assets and therefore have difficulties issuing straight debt Also, convertibles have fewer restrictive covenants, which makes them more attractive to managers This type of flexibility is likely to be most valuable for small firms with high growth opportunities where informational asymmetries make an equity

assets ratios rely heavily on convertibles.

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Consider the existence of two types of managers; one type of manager -

M A - always behaves in favor of her current stockholders The other type of

manager - M8-, besides caring for the wealth of her current stockholders, also

cares about the private benefits of control that arise from her position as the manager of the firm I assume that debt restricts the 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 negatively affect the wealth of the current stock holders of the firm It will also be assumed that the distribution of firm types is independent from the distribution of

types of managers:9 for each type of firm 9 there is a probability p of having a manager of type M 8 The ex ante probability of a firm being of type 0, is Aj The

timing and informational structure of the model is presented in Figure 1 Let’s

define B as the private benefits from control I assume that when there is an

agency problem, 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:

9 However, it can be argued that certain firm characteristics might attract more of one type of managers than other type of managers In that case, any signal about firm types will also be informative about manager types I do not allow for this possibility in the model.

r

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where VSH is the value of the firm accruing to its shareholders.10 It should be

noted that a manager’s utility function as defined in (4.8) 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

(4.8) 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 (4.9) 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.

I 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 (0*) In contrast, there exists a pooling equilibrium at

Proposition 1 (Existence o f a Bayesian Equilibrium)

For the Game defined by the above setup, there exists a Convertible Security

that induces a Bayesian Nash Equilibrium such that:

10 In equation (4.8) the utility function of the type A managers can just be defined as VSH However, the y is

included for tractability, and any monotonic transformation of the managers’ utility function represents the same underlying preferences as the original function.

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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;

of managers call and bondholders convert;

managers of type B call and bondholders convert, but type A managers

To show that such an equilibrium exists I 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

of manager that is in control of the firm, conditional on which G is revealed by

nature and on the decision of the manager regarding whether to call or not to call the convertibles.

Set of Beliefs {SB}

11 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, could have issued straight debt at time t = 0, separating

themselves from type B managers earlier.

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

Proposition 2 (Bond Holders Optimal Decision)

If the condition:

(4.10) D 2 ( F ) > a (V 2 - pB) > a ( V , - pB) > a ( V x- 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)

For the first inequality of condition (4.10) to hold, it must be assumed that there are no 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.12 The second inequality is a direct consequence

12 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.

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