Convertible Securities and Heterogeneity of Investor Beliefs

Current Version: February 2013

Abstract

We argue that convertible securities can better attract investors with different beliefs on

the firm’s future cash flows compared to straight bond and stock. We find that a firm is more

likely to issue convertibles rather than stock and straight bond when investors are more

heterogeneous in their beliefs. We also find that the positive impact of heterogeneous beliefs on

the likelihood of a convertible issuance is more pronounced when the amount of the security

issuance is larger. Overall, our findings provide a novel rationale based on investors’

heterogeneous beliefs for the use of convertibles in corporate external financing decisions.

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1. Introduction

Investors have heterogeneous prior beliefs on a firm’s value. The relation between the

heterogeneity of investor beliefs and security values has received a great deal of attention in the

finance literature. This research dates back to Miller (1977) and subsequently Harrison and

Kreps (1978), Mayshar (1983), and Morris (1996). Miller (1977) argues that, when investors

with heterogeneous beliefs are subject to short-sale constraints, stock prices would reflect the

opinion of optimistic investors and sell at a premium over fundamental values. Recently, many

studies follow this theoretical literature and empirically test Miller’s predictions. For example,

Chen, Hong, and Stein (2002) and Diether, Malloy, and Scherbina (2002) focus on the effect of

the heterogeneity of investor beliefs on future stock returns. They find evidence supporting the

predictions of Miller’s model.

However, most empirical researches in this literature focus on the effect of investors’

heterogeneous beliefs on the value of a firm’s stock. Few researches have studied the effect of

heterogeneous beliefs on the value of other types of securities. Also, it is not well understood

how the heterogeneity of investor beliefs affects a firm’s corporate financing decisions among

various security choices. In this paper, we attempt to partially answer these questions by focusing

on convertible securities, an important type of securities in corporate financing decisions. We

study how the heterogeneity of investor beliefs on a firm’s future cash flows affects the firm’s

incentive to issue convertible securities rather than straight bond and stock.

We conjecture that a firm is more likely to issue convertibles in its external financing

rather than straight bond and stock when investors are more heterogeneous in their beliefs on the

distribution of the firm’s future cash flows. In the following, we discuss briefly the intuition of

the conjecture. In Section 2, we will provide a numerical example and discuss the intuition in

more detail. Consider a risky firm which can generate either high or low cash flows with positive

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possibilities in the future. The firm needs to raise capital externally by issuing either straight

bond, stock, or convertible bond.1 There are two types of investors who could potential invest in

the firm’s securities. The first type of investors overestimate the upside of the firm’s future cash

flows and they assign a high probability to the possibility of high future cash flows. The second

type of investors underestimate the downside of the firm’s future cash flows and they assign a

low probability to the possibility of low cash flows.2 As a result, these two types of investors

value differently the same security so that they have different preferences over the firm’s

securities in their investment choices.

First consider stock and straight bond. Stock valuation is more sensitive to the upside

cash flows and bond valuation is more sensitive to the downside cash flows. Thus, the first type

of investors who overestimate the upside potential would overvalue stock to a larger degree than

straight bond. Correspondingly, they prefer stock over straight bond in their investment choices.

On the other hand, the second type of investors who underestimate the downside risk would

overvalue straight bond to a larger degree than stock. Correspondingly, they prefer straight bond

over stock in their investment choices. Such heterogeneous beliefs and the resulting different

investment preferences over the firm’s securities would not matter if the firm can manage to

issue stock only to the first type of investors and straight bond only to the second type of

1 In the discussion here and also in the numerical example in Section 2, we focus on only convertible bond to simply

exposition. However, our predictions are qualitatively the same for convertible bond and convertible preferred. In

our empirical test, we will test based on both types of convertible securities. 2 The investors we characterize here are both optimistic on the firm’s future cash flows, though in different ways.

We focus on optimistic investors since any securities issued by the firm will be purchased by only the investors who

are more optimistic than the other investors on the value of the firm (Miller (1977)). While we focus on only two

types of investors to simplify exposition of the paper, our intuition will go through for the existence of the other

types of investors. For example, some investors not only overestimate the upside of the future cash flows but also

underestimate the downside. These investors could prefer either stock or straight bond depending on whether their

overestimation of the upside dominates the underestimation of the downside or vice versa. Or some investors

underestimate the risk of the future cash flows. These investors would prefer straight bond over equity. The intuition

and the implications of our paper would remain unchanged if we consider these types of investors. As we will

discuss later, as long as there exist investors who have different preferences over the firm’s equity and bond,

convertibles would be a preferred means of external financing if the firm needs to attract these investors with

different preferences in its external financing.

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investors. However, when the amount of external financing is sufficiently large, the issuing firm

may have to finance from both types of investors. In this case, the firm could find it undesirable

to issue either straight bond or equity to both types of investors, since either straight bond or

stock is appealing only to one type of the investors but not the other type.

Unlike straight bond and stock, a convertible security can help attract the investors with

different preferences. A convertible security is a hybrid comprising a debt component and a

stock component. It has different consequences from straight bond and stock because the entire

issuance is in the form of debt if the convertible is never converted, and the entire issuance

becomes common stock upon conversion. The stock component helps the issuing firm attract the

first type of investors who prefer to invest in the firm’s equity. The debt component helps the

issuing firm attract the second type of investors who prefer to invest in the firm’s straight bond.

Thus, a convertible security has an advantage over straight bond and stock since it can help the

issuing firm attract the investors who have different beliefs and thus different investment

preferences over stock and straight bond.3

Following the above discussion, we argue that a convertible security is a preferred means

of external financing compared to straight bond and stock when (1) investors have heterogeneous

beliefs on the distribution of the firm’s future cash flows; and (2) the amount of external

financing is sufficiently large so that the firm has to finance from different investors with a

sufficiently large difference in their beliefs on the values of the firm’s securities. In consideration

of the first condition, our first hypothesis is that the likelihood of a convertible issuance rather

3 It is possible that the issuing firm can divide its external financing into partially stock financing and partially bond

financing, so that it can target stock financing at the investors who prefer to invest in stock and bond financing at the

investors who prefer to invest in bond. However, we argue that it is practically difficult and costly for the issuing

firm to estimate the financing capacities of the different investors with different beliefs and to divide its financing

accordingly to match the financing capacities of the different investors. Thus, the use of partially stock financing and

partially bond financing to match difference investor preferences, although theoretically possible, could be

practically infeasible (or prohibitively costly) to implement.

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than straight bond and stock issuances is higher when the heterogeneity of investor beliefs is

higher. In consideration of the second condition, we derive two hypotheses. Our second

hypothesis is that a firm is more likely to issue convertibles rather than straight bond and stock

when the amount of its external financing is larger. Our third hypothesis is that the impact of the

heterogeneity of investor beliefs on the likelihood of a convertible issuance (relative to the

likelihood of straight bond and stock issuances) is more pronounced when the amount of the

firm’s external financing is larger.

To test these three hypotheses, we need to proxy for the level of the heterogeneity of

investor beliefs. In most of our empirical studies, we use three proxies. Our first proxy is analyst

dispersion, based on the standard deviation of financial analysts’ forecasts on a firm’s one-year-

ahead earnings. A higher level of analyst dispersion indicates a higher level of heterogeneous

investor beliefs (Diether, Malloy, and Scherbina (2002)). Our second proxy is trading turnover of

a firm’s stock in the stock market. An increase in the heterogeneity of investor beliefs is

associated with an increase in trading turnover (see, e.g., Harris and Raviv (1993), Hong and

Stein (2003), and Scheinkman and Xiong (2003)). Our third proxy is idiosyncratic volatility. A

firm facing a higher level of heterogeneous investor beliefs experiences a larger idiosyncratic

volatility (see, e.g., Diether, Malloy, and Scherbina (2002), and Boehme, Danielsen, and Sorescu

(2006)).

Using these three proxies, we find evidence supporting our hypotheses. We find that the

likelihood of a firm issuing convertibles relative to the likelihood of issuing straight bond and

stock is higher when analysts disagree more on the firm’s earnings forecasts, when the firm’s

stock has a higher idiosyncratic volatility, or when the firm’s stock has a higher trading turnover.

We also find that the likelihood of a convertible issuance is higher when a firm raises a larger

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amount from its security offerings. Finally, we find that the positive effects of analyst dispersion,

trading turnover, and idiosyncratic volatility on the likelihood of a convertible issuance are more

pronounced when a firm raises a larger amount from its security offerings.

The literature on the use of convertible securities has provided some other explanations

other than the heterogeneous belief explanation. One important explanation is based on the

asymmetric information between firm insiders and outside investors regarding the issuing firm’s

true value. For example, Brennan and Kraus (1987) suggest that convertible securities can

costlessly mitigate investment inefficiencies resulting from information asymmetry.

Constantinides and Grundy (1989) and Stein (1992) suggest that convertible securities can signal

information about a firm’s true value in the presence of information asymmetry if the firm is

allowed to buy back its shares or if the firm faces a large cost of financial distress. Since our

heterogeneity variables could be affected by the degree of information asymmetry, one may

concern that our empirical findings could also be driven by information asymmetry. However,

we argue that our findings are better explained by the heterogeneous belief explanation than by

the asymmetric information explanations. First, one prediction from the asymmetric information

theories as in Constantinides and Grundy (1989) and Stein (1992) is that a convertible security is

more likely to be used as a signal when the firm faces a larger degree of information asymmetry.

However, in these theories, both convertibles and straight bond can serve as signals while equity

cannot. Thus, while these asymmetric information theories predict the use of convertibles versus

equity in a way consistent with our findings, they do not provide any predictions on the use of

convertibles versus straight bond.4

Second, to further distinguish between the information-related

4 The asymmetric information theories focus on separating equilibria when a firm faces a choice among convertibles,

straight bond, and equity in its external financing. A pooling equilibrium could also occur when the cost of

separation by using convertibles or straight debt (e.g., the financial distress cost as in Stein (1992)) is prohibitively

large. In the case of a pooling equilibrium, it can be shown that the higher-value firm would follow a pecking order

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explanations and the heterogeneous belief explanation, we also use breadth of mutual fund

ownership as another proxy for the heterogeneity of investor beliefs. We find that a firm is more

likely to issue convertibles rather than straight bond and stock when the firm’s breadth of mutual

fund ownership increases. Breadth of mutual fund ownership is negatively correlated with the

heterogeneity of investor beliefs (Chen, Hong, and Stein (2002)), and it is unlikely to be affected

by information asymmetry. Thus, while our result based on breadth of mutual fund ownership

supports the heterogeneous belief explanation, it cannot be explained by the information-related

explanations.

However, it is not our view that the heterogeneity of investor beliefs is the only factor

driving the issuance of convertibles. We discussed above that the asymmetric information

theories as in Stein (1992) can explain our findings on the choice between convertibles and

equity though they cannot explain our findings on the choice between convertibles and straight

bond. Green (1984) also argues that convertible securities can mitigate the risk shifting

incentives of equity holders in the presence of debt outstanding. Mayers (1998) argues that

convertible securities can allow the management of the firm with significant growth options to

better match capital inflow with expected investment outlays. Thus, similar to the issuances of

other securities like debt and equity, the issuance of convertibles could be potentially driven by

other factors in addition to the heterogeneity of investor beliefs that we analyze in the paper. We

choose to focus in the paper only on the heterogeneity of investor beliefs, abstracting away from

the other considerations to differentiate our paper from the other studies in the literature.

of financing: straight bond, convertibles, and stock. This is because the value of stock is most sensitive and the value

of straight debt is least sensitive to the problem of information asymmetry, with the value of convertibles in between.

Clearly, the pecking order predicted by the pooling equilibrium cannot explain our findings on the issuance of

convertibles versus the issuances of straight bond and equity.

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Our paper is related to the large literature on heterogeneous investor beliefs, including

some recent papers in behavioral finance. As we discussed earlier, the literature was set forth

originally by Miller (1977). Recently, several papers incorporate Miller’s insight in more formal

and refined models. For example, Chen, Hong, and Stein (2002) develop a model showing that

the combination of the heterogeneity of investor beliefs and the short-sale constraints cause

equity overpricing. Scheinkman and Xiong (2003) and Hong, Scheinkman, and Xiong (2006)

further study the asset trading and the asset pricing implications of heterogeneous beliefs. Apart

from the above theoretical work, many papers study empirically the impact of heterogeneous

beliefs on subsequent stock returns (see earlier discussions). Recently, a number of empirical

papers also focus on the impact of heterogeneous beliefs on corporate financing and investment

decisions. See, e.g., Moeller, Schlingemann, and Stulz (2007) and Chatterjee, John, and Yan

(2012) on the effect of heterogeneous investor beliefs on the pricing in mergers and acquisitions.

Unlike the previous studies, our study focuses on the impact of the heterogeneity of investor

beliefs on a firm’s convertible issuance.

The paper is organized as follows. Section 2 provides a numerical example and discusses

the intuition underlying the choice of convertibles in the presence of heterogeneous investor

beliefs. Section 3 develops our hypotheses. Section 4 describes our sample and specifies the

variables we use in our empirical tests. Section 5 empirically investigates the relative likelihood

of convertibles versus straight bond and stock in a firm’s external financing. Section 6 concludes.

2. A Numerical Example on Convertible Issuance

In this section, we present a numerical example on a firm’s external financing choice

among convertible bond, stock, and straight bond in the presence of heterogeneous investor

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beliefs on the distribution of the firm’s future cash flows.5 We focus on only convertible bond to

simply exposition, though our results will go through for convertible preferred as well. We then

discuss the intuition underlying the choice based on the numerical example. For simplicity, we

assume that all the agents, including the issuing firm and outside investors are risk-neutral. We

also assume that the risk-free rate of return is zero.

The example has two dates (time 0 and 1). Consider a risk-neutral entrepreneur owing an

all-equity firm.6 The firm has no internal capital and it needs to finance externally to invest in a

new positive net present value project. For simplicity, we assume that the firm has no other

ongoing projects, so that the cash flow received by the firm is the same as that generated by the

new project and the market value of the firm equals the value of the project.

The cash flow from the new project is realized at time 1. We assume that the cash flow of

the project at time 1 can be either high ($20), medium ($8), or low (0). Let the entrepreneur (firm

insider) believe that the firm will generate the high cash flow at time 1 with a probability of 30%,

the medium cash flow with a probability of 30%, and the low cash flow with a probability of

40%. Thus, the intrinsic value of the firm (i.e., the value of the project) under the entrepreneur’s

belief is (30% × $20) + (30% × $8) + (40% × 0) = $8.4.

2.1. Heterogeneous Investor Beliefs

The key feature of the example is that outside investors have heterogeneous beliefs about

a firm’s future cash flow distribution and their beliefs are different from the entrepreneur’s belief.

Miller (1977) argues that in the presence of heterogeneous beliefs on a firm’s value, the firm’s

5 Our numerical example in this section will be used to motivate our empirical studies. For this purpose, we use the

numerical example to demonstrate that there exists a parameter space where the equilibrium as characterized in the

example could occur. We will later develop testable hypotheses based on this parameter space. There could exist

other equilibria in the other parameter spaces. Due to space constraint, we will not characterize all the other

equilibria. 6 We assume here that the firm is an all-equity firm and the entrepreneur owns all the equity in the firm for the sake

of simplifying exposition. If we assume that the firm has a positive financial leverage and the entrepreneur owns

only a fraction of the equity, the intuition and the implications in the paper would remain qualitatively unchanged.

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stock is bought and held by the investors whose beliefs are more optimistic than those of the

other investors in the market. Following Miller’s argument, we focus only on optimistic

investors in this example.7 We assume there are two types of optimistic investors. The difference

between these two types of optimistic investors is characterized by their different beliefs on the

distribution of the firm’s future cash flows. The first type of optimistic investors overestimate

and assign a high probability to the upside potential of the future cash flows. The second type of

optimistic investors underestimate and assign a low probability to the downside risk of the future

cash flows.8 In particular, we assume that the belief of the first type of optimistic investors is

such that the firm will generate the high cash flow ($20) at time 1 with a probability of 40%, the

medium cash flow ($8) with a probability of 20%, and the low cash flow (0) with a probability of

40%. Under this belief, the first type of investors would value the firm optimistically at $9.6,

which is above the intrinsic value of the firm ($8.4). We also assume that the belief of the second

type of optimistic investors is such that the firm will generate the high cash flow ($20) at time 1

with a probability of 30%, the medium cash flow ($8) with a probability of 40%, and the low

cash flow (0) with a probability of 30%. Under this belief, the second type of investors would

value the firm at $9.2, which is also above the firm’s intrinsic value.

2.2. Menu of Securities to Issue

We assume that the entrepreneur has to finance an amount of $6 externally to fund the

investment in the new project. He can issue one of the three securities to raise the required

external capital: straight risky bond, convertible bond, or stock. If the entrepreneur chooses to

7 In other words, we focus on investors who overvalue the firm’s securities relative to their respective fundamental

values. It is also possible that investors buy a security when they undervalue the security but undervalue to a less

degree compared to the other investors in the market. This possibility is likely to happen when the market as a whole

is pessimistic on the firm’s value. The implications of our example will go through in this pessimistic market as well

if we focus on the types of investors who are less pessimistic than the other investors. 8 As we discussed in the introduction, optimistic investors could be different in their beliefs on the firm’s future cash

flows in different ways. As it will be clear later, the implications of the example will go through as long as these

optimistic investors have different preferences over the firm’s straight bond and stock in their investment choices.

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issue straight bond, he receives the financed amount up-front at time 0 and promises to pay a

fixed amount C (i.e., the face value of bond) to the bondholder at time 1. If he chooses to issue

convertible bond, he determines the face value F, the conversion ratio e, and the call price K at

time 0. Before time 1, the entrepreneur has the right to redeem (“call”) the convertibles at the call

price, at which point convertible holders will decide whether or not to convert. If convertible

holders do convert, they receive a faction e of the total equity based on the pre-specified

conversion ratio. On the other hand, if the convertibles are not called, they are equivalent to

straight debt, with the firm obligated to pay the face value F to convertible holders at time 1. The

objective of convertible holders in their conversion decision is to maximize the expected value of

the cash flows they obtain from the issuing firm. Thus, convertible holders choose to convert

their convertibles to equity only when the value of the equity obtained through the conversion

exceeds the promised payment (face value) of the convertibles. Finally, if the entrepreneur

chooses to issue stock, he exchanges a fraction s of the total equity to investors for the financed

amount.

We also assume that each type of optimistic investors is endowed with an amount of $3.

Thus, to raise the required external financing of $6, the entrepreneur needs to design the security

so that the security will be bought by both types of optimistic investors. In sum, the objective of

the entrepreneur in his external financing is to maximize the expected long-term (time 1) value

of the equity held by him (or equivalently, his time 0 expectation of the cash flows accruing to

the equity retained by him at time 1), subject to the break-even constraints that both types of

investors will break even by buying the issued security.

2.3. Convertible Bond versus Straight Bond and Stock

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In the following, we first study the value of the entrepreneur’s objective if he chooses to

issue each of the above securities. We then compare these values and discuss which security is

better off for the entrepreneur to issue.

First, consider the case where the entrepreneur chooses to issue straight bond for the

external financing of $6. In this case, the entrepreneur has to set the face value of the bond, F, so

that the following break-even constraints have to be satisfied:

40% × Min(F, $20) + 20% × Min(F, $8) + 40% × Min(F, $0) ≥ $6, and (1)

30% × Min(F, $20) + 40% × Min(F, $8) + 30% × Min(F, $0) ≥ $6. (2)

Constraints (1) and (2) ensure that the bond issued by the entrepreneur will be accepted by both

the first type of optimistic investors who overestimate the upside and the second type of

optimistic investors who underestimate the downside. Constraint (1) yields F ≥ $11 and

constraint (2) yields F ≥ $9.33. Thus, to satisfy both constraints and to maximize the

entrepreneur’s objective, it is better off for the entrepreneur to set the face value of the straight

bond F* = $11. The expected payoff under F

* to the entrepreneur is П (bond) = 30% × ($20 – F

*)

= $2.7.

Second, consider the case where the entrepreneur issues stock as the only security for the

external financing of $6. In this case, the entrepreneur has to set s, the fraction of the total equity

in exchange for the financed amount, to satisfy the following break-even constraints:

s × (40% × $20 + 20% × $8 + 40% × $0) ≥ $6, and (3)

s × (30% × $20 + 40% × $8 + 30% × $0) ≥ $6. (4)

Constraints (3) and (4) ensure that the stock issued by the entrepreneur will be accepted by both

types of optimistic investors. Constraint (3) yields s ≥ 0.625 and constraint (4) yields s ≥ 0.652.

Thus, to satisfy both constraints and to maximize the entrepreneur’s objective, it is better off for

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the entrepreneur to set the exchange ratio s* = 0.652. The expected payoff under s

* to the

entrepreneur is П (stock) = (1 – s*) × (30% × $20 + 30% × $8) = $2.92.

Third, consider the case where the entrepreneur issues convertible bond as the only

security for the external financing of $6. In this case, the entrepreneur has to set e, the conversion

ratio, F, the face value, and K, the call price, to satisfy the following constraints:

40% × e × $20 + 20% × Min(F, $8) + 40% × Min(F, $0) ≥ $6, (5)

30% × e × $20 + 40% × Min(F, $8) + 30% × Min(F, $0) ≥ $6, (6)

e × $20 ≥ F (7)

Constraints (5) and (6) ensure that the convertibles issued by the entrepreneur will be accepted

by both types of optimistic investors. Both constraints incorporate the consideration that the call

price will be set at $10 ≤ K* ≤ $20, so that the convertibles will be called prior to time 1 at the

high cash flow but not at the medium and the low cash flows. It can be shown that it is more

costly for the entrepreneur to set K < $10 compared to the case where $10 ≤ K* ≤ $20.

Constraint (7) ensures that the convertible holders will convert their convertibles to equity once

the convertibles are called at the high cash flow.

In this numerical example, we consider the case where convertible bond will be sold at

par so that F* = $6. Both constraints (5) and (6) yield e ≥ 0.6. Thus, it is better off for the

entrepreneur to set the conversion ratio e* = 0.6 and the call price K

* ≥ $10. The entrepreneur’s

expected payoff under this design is П (convertibles) = 30% × (1 – e*) × $20 + 30% × ($8 - $6) =

$3.

Finally, we compare three types of securities, i.e., convertible bond, straight bond, and

stock. According to the above discussions, the expected payoffs to the entrepreneur by issuing

straight bond, stock, and convertible bond are $2.7, $2.92, and $3, respectively. Thus, it is better

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off for the entrepreneur to issue convertible bond rather than stock or straight bond, since his

expected payoff is the highest from issuing convertible bond.

2.4. Intuitive Analysis

In the following, we discuss the intuition underlying the numerical example above. In the

above numerical example, the key assumption is that investors have different beliefs on the

distribution of the firm’s future cash flows and thus different preferences for stock, straight bond,

and convertible bond. In particular, the first type of investors, who overestimate the probability

of the upside cash flow, overvalue all three of the firm’s securities relative to their respective

fundamental values. However, under their optimistic belief on the upside, the first type of

investors would overvalue equity to the highest degree followed by convertible bond, and

overvalue straight bond to the lowest degree. This is because stock can help investors capture the

upside cash flow while straight bond cannot. This is also because convertible bond is a hybrid of

both stock and straight bond, so that its level of overvaluation falls between those of straight

bond and stock. Thus, if the entrepreneur wants to price his security to ensure the participation

from the first type of investors, the financing cost to the entrepreneur would be the highest for

straight bond, followed by convertible bond, and equity. Here and also in the following, we

define the financing cost as the cost of the security to the issuing firm under the entrepreneur’s

belief. In our numerical example, it can be shown that the entrepreneur has to incur a financing

cost of $5.7 to attract the first type of investors to buy the straight bond, $5.4 to buy the

convertible bond, and $5.25 to buy the stock.9

9 To attract the first type of investors to buy convertible bond, the entrepreneur would set the convertibles at F=$6,

e=0.6, and K≥$10. The financing cost to the entrepreneur is 30%×$20×0.6+30%×$6=$5.4 and the payoff to the

entrepreneur is $3 ($5.4+$3=$8.4, which is the true value of the project). To attract the first type of investors to buy

bond, the entrepreneur would set the face value of bond F=$11. The financing cost to the entrepreneur is

30%×$11+30%×$8=$5.7 and the payoff to the entrepreneur is $2.7. To attract the first type of investors to buy

stock, the entrepreneur would set the fraction of equity e=0.625. The financing cost to the entrepreneur is

(30%×$20+30%×$8)×0.625 =$5.25 and the payoff to the entrepreneur is $3.15.

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On the other hand, the second type of investors underestimate the probability of the

downside cash flow, so that they also overvalue all three securities relative to their respective

fundamental values. However, in contrast to the first type, the second type of investors would

overvalue straight bond to the highest degree and stock to the lowest degree, with convertible

bond in between. This is because bond is most sensitive to the underestimation of the downside

(thereby most overvalued) while stock is least sensitive (thereby least overvalued). Thus, if the

entrepreneur wants to price his security to ensure the participation from the second type of

investors, his financing cost would be the highest for stock, followed by convertible bond and

straight bond. In our numerical example, it can be shown that the entrepreneur has to incur a

financing cost of $5.478 to attract the second type of investors to buy the stock, $5.4 to buy the

convertible bond, and $5.2 to buy the straight bond.10

From the discussion above, it is clear that straight bond is the most costly security for the

entrepreneur to issue to the first type of investors, while stock is the most costly security for the

entrepreneur to issue to the second type of investors. However, to raise the required amount of $6,

the entrepreneur has to seek financing from both types of investors. In this case, if the

entrepreneur chooses to issue any security, he has to price the security so that both investors will

participate and invest in the security. As a result, it is costly for the entrepreneur to issue either

straight bond or equity since for each security, the entrepreneur has to lower the price of the

security to appeal to the type of the investors who value the security the least among all three

securities.

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To attract the second type of investors to buy convertible bond, the entrepreneur would set the convertibles at

K≥$10, e=0.6, and F=$6. The financing cost to the entrepreneur is 30%×$20×0.6+30%×$6=$5.4 and the payoff to

the entrepreneur is $3. To attract the second type of investors to buy bond, the entrepreneur would set the face value

of bond F=$9.33. The financing cost to the entrepreneur is 30%×$9.33+30%×$8=$5.2 and the payoff to the

entrepreneur is $3.2. To attract the second type of investors to buy stock, the entrepreneur would set the fraction of

equity e=0.652. The financing cost to the entrepreneur is (30%×$20+30%×$8)×0.652 =$5.478 and the payoff to the

entrepreneur is $2.922.

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In our numerical example, if the entrepreneur chooses to issue stock, he has to price its

stock to appeal to the second type of investors who value stock the least among all three

securities. The financing cost of issuing stock is $5.478. On the other hand, if the entrepreneur

chooses to issue straight bond, he has to price the bond to appeal to the first type of investors

who value straight bond the least among all three securities. The financing cost of issuing bond

is $5.7.

In comparison to straight bond and equity, convertible bond could be less costly for the

entrepreneur to issue. Convertible bond, being a hybrid of debt and equity, is valued in between

stock and straight bond by both types of investors, thereby having a financing cost in between

stock and straight bond. Thus, unlike straight bond and stock, which are priced based on the most

unfavorable investor valuations among all three securities, convertible bond could be priced in a

better term. In our example, if the entrepreneur chooses to issue convertible bond, he has to incur

a financing cost of $5.4, which is lower than both the financing cost of equity ($5.478) and the

financing cost of straight bond ($5.7).

2.5. Discussions

It is possible that the entrepreneur can raise $3 of its financing by issuing stock and

another $3 by issuing straight bond. The entrepreneur could price stock and straight bond in such

a way that only the first type of investors will accept stock (by incurring a financing cost of

($3/$6) × $5.25) and only the second type of investors will accept straight bond (by incurring a

financing cost of ($3/$6) × $5.2). In this way, the entrepreneur would incur a total financing cost

of 0.5× $5.25 + 0.5 × $5.2 = $5.225, which is lower than the financing cost of an all-convertible

issuance ($5.4).

17

We argue that such a financing of partially stock and partially bond, although

theoretically better off to the entrepreneur, could be practically infeasible. The entrepreneur can

divide the financing to exactly match the endowment of each type of investors only when the

information on investors’ endowments is common knowledge to the entrepreneur. However, in

practice, the entrepreneur may not have such information unavailable to himself. Consider a

modification of our numerical example. Assume that the first and the second types of investors

turn out to be endowed with $4 and $2 respectively and this information is unknown to the

entrepreneur. Also assume that the entrepreneur, without the knowledge of the endowments,

decides to divide its external financing into stock financing of $3 and bond financing of $3. In

this case, two possible equilibria could happen. First, the entrepreneur could incur a financing

cost of ($3/$6) × $5.25 from stock financing to the first type of investors and a cost of ($3/$6) ×

$5.7 from bond financing to both types of investors, a total cost of $5.475. Second, the

entrepreneur could also incur a financing cost of ($3/$6) × $5.7 from bond financing to the first

type of investors and a cost of ($3/$6) × $5.478 from stock financing to both types of investors, a

total cost of $5.599. In both scenarios, the financing cost of partially stock and partially bond is

higher than that of all-convertible ($5.4).

Thus, the entrepreneur could find it more costly to issue partially stock and partially bond

compared to issuing all-convertible if he has little information on how much can be raised from

each type of investors and if he cannot divide his external financing to exactly match the

financing capacity of each type of investors.

3. Testable Hypotheses

18

It is worth noting that although our numerical example focuses on convertible bond, the

intuition and the implication can be applied to convertible preferred as well. Thus, our numerical

example implies that when investors have heterogeneous beliefs on the firm’s future cash flows,

it could be better off for the entrepreneur to finance by convertible securities compared to stock

or straight bond. When investors become more heterogeneous on their valuations of stock and

straight bond, the issuing firm would find it more costly to issue stock or straight bond to attract

these investors with a higher heterogeneity of beliefs. As a result, the issuing firm is more likely

to issue convertible securities rather than stock and straight bond. Thus, we predict that the

likelihood of issuing convertible securities rather than straight bond and stock becomes higher

when the heterogeneity of investor beliefs is higher. This is our first hypothesis (H1) to test.

In Section 2, an important condition for convertibles to emerge as the preferred security

to issue in the presence of heterogeneous investor beliefs is that the amount of external financing

should be sufficiently large. In the case of a large amount of external financing, the entrepreneur

would find it insufficient to raise the required capital from a certain type of investors with

homogeneous beliefs, so that the entrepreneur has to price the issued securities to attract the

investors with heterogeneous beliefs. Thus, we predict that a firm is more likely to issue

convertible securities rather than straight bond and stock when the amount of its external

financing is larger. This is our second hypothesis (H2) to test. We also predict that the impact of

the heterogeneity of investor beliefs on the likelihood of a convertible issuance is more

pronounced when the amount of the firm’s external financing is larger. This is the third

hypothesis (H3) we test.

3. Sample and Variable Construction

19

3.1. Data and Sample Selection

We create our initial sample of security issuances from the Securities Data Corporation’s

(SDC) New Issues database. We identify all bond offerings, convertible offerings, and stock

offerings in the United States between 1986 and 2005. We require all issuing firms to be

incorporated in the U.S. For equity offerings, we limit our sample to those firms that are

identified by CRSP share type codes of 10 and 11. For debt offerings, we exclude leveraged buy-

outs, multi-currency offerings, exchangeable debt or debentures, mortgages, and medium-term

notes. For convertible offerings, we include both convertible debentures and convertible

preferred, but we exclude mandatory convertibles. We also exclude 144A shelf registered

offerings and any simultaneous offerings of bond, equity, convertibles, preferred stock, and

warrants. For most of our studies, we focus on public offerings in the U.S. market. Our sample of

public offerings consists of 681 convertible offerings, 4,750 straight bond offerings, and 5,827

seasoned equity offerings. In one of the robustness checks, we also study private placements of

convertibles, debt, and equity. Our sample of private offerings consists of 242 convertible

offerings, 2,171 straight bond offerings, and 1,217 equity offerings. Table 1 provides a

description of our sample broken down by years, by securities, and by the public/private status of

offerings.

We then match our sample of issuing firms to Standard & Poor’s Compustat files to

extract financial statement information; to the Center for Research in Securities Prices (CRSP) to

extract stock prices and stock trading volume; to the Institutional Brokers Estimate System

(IBES) to extract data on analyst coverage; and finally to the CDA/Spectrum Mutual Funds

Historical Files to extract data on mutual fund holdings. As a result of these matches, our final

20

sample size reduces somewhat and it varies in the different tests based on the data availability of

the relevant variables.

3.2. Measuring the Heterogeneity of Investor Beliefs

A central variable of interest in our study is the heterogeneity of investor beliefs. We use

three proxies. Our first proxy is the dispersion of financial analysts’ forecasts on the firm’s one-

year-ahead earnings (see Diether, Malloy, and Scherbina (2002)).11

The higher the dispersion in

analysts’ earnings forecasts, the higher the level of the heterogeneity in investor beliefs. We

calculate analyst forecast dispersion (DISP) as the standard deviation of analysts’ earnings

forecasts on the last reporting date prior to the announcement date of the security issuance,

scaled by the firm’s market price at the prior fiscal year end. We code DISP as missing if there

are less than three financial analysts covering the firm.

Many studies suggest that trading volume contains information about investors’

heterogeneous beliefs. For example, Harris and Raviv (1993), Hong and Stein (2003), and

Scheinkman and Xiong (2002) present models suggesting that difference of investor opinions

motivates trades and causes stock mispricing. In view of these studies, we use trading turnover as

the second proxy for the heterogeneity of investor beliefs. An increase in trading turnover

indicates an increase in the heterogeneity of investor beliefs. We calculate trading turnover

(TUNROVER) as trading volume/shares outstanding, adjusted by the average of the exchange

where the stock is trading, over the last 180 days prior to the announcement date of the security

issuance.

Our third proxy for the heterogeneity of investor beliefs is idiosyncratic volatility (RISK),

calculated as 100 times the standard deviation of the market-adjusted stock returns in the last 180

11

The data we use in the calculation of earnings forecasts come from the Summary History file of I/B/E/S. Diether

et al. (2002) report a rounding bias due to stock splits, but they find that the bias does not affect their results.

21

days prior to the announcement date of the security issuance. Many studies argue that a higher

idiosyncratic volatility indicates a larger degree of the heterogeneity of investor beliefs (see, e.g.,

Diether, Malloy, and Scherbina (2002), and Boehme, Danielsen, and Sorescu (2005)).

We provide in Table 2 the sample statistics of the above three heterogeneity variables.

We also compare the values of these heterogeneity variables pair-wise among convertible,

straight bond, and stock issuers. The pair-wise differences are tested by both the t-test and the

Wilcoxon rank-sum test. Table 2 shows that convertible issuers have higher values of analyst

dispersion (DISP) and abnormal trading turnover (TURNOVER) than both straight bond issuers

and stock issuers. Convertible issuers also have a higher value of idiosyncratic volatility (RISK)

than bond issuers. All these differences are significant at the 1% level in both the t-test and the

Wilcoxon test. They are consistent with notion that convertible issuers face more heterogeneous

investor beliefs compared to straight bond issuers and stock issuers. Table 2 also shows that

convertible issuers have a smaller value of idiosyncratic volatility than stock issuers. However,

in an unreported result, we find that this negative difference in idiosyncratic volatility between

convertible and stock issuers disappears after we control for firm size.

In one of our robustness checks, we also proxy for the heterogeneity of investor beliefs

by breadth of mutual fund ownership, using the quarterly mutual fund holdings data from

CDA/Spectrum. Chen, Hong, and Stein (2002) suggest that breadth of mutual fund ownership is

negatively correlated with diversity of opinion. They also suggest that change in breadth of

mutual fund ownership (ΔBreadth) is a better proxy than is the level, since ΔBreadth purges firm

fixed effects. Following their approach, we also use ΔBreadth in our study, where ΔBreadth is

the change in the number of mutual funds who hold the firm’s shares from the previous quarter

to the current quarter, divided by the total number of mutual funds in the previous quarter. A

22

lower level of ΔBreadth indicates a higher level of the heterogeneity of investor beliefs. Chen,

Hong, and Stein (2002) also suggest that any analysis on ΔBreadth needs to control for the

change in mutual fund holdings (ΔHold), since ΔBreadth could be correlated with ΔHold. We

calculate ΔHold as the change in the percentage of the firm’s shares held by all mutual funds.

We provide in Table 2 sample statistics for ΔBreadth, as well as the pair-wise differences

in ΔBreadth between the different kinds of security issuers. Table 2 shows that convertible

issuers on average have a lower value of ΔBreadth than stock issuers. This difference is

consistent with most of the sample statistics of the other three heterogeneity variables. It suggests

that the level of the heterogeneity of investor beliefs is higher on convertible issuers than on

equity issuers. However, convertible issuers on average have a higher value of ΔBreadth than

straight bond issuers. In an unreported result, we find that the positive difference in ΔBreadth

between convertible and bond issuers turns to negative once we control for firm size.

3.3. Construction of Other Variables

We also construct the following control variables. We calculate firm size (SIZE) as the

logarithm of the market value of assets where the market value of assets equals the book value of

debt plus the market value of equity; market-to-book ratio (MB) as the ratio between the book

value to the market value of equity; long-term debt ratio (LTDEBT) as the ratio of the amount of

long-term debt to the book value of total assets; operating performance (PROFIT) as operating

income before interest, taxes, depreciation, and amortization scaled by the book value of assets;

capital expenditures (CAPEX) as the amount of capital expenditures scaled by the book value of

assets; offering size (VALUE) as the log amount raised in the offering; cash dividends (DIVD)

as a dummy variable of non-zero cash dividends; historical stock return (RETURN) as the

cumulative market-adjusted stock return in the 180 trading days prior to announcement; and

23

number of analysts (NUMEST) as the number of financial analysts covering the firm as reported

in I/B/E/S.

We provide in Table 2 the sample statistics of some control variables, grouped by

convertible offerings, straight bond offerings, and stock offerings. As can be seen, the offering

size (VALUE) of convertible issuers is larger than that of equity issuers but smaller than that of

straight bond issuers. However, it is worth noting that the smaller average offering size of

convertible issuers compared to bond issuers is due to the smaller firm size of convertible

issuers. As we find in an unreported test, if we control for firm size by scaling offering size by

market capitalization, the ratio of offering size to market capitalization is larger for convertible

issuers than for bond issuers.

Table 2 also shows that, compared to equity issuers, convertible issuers have a larger firm

size (SIZE), a lower market-to-book ratio (MB), a lower historical stock return performance

(RETURN), a higher long-term debt ratio (LTDEBT), and a higher operating performance

(PROFIT). Compared to straight bond issuers, convertible issuers have a smaller firm size

(SIZE), a higher market-to-book ratio (MB), a higher historical stock return performance

(RETURN), a lower long-term debt ratio (LTDEBT), and a lower operating performance

(PROFIT).

4. Empirical Findings

4.1. Likelihood of Issuing Convertibles versus Stock and Straight Bond

In this subsection, we test the first two hypotheses. Our first two hypotheses state that a

firm is more likely to issue convertibles rather than stock and straight bond when the firm faces a

higher level of the heterogeneity of investor beliefs and when the firm raises a larger amount of

24

external capital. We test these two hypotheses by running the following multinomial logistic

model:

, j)Pr(y321

ZZZ

Z

eee

e j

(8)

where j = 1, 2, 3 stands for unordered choices for convertible offerings, straight bond offerings,

and stock offerings, respectively. The vector of independent variables Z consists of a proxy for

the heterogeneity of investor beliefs, offering size (VALUE), and the control variables. The

heterogeneity variable is analyst dispersion (DISP), abnormal trading turnover (TURNOVER),

or idiosyncratic volatility (RISK). The control variables consist of firm size (SIZEt-1), market to

book ratio (MBt-1), long term debt ratio (LTDEBTt-1), historical operating performance

(PROFITt-1), historical stock return performance (RETURNt-1), dummy of cash dividend (DIVDt-

1), and capital expenditures (CAPEXt-1). In the regressions where DISP is the heterogeneity

variable, we also control for the number of analyst following (NUMEST).

We estimate model (8) using the method of maximum likelihood estimation. We treat

convertible offerings (j = 1) as the base category so that in this regression model, we estimate the

likelihood of straight bond offerings relative to the likelihood of convertible offerings (“bond

equation”) and the likelihood of stock offerings relative to the likelihood of convertible offerings

(“stock equation”). To be consistent with the first hypothesis, we expect the coefficients of all

three heterogeneity variables, i.e., DISP, TURNOVER, and RISK, to be negative in both the

bond equation and the stock equation. To be consistent with the second hypothesis, we expect

the coefficient of offering size, i.e., VALUE, to be negative in both the bond equation and the

stock equation.

We present the results from regression (8) in Table 3. We first run regressions with year

dummies but not industry dummies as controls, followed by regressions with controls for both

25

year and industry dummies. Industries are defined by the first two-digit SIC codes.

Heterogeneity of investor beliefs could be time varying and industry specific. Thus, controlling

for both year and industry dummies could potentially reduce the economic significance of our

results. Nevertheless, we choose to control for both dummies in regression (8) to ensure

robustness of our results.

Our results in Table 3 are consistent across all three heterogeneity variables. The

coefficients of DISP, TURNOVER, and RISK are negative and they are statistically significant

in both the bond equation and the stock equation. These results show that a firm is less likely to

issue straight bond or stock rather than convertibles when the firm experiences a higher level of

dispersion among financial analysts on its earnings forecasts, a higher share trading turnover, or

a higher idiosyncratic volatility in its stock returns.

In unreported results, we have also calculated the marginal effect of each heterogeneity

variable on the likelihood of a firm issuing stock or straight bond (rather than convertibles). We

calculate the marginal effect of DISP, TURNOVER, or RISK as the sample mean of the

individual marginal effects, where each individual marginal effect is based on each firm-level

observation in our sample. For example, for the regression in column (2) in Table 3, we find that

the marginal effect is -1.212 for DISP. For the regressions in columns (4) and (6), the marginal

effects are -0.0143 and -0.151 for TURNOVER and RISK, respectively. These numbers show

that a one-standard-deviation increase in DISP, TURNOVER, or RISK from the respective mean

will decrease the likelihood of a straight bond offering or a stock offering, rather than a

convertible offering, by 0.99%, 1.32%, or 1.50%, respectively. Overall, our results in Table 3

support our first hypothesis. They suggest that a firm is more likely to issue convertibles rather

than straight bond and stock when the firm’s heterogeneity of investor beliefs is greater.

26

Table 3 also shows that the coefficient of VALUE, the amount raised from security

offerings, is negative in both the bond equation and the stock equation. It is statistically

significant at the 1% level in all regressions. In unreported results, we have also calculated the

marginal effect of VALUE on the likelihood of a firm issuing straight bond or stock. For

example, for the regressions reported in column (2), (4), and (6), the marginal effects of VALUE

are -0.0488, -0.0557, and -0.0613, respectively. These numbers show that a one-standard-

deviation increase in VALUE from its mean will decrease the likelihood of a straight bond

offering or a stock offering, rather than a convertible offering, by 5.38%, 7.17%, and 7.81%,

respectively. These results support our second hypothesis that a firm is more likely to issue

convertibles rather than straight bond and stock when the firm has to raise a large amount of

external capital and thereby has to attract more investors with heterogeneous investor beliefs.

Finally, Table 3 also shows that a firm is more likely to issue straight bond and less likely

to issue convertibles when the firm has a larger firm size, a lower market-to-book ratio, a higher

long-term debt ratio, a better historical operating performance, and a poorer historical stock

return performance. On the other hand, a firm is more likely to issue stock and less likely to issue

convertibles when the firm has a larger firm size, a higher market-to-book ratio, and a better

historical stock return performance.

4.2. Robustness checks

First, we run a robustness check based on an alternative proxy for the heterogeneity of

investor beliefs. One potential concern for our tests above is that all three heterogeneity

variables, DISP, TURNOVER, and RISK, could be affected by the degree of information

asymmetry. To address this concern, we re-run regression (8) with change in breadth of mutual

fund ownership, ΔBreadth, as the proxy for the heterogeneity of investor beliefs. On the one

27

hand, ΔBreadth is negatively related to the heterogeneity of investor beliefs. On the other hand,

ΔBreadth is unlikely to be affected by asymmetric information. Thus, our results based on

ΔBreadth can help demonstrate that the heterogeneity of investor beliefs is indeed an important

determinant of convertible financing. As we discussed earlier, we use convertible issuances as

the base category and we estimate the likelihood of straight bond and stock issuances relative to

convertible issuances in regression (8). Thus, to be consistent with our first hypothesis, we

expect the coefficient of ΔBreadth in regression (8) to be positive.

We present the results from the regressions on ΔBreadth in Table 4. In column (1) of

Table 4, we control for ΔHold as suggested by Chen, Hong, Stein (1992). Chen, Hong, Stein

(1992) also suggests that ΔBreadth could be correlated to trading turnover. To ensure that our

results on ΔBreadth are not driven by trading turnover, we further control for abnormal trading

turnover (TURNOVER) in columns (2) and (3). In all three regressions, the coefficient of

ΔBreadth is positive and significant in both the stock and the bond equations. These results show

that the likelihood of straight bond and stock issuances relative to the likelihood of convertible

issuances decreases when breadth of mutual fund ownership decreases, presumably when

investors are more heterogeneous in their beliefs on the firm’s future cash flows. These results

support our first heterogeneous belief hypothesis. But they cannot be explained by the

asymmetric information theories.

In the second robustness check, we rerun regression (8) based on a sample of private

offerings of convertibles, straight bond, and stock. In our earlier regressions, we base on a

sample of public offerings of convertibles, straight bond, and stock. However, it is also

interesting to know whether the heterogeneity of investor beliefs affect private offerings in the

same way as how it affects public offerings. We present the results from the new regressions

28

based on the sample of private offerings in panel A in Table 5. As can be seen, the coefficients of

all three heterogeneity variables remain negative in both the bond and the stock equations. They

are also mostly significant, except for the coefficient of TURNOVER in the stock equation.

In panel B, we further run regression (8) based on a combined sample of private offerings

and public offerings. Again, the coefficients of all three heterogeneity variables remain negative.

They are also mostly significant except for the coefficient of DISP in the stock equation. Overall,

our results in table 5 suggest that our findings on the heterogeneity of investor beliefs and the

likelihood of convertible offerings hold not only for the sample of public offerings but also for

the sample of private offerings.

4.3. Interaction between Heterogeneity of Investor Beliefs and Offering Size

In this subsection, we test the third hypothesis (H3). Our third hypothesis states that the

positive relation between the likelihood of convertible offerings and the heterogeneity of investor

beliefs is more pronounced if a firm needs to raise a larger amount of external capital. To test his

hypothesis, we run a regression that is similar to regression (8), but with the interaction term

between the heterogeneity variable and the amount of offerings as an additional independent

variable. In particular, we interact VALUE with DISP, TURNOVER, and RISK respectively.

We expect the coefficients of these interaction terms to be negative to be consistent with our

third hypothesis.

We present the results from the test of H3 in Table 6. As can be seen, the coefficients are

negative and statistically significant for the interaction term between DISP and VALUE in the

stock equation, for the interaction term between TURNOVER and VALUE in both the bond and

the stock equations, and for the interaction term between RISK and VALUE in the stock

equation. However, the coefficient is insignificant for the interaction term between DISP and

29

VALUE and the interaction term between RISK and VALUE in the bond equation. In general,

our results in Table 6 are consistent with the third hypothesis. They suggest that the positive

relation between the heterogeneity of investor beliefs and the likelihood of convertible offerings

is more pronounced when the firm needs to raise more external capital (and thereby finances

from more investors with heterogeneous beliefs).

5. Conclusion

In the paper, we study how the heterogeneity of investor beliefs on a firm’ future cash

flows affects the firm’s security issuance choices among convertibles, straight bond, and equity.

We conjecture that a firm is more likely to issue convertibles rather than straight bond or equity

when the firm faces a higher level of the heterogeneity of investor beliefs. In particular, when

investors have heterogeneous beliefs on a firm’s future cash flows, they would value the firm’s

securities differently. Some investors may overvalue straight bond to the largest degree and

overvalue equity to the lowest degree (or even undervalue it) relative to their respective

fundamental values. On the other hand, some investors may overvalue equity to the highest

degree and straight bond to the lowest degree relative to their respective fundamental values.

When the firm has to finance a sufficiently large amount of external capital, it has to appeal to

both kinds of investors. In this case, both straight bond and equity could be costly securities to

issue since both securities can only appeal to one kind of investors but not the other kind of

investors. Unlike straight bond and equity, a convertible security can appeal to both kinds of

investors given its nature being a hybrid of equity and debt.

To test this heterogeneous belief argument, we use a sample of convertible, stock, and

straight bond offerings. We also use different proxies for the heterogeneity of investor beliefs.

30

Our findings suggest that a firm is more likely to issue convertibles rather than equity and

straight bond when investors are more heterogeneous in their beliefs on the firm’s future cash

flows and when the firm raises a larger amount of external capital. We also study the interaction

between the heterogeneity of investor beliefs and the amount of external capital. We find that the

high likelihood of convertible offerings in the presence of high heterogeneity of investor beliefs

is more pronounced when the firm raises a large amount of external capital. Overall, our findings

provide a novel rationale based on the heterogeneity of investor beliefs for the use of convertible

securities in corporate external financing decisions.

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Year Convt. Bond Stock Convt. Bond Stock Convt. Bond Stock

1986 96 329 240 84 188 223 12 141 17

1987 150 445 289 137 272 269 13 173 20

1988 114 299 200 106 157 181 8 142 19

1989 34 366 106 26 128 84 8 238 22

1990 36 299 169 33 116 138 3 183 31

1991 22 309 117 18 133 101 4 176 16

1992 32 402 344 25 267 315 7 135 29

1993 52 373 325 41 262 288 11 111 37

1994 52 439 435 45 296 390 7 143 45

1995 22 291 311 14 184 273 8 107 38

1996 19 397 464 14 289 432 5 108 32

1997 36 398 557 30 329 532 6 69 25

1998 32 437 536 23 352 511 9 85 25

1999 18 553 402 11 474 393 7 79 9

2000 12 331 333 9 259 303 3 72 30

2001 22 220 350 16 176 291 6 44 59

2002 56 309 442 23 254 251 33 55 191

2003 52 298 389 5 261 224 47 37 165

2004 44 251 492 11 210 275 33 41 217

2005 22 175 543 10 143 353 12 32 190

Total 923 6,921 7,044 681 4,750 5,827 242 2,171 1,217

Whole Sample Sample of Public Offerings Sample of Private Offerings

Table 1: Sample Distribution. This table reports the number of convertible, straight bond, and

equity offerings by years between 1986 and 2005 and by the public/private status of offerings.

32

Variables # of Obs. Mean Median # of Obs. Mean Median # of Obs. Mean Median Mean Median Mean Median

DISP 363 0.007 0.002 3,112 0.003 0.001 2,570 0.005 0.002 0.004*** 0.001*** 0.002*** 0.001***

TURNOVER 644 1.67 1.34 4,608 1.05 0.91 5,282 1.3 1 0.61*** 0.43*** 0.37*** 0.34***

RISK 497 0.2 0.19 2,262 0.14 0.13 3,486 0.24 0.23 0.07*** 0.06*** -0.04*** -0.04***

ΔBRREADTH 490 0.05 0.13 2,355 -0.12 0.04 4,534 0.13 0.11 0.16*** 0.09*** -0.08*** 0.02*

SIZEt-1 457 6.31 6.12 3,327 9.13 9.17 3,742 5.93 5.8 -2.81*** -3.05*** 0.38*** 0.32***

MBt-1 457 2.11 1.56 3,327 1.79 1.48 3,742 3.27 2.08 0.32*** 0.09** -1.16*** -0.52***

LTDEBTt-1 457 0.22 0.2 3,327 0.27 0.24 3,741 0.2 0.14 -0.04*** -0.04*** 0.02* 0.06***

PROFITt-1 456 0.08 0.1 3,288 0.11 0.11 3,734 0.01 0.08 -0.03*** -0.01*** 0.07*** 0.01***

CAPEXt-1 447 0.3 0.06 3,291 0.1 0.07 3,651 0.65 0.05 0.20*** -0.003 -0.36 0.01**

VALUE 681 4.17 4.17 4,750 4.75 5.01 5,827 3.94 3.98 -0.58*** -0.84*** 0.23*** 0.20***

RETURNt-1 502 0.1 0.08 2,283 0.01 0.01 3,520 0.22 0.17 0.09*** 0.08*** -0.12*** -0.08***

Convertible Offerings Bond Offerings Stock Offerings Convertible - Bond Convertible - Stock

Table 2: Descriptive Statistics. This table reports the means and medians of the variables used in the paper. DISP is the standard deviation of

earnings forecasts deflated by the pre-announcement stock price. RISK is idiosyncratic volatility calculated as 100 times the standard deviation of

the daily market-adjusted stock returns in 180 trading days prior to the announcement date. RETURN is the cumulative market-adjusted stock

return in the 180 trading days prior to announcement. SIZE is the log of the market value of total assets. MB is the ratio of the market value to the

book value of equity. PROFIT is the ratio of earnings before interest, taxes, depreciation, and amortization to the book value of total assets.

CAPEX is capital expenditures scaled by the book value of assets. VALUE is the log amount raised in the offering. ΔBreadth is the change in the

fraction of all mutual funds long in the stock in the quarter prior to announcement. TURNOVER is the share trading turnover (trading

volume/outstanding shares) divided by the average turnover in the same exchange, averaged in 180 days prior to announcement. LTDEBT is the

amount of long term debt over the book value of assets.

33

bond stock bond stock bond stock bond stock bond stock bond stock

Constant -5.175*** 2.677*** -4.176*** 3.331*** -3.984*** 2.868*** -4.097*** 3.263*** -2.996*** 3.280*** -2.833** 4.060***

[0.607] [0.465] [1.209] [1.250] [0.520] [0.356] [1.102] [1.090] [0.658] [0.490] [1.186] [1.217]

SIZEt-1 1.187*** 0.282** 1.125*** 0.196 1.136*** 0.190** 1.105*** 0.152* 1.018*** 0.121 0.988*** 0.086

[0.131] [0.115] [0.138] [0.121] [0.092] [0.077] [0.099] [0.084] [0.097] [0.085] [0.104] [0.091]

MBt-1 -0.716*** 0.242*** -0.652*** 0.234*** -0.650*** 0.238*** -0.554*** 0.267*** -0.586*** 0.252*** -0.486*** 0.270***

[0.117] [0.062] [0.123] [0.068] [0.110] [0.062] [0.117] [0.072] [0.109] [0.063] [0.115] [0.070]

LTDEBTt-1 1.349*** 0.666* 0.873 1.059** 1.396*** 0.705** 1.132** 1.063*** 1.732*** 0.892*** 1.408*** 1.222***

[0.471] [0.388] [0.579] [0.478] [0.425] [0.344] [0.493] [0.400] [0.434] [0.345] [0.500] [0.404]

PROFITt-1 7.551*** -0.142 7.374*** 0.708 7.234*** 0.456 6.484*** 0.740*** 6.314*** 0.156 5.413*** 0.466

[1.224] [0.614] [1.367] [0.693] [1.032] [0.282] [1.119] [0.264] [1.071] [0.352] [1.157] [0.298]

DIVDt-1 1.184*** 0.205 1.082*** 0.203 0.742*** -0.055 0.675*** -0.07 0.772*** 0.045 0.661*** 0.006

[0.207] [0.174] [0.218] [0.181] [0.189] [0.154] [0.200] [0.160] [0.188] [0.152] [0.201] [0.159]

CAPEXt-1 0.153 0.156 0.243 0.248 0 0.005 -0.001 0.005 0.003 0.006 0.001 0.005

[0.208] [0.208] [0.270] [0.269] [0.007] [0.007] [0.005] [0.005] [0.008] [0.008] [0.005] [0.005]

VALUE -0.983*** -1.141*** -1.060*** -1.202*** -0.724*** -1.024*** -0.744*** -1.035*** -0.741*** -1.064*** -0.767*** -1.088***

[0.144] [0.137] [0.154] [0.147] [0.126] [0.111] [0.132] [0.118] [0.123] [0.110] [0.131] [0.118]

RETURNt-1 -3.678*** 1.412*** -3.681*** 1.523*** -2.728*** 2.221*** -2.876*** 2.261*** -3.003*** 2.110*** -3.145*** 2.200***

[0.629] [0.438] [0.669] [0.464] [0.516] [0.363] [0.544] [0.377] [0.510] [0.358] [0.533] [0.366]

DISP -31.689*** -20.955*** -36.962*** -27.257***

[9.552] [7.611] [10.589] [7.355]

TURNOVER -0.435*** -0.241*** -0.475*** -0.238***

[0.084] [0.059] [0.088] [0.062]

RISK -5.383*** -2.050* -6.242*** -2.321**

[1.547] [1.169] [1.602] [1.182]

Year dummies

Industry dummies

Observations

Pseudo R Square

(6)(1) (2) (3) (4) (5)

Yes

No

3,428

0.468

Yes

Yes

3,428

0.497

Yes

No

4,316

0.47

Yes

Yes

4,316

0.495

Yes

No

4,488

0.471

Yes

Yes

4,388

0.497

Table 3: Likelihood of Offering Convertibles versus Bond and Stock. The results are from multinomial logistic regressions for unordered choices of convertible (base category), stock, and straight bond offerings. DISP is the standard deviation of earnings forecasts deflated by the pre-announcement stock price; RISK, 100 times the standard

deviation of the daily market-adjusted stock returns in 180 days prior to announcement; and TURNOVER is share trading turnover (trading volume/outstanding shares) divided by the average turnover in the same exchange, averaged in 180 days prior to announcement. RETURN is the cumulative market adjusted return in 180 trading days

prior to announcement. SIZE is the log of the market value of total assets. MB is the ratio of the market value to the book value of equity. PROFIT is the ratio of EBITDA to

the book value of total assets. CAPEX is capital expenditures scaled by the book value of assets. VALUE is the log amount raised in the offering. LTDEBT is long term debt over the book value of assets. DIVD is a dummy variable of non-zero cash dividends. The coefficients of NUMEST (number of analysts following) are not reported. Standard

errors are provided in brackets. *, **, and *** indicate a significant difference from zero at the 10, 5, and 1 percent levels, respectively.

34

bond stock bond stock bond stock

Constant -5.036*** 2.179*** -4.790*** 2.431*** -4.769*** 2.921**

[0.548] [0.415] [0.574] [0.434] [1.228] [1.201]

SIZEt-1 1.171*** 0.185** 1.225*** 0.206** 1.205*** 0.179*

[0.097] [0.085] [0.100] [0.088] [0.108] [0.095]

MBt-1 -0.620*** 0.317*** -0.645*** 0.309*** -0.542*** 0.346***

[0.110] [0.061] [0.115] [0.062] [0.122] [0.067]

LTDEBTt-1 1.731*** 1.016*** 1.519*** 0.812** 1.329** 1.215***

[0.447] [0.355] [0.450] [0.359] [0.525] [0.430]

PROFITt-1 7.812*** 0.813* 8.154*** 0.756 7.689*** 1.427***

[1.075] [0.483] [1.120] [0.484] [1.245] [0.501]

DIVDt-1 0.918*** 0.153 0.773*** 0.032 0.705*** 0.017

[0.192] [0.160] [0.197] [0.164] [0.208] [0.169]

CAPEXt-1 -0.003 0.001 -0.003 0 -0.004 0.002

[0.004] [0.004] [0.004] [0.004] [0.005] [0.004]

VALUE -0.780*** -1.088*** -0.792*** -1.069*** -0.825*** -1.102***

[0.130] [0.117] [0.134] [0.121] [0.144] [0.130]

RETURNt-1 -3.119*** 1.908*** -2.856*** 2.404*** -2.953*** 2.506***

[0.556] [0.402] [0.562] [0.411] [0.580] [0.418]

TURNOVER -0.350*** -0.241*** -0.399*** -0.248***

[0.079] [0.055] [0.082] [0.059]

ΔHOLD -2.054 -1.411 -1.713 -0.914 -1.764 -1.242

[1.498] [1.285] [1.504] [1.304] [1.512] [1.297]

ΔBREADTH 0.187** 0.489*** 0.192** 0.491*** 0.220** 0.505***

[0.093] [0.091] [0.093] [0.091] [0.088] [0.089]

Year dummies

Industry dummies

Observations

Pseudo R Square

(3)

Yes

No

4,040

0.484

Yes

No

4,040

0.51

4,153

0.476

Yes

No

(1) (2)

Table 4: Likelihood of Offering Convertibles versus Bond and Stock, An Alternative

Measure. This table reports the results from multinomial logistic regressions for unordered

choices of convertible, stock, and straight bond offerings. The group of convertible deals is the

base category. ΔΗOLD and ΔΒREADTH are the changes in the percentage of the shares held by

mutual funds and in the fraction of all mutual funds long in the stock in the quarter prior to

announcement. TURNOVER is share trading turnover (trading volume/outstanding shares)

divided by the average turnover in the same exchange averaged in 180 days prior to

announcement. RETURN is the cumulative market-adjusted stock return in 180 trading days

prior to announcement. SIZE is the log of the market value of total assets. MB is the ratio of the

market value to the book value of equity. PROFIT is the ratio of earnings before interest, taxes,

depreciation, and amortization to the book value of total assets. CAPEX is capital expenditures

scaled by the book value of assets. VALUE is the log amount raised in the offering. LTDEBT is

the amount of long term debt over the book value of assets. DIVD is a dummy variable of non-

zero cash dividends. Standard errors are provided in brackets. *, **, and *** indicate a

significant difference from zero at the 10, 5, and 1 percent levels, respectively.

35

Panel A: Sample consists of private offerings

bond stock bond stock bond stock

Constant 7.822*** 10.526 4.132 30.623*** 7.060*** 32.096***

[1.680] [0.000] [9.873] [1.653] [2.128] [1.861]

SIZEt-1 1.039*** 1.201*** 0.673*** 0.425*** 0.393*** 0.331***

[0.302] [0.315] [0.129] [0.122] [0.137] [0.118]

MBt-1 -0.550*** -0.122** -0.416*** 0.026 -0.491*** -0.002

[0.162] [0.061] [0.110] [0.040] [0.116] [0.036]

LTDEBTt-1 0.756 -0.827 0.006 -0.738 0.687 -0.466

[1.325] [1.068] [0.881] [0.753] [0.889] [0.762]

PROFITt-1 10.904*** -1.098 8.133*** -0.633* 7.422*** -0.954**

[2.633] [0.926] [1.651] [0.372] [1.673] [0.388]

DIVDt-1 0.078 -1.058* 0.766** -0.066 0.791** -0.063

[0.523] [0.591] [0.358] [0.325] [0.360] [0.316]

CAPEXt-1 -1.269*** -0.675*** -0.754*** -0.055** -0.705*** -0.015

[0.398] [0.257] [0.247] [0.026] [0.224] [0.012]

VALUE 0.031 -0.946*** 0.487*** -0.430*** 0.372** -0.493***

[0.232] [0.251] [0.149] [0.136] [0.149] [0.134]

RETURNt-1 -3.018*** 0.313 -1.233** 0.677 -1.675*** 0.811**

[1.091] [0.967] [0.593] [0.412] [0.561] [0.389]

NUMEST 0.101 -0.412

[0.567] [0.605]

DISP -19.568* -2.098*

[11.462] [1.152]

TURNOVER -0.563*** -0.154

[0.134] [0.111]

RISK -7.887*** -2.603***

[1.675] [0.969]

Year dummies

Industry dummies

Observations

Pseudo R Square

(1) (2) (3)

Yes Yes Yes

0.638 0.61 0.617

Yes Yes Yes

1,008 1,544 1,577

Table 5: Likelihood of Offering Convertibles versus Bond and Stock, Alternative Samples.

The results are from multinomial logistic regressions for unordered choices of convertible (base

category), stock, and straight bond offerings. DISP is the standard deviation of earnings forecasts

deflated by the pre-announcement price; RISK, 100 times the standard deviation of the daily

market-adjusted stock returns in 180 days prior to announcement; and TURNOVER is share

trading turnover (trading volume/outstanding shares) divided by the average turnover in the same

exchange, averaged in 180 days prior to announcement. RETURN is the cumulative market-

adjusted stock return in 180 trading days prior to announcement. SIZE is the log of the market

value of total assets. MB is the ratio of the market value to the book value of equity. PROFIT is

the ratio of earnings before interest, taxes, depreciation, and amortization to the book value of

total assets. CAPEX is capital expenditures scaled by the book value of assets. VALUE is the log

amount raised in the offering. LTDEBT is the amount of long term debt over the book value of

assets. DIVD is a dummy variable of non-zero cash dividends. PRIVATE is a dummy variable of

private offerings. Standard errors are provided in brackets. *, **, and *** indicate a significant

difference from zero at the 10, 5, and 1 percent levels, respectively.

36

Panel B: Sample consists of both public and private offerings

bond stock bond stock bond stock

Constant -4.833*** 2.938** -4.684*** 2.988*** -2.869*** 3.853***

[1.151] [1.152] [1.070] [1.069] [1.113] [1.134]

SIZEt-1 1.033*** 0.209** 0.878*** 0.052 0.729*** -0.01

[0.113] [0.099] [0.070] [0.060] [0.071] [0.062]

MBt-1 -0.776*** 0.09 -0.611*** 0.163*** -0.589*** 0.138***

[0.113] [0.085] [0.087] [0.058] [0.083] [0.053]

LTDEBTt-1 0.506 0.591 0.750* 0.583* 0.957** 0.706**

[0.505] [0.435] [0.409] [0.348] [0.412] [0.349]

PROFITt-1 9.232*** 0.883* 7.609*** 0.488** 6.524*** 0.185

[1.157] [0.467] [0.861] [0.216] [0.858] [0.258]

DIVDt-1 0.821*** -0.038 0.583*** -0.172 0.549*** -0.123

[0.191] [0.169] [0.161] [0.137] [0.162] [0.136]

CAPEXt-1 -0.189 0 -0.023** -0.001 -0.022 0

[0.294] [0.003] [0.012] [0.002] [0.030] [0.002]

VALUE -0.622*** -0.985*** -0.14 -0.618*** -0.204** -0.689***

[0.118] [0.115] [0.090] [0.082] [0.091] [0.081]

RETURNt-1 -3.041*** 1.287*** -2.123*** 1.409*** -2.542*** 1.384***

[0.555] [0.396] [0.403] [0.271] [0.391] [0.264]

PRIVATE 2.572*** -1.451*** 2.462*** -1.782*** 2.620*** -1.767***

[0.234] [0.245] [0.180] [0.167] [0.187] [0.176]

NUMEST 0.172 -0.142

[0.178] [0.153]

DISP -22.486*** -1.817

[7.396] [1.141]

TURNOVER -0.441*** -0.198***

[0.071] [0.053]

RISK -7.019*** -2.264***

[1.051] [0.747]

Year dummies

Industry dummies

Observations

Pseudo R Square 0.503 0.498 0.505

Yes Yes Yes

4,436 5,860 5,965

Yes Yes Yes

(1) (2) (3)

37

bond stock bond stock bond stock

Constant -4.546*** 1.959 -4.979*** 2.039*** -3.179** 2.147

[1.198] [1.365] [0.651] [0.450] [1.560] [1.430]

SIZEt-1 1.391*** 0.589*** 1.134*** 0.189** 0.959*** 0.073

[0.123] [0.106] [0.093] [0.078] [0.105] [0.091]

MBt-1 -0.500*** 0.319*** -0.661*** 0.232*** -0.468*** 0.279***

[0.120] [0.076] [0.111] [0.062] [0.115] [0.069]

LTDEBTt-1 0.746 0.840** 1.415*** 0.728** 1.449*** 1.279***

[0.524] [0.415] [0.427] [0.346] [0.504] [0.406]

PROFITt-1 5.422*** -1.476** 7.149*** 0.362 5.627*** 0.711**

[1.290] [0.735] [1.029] [0.282] [1.172] [0.343]

DIVDt-1 0.672*** -0.316* 0.744*** -0.054 0.659*** 0.006

[0.194] [0.165] [0.189] [0.154] [0.201] [0.159]

CAPEXt-1 0.115 0.123 0 0.004 0.001 0.005

[0.216] [0.216] [0.007] [0.007] [0.005] [0.005]

VALUE -0.645*** -0.676*** -0.487*** -0.819*** -0.619** -0.609***

[0.126] [0.121] [0.152] [0.130] [0.247] [0.215]

RETURNt-1 -3.109*** 2.262*** -2.687*** 2.233*** -3.071*** 2.380***

[0.593] [0.420] [0.517] [0.365] [0.543] [0.373]

NUMEST -0.375** -0.909***

[0.180] [0.163]

DISP -81.766** 21.425

[36.679] [29.030]

DISP × VALUE -7.333 -13.466*

[7.172] [7.636]

TURNOVER 0.34 0.352

[0.345] [0.218]

TURNOVER × VALUE -0.177** -0.143***

[0.075] [0.052]

RISK -6.248 6.364*

[5.651] [3.564]

RISK × VALUE -0.223 -2.178***

[1.172] [0.832]

Year and industry dummies

Observations

Pseudo R Square

4388

0.499

(1) (2) (3)

Yes

3428

0.458

Yes

4316

0.471

Yes

Table 6: Interaction between the Amount Raised and the Heterogeneity of Beliefs. This table

reports the results from multinomial logistic regressions for unordered choices of convertible

(base category), stock, and straight bond offerings. DISP is the standard deviation of earnings

forecasts deflated by the pre-announcement stock price; RISK, 100 times the standard deviation of

the daily market-adjusted stock returns in 180 days prior to announcement; and TURNOVER is

share trading turnover (trading volume/outstanding shares) divided by the average turnover in the

same exchange averaged in 180 days prior to announcement. RETURN is the cumulative market-

adjusted stock return in 180 trading days prior to announcement. SIZE is the log of the market

value of total assets. MB is the ratio of the market value to the book value of equity. PROFIT is

the ratio of earnings before interest, taxes, depreciation, and amortization to the book value of

total assets. CAPEX is capital expenditures scaled by the book value of assets. VALUE is the log

amount raised in the offering. LTDEBT is long term debt over the book value of assets. DIVD is a

dummy variable of non-zero cash dividends. Standard errors are provided in brackets. *, **, and

*** indicate a significant difference from zero at the 10, 5, and 1 percent levels, respectively.

38