Market Participants' Evaluation of the Economic Substance of

Convertible Debt

Richard Carrizosa

Abstract

U.S. GAAP currently mandates that convertible debt be reported as a liability in its en-

tirety, and the FASB and IASB have recently decided to continue this liability classi�cation

despite the hybrid nature of convertibles. I use market measures to determine whether three

di�erent approaches to convertible debt accounting correspond with views of shareholders

and creditors: 1) liability measured at fair value (FV), 2) the debt component measured

as comparable non-convertible debt and the incremental conversion option value as equity

(FC), and 3) debt and equity components measured using probability-weighted discounted

debt and equity settlement values (PB). My tests relating leverage to credit risk suggest that

creditors view convertible debt consistent with the FC method. In contrast, my tests linking

leverage to systematic equity risk suggest the PB method corresponds best with shareholder

perceptions. My results suggest that neither creditors nor shareholders view convertible debt

as a homogeneous liability. Instead, investors recognize the debt and equity components of

convertible debt di�erently according to their asymmetric risk exposure. The evidence sug-

gests supplemental disclosures can improve convertible debt accounting by helping investors

more accurately and e�ciently estimate the debt and equity components of convertible debt.

1

Email address: rcarrizo@stern.nyu.edu (Richard Carrizosa)1New York University. I wish to thank my thesis advisors for their guidance and valuable comments:

Daniel Cohen, William Greene, Baruch Lev (Chair), Stephen Ryan, and Rangarajan Sundaram. This paperhas also bene�ted from discussions with Karthik Balakrishnan, Jaewon Choi, Andre DeSouza, Lucile Faurel,Kalin Kolev, Melissa Martin, Lorenzo Naranjo, and workshop participants at New York University.

Preprint submitted to Elsevier January 13, 2010

1. Introduction

Convertible debt is a hybrid �nancing instrument that, at the option of the holder, settles

as either debt or equity.2 U.S. GAAP currently requires �rms to record the entire proceeds

of convertible debt as a liability at issuance, despite the inherent equity characteristics of the

security.3 The Financial Accounting Standards Board (FASB) and International Accounting

Standards Board (IASB) are considering changes to the accounting for convertible debt as

part of a larger e�ort to improve accounting for �nancial instruments with characteristics

of equity. Prior literature has introduced several possible methods to measure the debt and

equity characteristics of convertible debt. These methods di�er in their assumptions and

measurements. So far, no empirical evidence exists to evaluate whether the methods re�ect

market participants' evaluation of the economic substance of convertible debt. Creditors

and shareholders can di�er in their convertible debt component assessments as a result of

their di�erent risk exposures. Using theory that links leverage to both credit and equity

market risk measures, I examine empirically the degree to which three di�erent methods of

accounting for the debt and equity characteristics of convertible debt are consistent with

views held by creditors and shareholders.

Hybrid �nancing instruments like convertible debt settle in one of two or more forms.

Whether a convertible settles as a liability or equity depends primarily on which outcome

is more favorable to the security holder. In addition, the probability that convertible debt

will settle in a particular state changes over time. Given the various possible outcomes,

accounting for convertible debt as a single instrument will not fully re�ect its economic

substance. Using a more dynamic approach to account for the distinct liability and equity

components can more fully capture the debt and equity characteristics of convertible debt.

2Convertible debt has become an increasingly popular �nancing alternative for U.S. �rms. The amountof outstanding convertible debt reported by �rms covered by Compustat has increased from less than $50Bin 2000 to over $240B in 2007.

3Convertible debt accounting subsequent to issuance mirrors that of straight debt. Upon conversion,however, the book value of the convertible is transferred to equity. Firms can choose to record the marketvalue of the convertible as equity, though the book method is most common.

2

Distinguishing liabilities from equity serves two important purposes: 1) insolvency risk

assessment, and 2) common equity valuation (Wahlen et al. [27]). Insolvency occurs when

a �rm is unable to satisfy its obligations, and therefore insolvency risk assessment requires

an analysis of contractual cash out�ows. On the other hand, equity is a residual claim,

so distinguishing other claims by their relative seniority is more useful for common equity

valuation. Given the hybrid nature of convertible debt, investors can adopt di�erent views

of the economic substance of convertibles that best suit their particular motivations for

distinguishing liabilities from equity.

Creditors and shareholders have di�erent risk exposures that arise from their di�ering

claims on �rm value. Potential cash �ows to creditors are bounded above, making creditors

less sensitive to upside risk than are shareholders. On the other hand, creditors absorb all

decreases when �rm value falls below the default boundary, and are more sensitive to down-

side risk than are shareholders. Consequently, creditors are more concerned with insolvency

when measuring the debt component of a convertible, and are more likely to focus on the

contractual obligation. Shareholders are concerned with valuing their residual claim, and

will prefer a method that best measures the value of total equity available to both current

and potential common shareholders.4 In sum, I expect that asymmetric exposure to �rm

risk will cause investors to view convertible debt di�erently.

The three methods used in this study to measure the debt and equity components of

convertible debt (FC, PB, and FV) di�er primarily according to which liability de�nitions

they implicitly assume. First, Both King [21] and Barth et al. [2] use option-pricing based

estimation techniques to measure the debt component of a convertible as the debt of a

similar non-convertible debt issue, and the equity component as the di�erence between the

convertible fair value and debt component value (FC method). Both studies report relatively

large equity components using the FC method. This approach implicitly assumes the issue

4An analysis of the dilutive e�ect of conversion yields the same prediction. Shareholders bear the totalcost of dilution, and may choose to measure convertible components in a manner that most conservativelyestimates this cost.

3

will settle as a liability at maturity. The FC method produces estimates of debt components

that are most useful for insolvency risk assessment. Second, Ryan et al. [26] argue that a

measure of the separate components more meaningful for equity valuation purposes can be

obtained by incorporating the probability that the convertible will settle as debt or equity.

The proposed method measures the debt and equity components of convertible debt as the

probability-weighted discounted values attributable to states in which the security settles as

a liability or as equity (PB method). Lastly, Ohlson and Penman [24] argue that the most

accurate method for capturing the dilutive e�ect of conversion involves recording changes

in the fair value of convertible debt in income. This method achieves the goal of reporting

focused on the current shareholder. Ohlson and Penman [24] support reporting the fair

value of convertible debt as a liability on the balance sheet (FV method) because, prior to

settlement, the full value represents a claim on current shareholder wealth. The proposed

accounting methods mentioned above emphasize di�erent aspects of the economic substance

of convertible debt, and all three have been considered during the FASB/IASB deliberation.5

Structural models of default provide a direct link between �rm leverage and credit risk

(Merton [23]). These models are useful when examining how creditors perceive the debt

and equity characteristics of convertible debt. I regress credit default swap (CDS) spreads

on convertible debt components, as measured by the FV, PB, and FC methods, to infer

which method is most consistent with the view held by creditors. Both the PB and FC

methods produce equity components that have signi�cantly weaker associations with CDS

spreads than do the debt components, indicating that creditors bifurcate the fair value of

the convertible when measuring its e�ect on credit risk. Model selection tests reject the

PB model in favor of the FC model, however, and suggest that creditors view the debt

component of a convertible in a comparable manner to that of a similar non-convertible debt

5Two logical alternatives that are not examined in this study include accounting for convertible debtentirely as equity, or as equity �rst and the remainder as debt. One can make a case for these alternativesparticularly when conversion option values are large, or for puttable stock (similar payo� structure but withequity as the host instrument).

4

issue. This result is consistent with the assumption that creditors focus on the contractual

obligation of the instrument due to their downside risk exposure.

To explore the issue from a shareholder's perspective, I rely on theory that links leverage

to systematic equity risk (Hamada [16], Bowman [6]). Results from regressions of equity

betas on measures of operating risk and debt/equity ratios show that leverage is overstated

when one includes the entire fair value of convertible debt in debt/equity ratios. Speci�cally,

I decompose the FV debt/equity ratio into a PB component (D/E adjusted by reclassifying

the PB�measured equity component), and an error term (the di�erence between FV D/E

and PB D/E). I �nd that the PB ratio is positively associated with equity risk while the

error term is not. This result suggests that shareholders separately measure the debt and

equity components of convertible debt in a manner that incorporates settlement probability.

Shareholders' preferred method dynamically measures equity value, which is consistent with

risk exposure a�ecting the way shareholders view convertible debt.

Combined, the credit and equity risk results indicate that neither shareholders nor cred-

itors view the fair value of convertible debt as a liability. The FV approach attempts to

capture the economic substance of a hybrid �nancing instrument using only a single value,

so it is not surprising that investors do not �nd this approach useful. The results also suggest

that shareholders and creditors hold di�erent views regarding the economic substance of con-

vertible debt, and that the di�erences between creditor and shareholder views are consistent

with their focus on measuring insolvency risk and valuing common equity, respectively.

This study provides empirical evidence about investor perceptions of convertible debt.

While prior literature typically focuses on the association between hybrid �nancing instru-

ments and equity market measures (e.g., Dhaliwal [11], Kimmel and War�eld [20], Cheng

et al. [7]), my �ndings show that perceptions di�er between shareholders and creditors in a

manner consistent with their asymmetric risk exposure. I also provide information relevant to

the FASB/IASB proceedings regarding proposed accounting guidelines for convertible debt.

5

Recent decisions by the FASB/IASB favor classi�cation of convertible debt as a liability.6

However, my �ndings suggest that fair-value reporting of convertible debt is inconsistent with

the views of both debt and equity holders. To improve convertible debt accounting, regula-

tors may consider requiring additional disclosures that would help investors more accurately

and e�ciently measure debt and equity components.

2. Current and Proposed Accounting for Convertible Debt

Current accounting rules for conventional convertible debt were introduced nearly 40

years ago by Accounting Principles Board Opinion No. 14, Accounting for Convertible Debt

and Debt Issued with Stock Purchase Warrants (APB 14). These rules require the entire

convertible debt issuance proceeds to be recorded in the balance sheet as a liability, and the

discount or premium to be amortized over the life of the issue. Firms record a reduction in

the book value of the convertible upon conversion. They can choose to recognize either the

book value of the liability or the market value of the converted shares as equity.7

Critics of APB 14 claim that it understates the �rm's true �nancing cost, that it fails to

accurately report dilution to shareholders, and that it overstates the e�ect of the convertible

issue on future cash �ows. The reported interest required by lenders under APB 14 is

equal to the interest required for an identical non-convertible issue, minus the value of the

conversion option. A �rm that issues debt with a conversion option value that completely

o�sets the required interest will appear to have zero �nancing costs. In addition, the book

method to account for conversion fails to capture the additional dilution to shareholders

that occurs when the conversion value exceeds the book value. Lastly, conversion results

in an issuance of shares rather than a reduction of assets. Therefore the conversion option

6Recent FASB/IASB decisions indicate that convertible debt will be classi�ed as a liability in its entirety(FASB Project Financial Instruments with Characteristics of Equity, Summary of Decisions dated October26, 2009). Additional documentation suggests that �rms may be required to report both the amortized costand the amount by which to adjust the amortized cost to fair value (FASB Project Accounting for FinancialInstruments, Summary of Decisions dated November 4, 2009).

7Recognition of the market value of the converted shares requires the �rm to report a loss. As a result,the book method is commonly chosen.

6

introduces uncertainty into the estimation of the e�ect of the convertible on future cash

�ows, and it complicates leverage measurement.

International Accounting Standards (IAS 32) adopt a fundamentally di�erent approach

to convertible debt accounting.8 This regulation requires that �rms bifurcate the debt and

equity components at issuance. Firms must measure the debt component as the fair value

of an otherwise identical debt issue without the conversion option. The di�erence between

the proceeds and the fair value of the non-convertible issue is recognized as equity. Upon

conversion the �rm reclassi�es the liability component as equity, and it makes no adjustment

to the equity component recognized at issuance. King [21] and Barth et al. [2] use option-

pricing methods to implement the the IAS 32 bifurcation method (FC method).9 The FC

method improves upon APB 14 by reporting both debt and equity components of the hybrid

�nancing instrument. By measuring equity as the value incremental to the comparable non-

convertible debt issue, however, it implicitly assumes the convertible will settle as debt. As

a result, even when applied periodically (not just at issuance), the FC method fails to fully

capture cash �ow uncertainty.

Ryan et al. [26] and Arak and Martin [1] present an alternative option-pricing based

method. It weights the debt and equity portions of the fair value of convertible debt by

the probability of settlement in each state (PB method).10 The PB method allocates the

fair value across debt and equity in an economically meaningful way if applied periodically.

For example, when the conversion probability approaches one (zero) and the fair value ap-

proaches the conversion (bond) value, then the fraction allocated to equity approaches one

(zero). Consequently, the PB method e�ectively captures the value of equity to potential

8Only recently has the FASB begun to consider the bifurcation of liability and equity components forcertain convertible issues that may be settled partially or wholly in cash (FASB Sta� Position No. APB14-1, Accounting for Convertible Debt Instruments That May Be Settled in Cash upon Conversion, May 9,2008).

9Their bifurcation method is the same as that used by IAS 32. However, they use it to separate the fairvalue of convertible debt at a �nancial reporting date that occurs beyond the issuance date, while IAS 32only bifurcates the issuance proceeds.

10The methods in Ryan et al. [26] and Arak and Martin [1] are guided by the same underlying principlebut di�er in implementation.

7

shareholders as it changes over time, and it assigns the full fair value to equity upon con-

version. From a current shareholder's perspective, however, dilution reduces the value of

existing equity. Therefore, by failing to re�ect dilutive costs as reductions in current equity,

the PB method fails to capture dilution to current shareholders.

The last approach aims to make accounting consistent with stock prices by capturing

the dilutive e�ect of convertible debt to current shareholders. It classi�es the fair value

of convertible debt as a liability and recognizes fair-value changes in income over time (FV

method, see Ohlson and Penman [24]). Prior to conversion, the cost to shareholders of issuing

shares at a discount is fully captured in income (i.e., the cost equals the di�erence between

current fair value and cash received from the issue). When the issue is converted, the fair

value of the liability is transferred to equity and the net e�ect is an increase in equity equal

to the proceeds. Ohlson and Penman [24] argue that liability classi�cation is appropriate

because the entire fair value prior to settlement represents a claim on shareholder wealth.

As fair value increases, however, so does the probability of conversion. Therefore any market

participant concerned with either the contractual debt obligation or the e�ect of the issue

on future cash �ows will �nd that the FV method grossly overstates liabilities as conversion

probability increases. The FASB and IASB have recently chosen liability classi�cation for

convertible debt.

3. Background

Prior research has found that investors incorporate information beyond the balance sheet

when determining the debt-like or equity-like nature of hybrid �nancing instruments. Results

from the experimental study conducted by Hopkins [18] suggest that the balance sheet classi-

�cation of mandatory redeemable preferred stock a�ects the valuation decisions of �nancial

analysts. On the other hand, Kimmel and War�eld [20] and Cheng et al. [7] use market

measures to determine the perceived economic substance of hybrid �nancing instruments.

They �nd that investors incorporate balance sheet classi�cation and disclosed issue charac-

teristics in their decisions. Taken together, these �ndings indicate that investors use balance

8

sheet classi�cation, combined with supplemental information, to determine the economic

substance of hybrid �nancing instruments.

Huson et al. [19] �nd that shareholder anticipation of dilution from convertible debt causes

attenuation in the relationship between returns and earnings. The attenuation is found to

be more pronounced for �rms that have experienced prior increases in stock price, and that

in turn have higher expected dilution due to the convertible issue. In addition, credit rat-

ing agencies formally assign convertible securities to categories based on their debt/equity

characteristics, and they recognize only certain fractions of the debt when determining rat-

ings.11 I expect that creditors recognize the equity characteristics of convertible debt when

making valuation decisions, either directly by incorporating issue-speci�c and �rm-speci�c

information, or indirectly by relying on credit ratings. While evidence indicates both cred-

itors and shareholders recognize and remeasure the equity characteristics of convertibles,

prior research sheds no light on the speci�c methods used.

Creditors use liability and equity measurements to assess �rm solvency. Financial debt

a�ects solvency primarily by requiring the �rm to make future payments of interest and

principal. Unlike straight debt, the possibility that the convertible debt obligation might

be satis�ed with shares adds uncertainty to estimates of the convertible debt's impact on

future cash �ows. The PB method incorporates settlement probabilities and produces debt

components that re�ect the expected discounted cash �ows associated with the convertible

issue. Given their loss exposure at default, however, I expect creditors to ignore settlement

uncertainty and instead act in a manner consistent with the FC method, which recognizes

the discounted value of the cash �ows contractually required until the time the debt is

extinguished (e.g., converted, paid at maturity, called). Lastly, the FV method classi�es

the entire fair value of the convertible as debt. It produces liability measurements more

in excess of the contractual obligation when the conversion option is deeper in the money.

11The `equity credit' concept for hybrids is laid out in Moody's ratings methodology doc-ument entitled �Moody's Tool Kit: A Framework for Assessing Hybrid Securities�, 1999(http://www.moodys.com/moodys/cust/research/mdcdocs/18/2000400000298286.pdf).

9

In addition, increases in �rm value cause FV�measured liabilities to increase more than

an identical non-convertible issue would, due to the increase in conversion option value.

Given the potential overstatement of liabilities and credit risk associated with fair-value

accounting for convertible debt, the FV approach should be least consistent with observed

creditor assessments of the impact of convertibles on future cash �ows.

To examine which accounting method is consistent with shareholder actions, I focus

on the measurement of the debt and equity components of convertible debt, rather than

the estimation of the dilutive e�ect of the issue on current shareholder wealth. As Ohlson

and Penman [24] point out, the dilutive e�ect of convertible debt is due to the issuance of

shares at a discount upon conversion. By incorporating fair-value changes in income, the FV

method captures the full dilutive e�ect over time, with no additional dilution resulting from

the actual conversion (at conversion the shares are e�ectively issued at market value because

the discount has already been incorporated in income). Therefore the FV method should

be consistent with equity valuation for current shareholders. For the purpose of measuring

leverage, however, the FV method will overstate debt. Consider a convertible issue that

increases in fair value over time. The probability of share settlement of the convertible

and the reported liability increase with fair value, while income and equity decrease to

re�ect potential dilution. The resulting FV book debt/equity ratio increases as conversion

probability increases, even though conversion ultimately leads to lower leverage. Both the

FC and PB methods appropriately produce debt/equity ratios that decrease as convertible

fair value increases. However, I expect shareholders' actions to be consistent with the PB

method because the PB method produces equity components that best capture the total

value of common equity.

I empirically assess the degree to which the three convertible debt accounting methods

re�ect the views of creditors and shareholders. The research design relies on theory that

links leverage to both credit and equity risk. The next section describes the research design

in detail.

10

4. Research Design

4.1. Debt/equity component estimation

The FC and PB methods estimate the debt and equity components of convertible debt

using a procedure derived from the binomial option-pricing model of Cox et al. [9] and

Rendleman and Bartter [25]. The procedure is described in detail in Barth et al. [3], and

is based on the notion that securities issued by a �rm can be priced as claims whose values

are contingent on the entire value of the �rm.12 The procedure begins with estimates of the

initial �rm value and the parameters that determine the evolution of �rm value. The possible

future �rm values are mapped to each state of a binomial tree that spans a period covering

the longest-maturity debt issue. The initial security values are then obtained by a recursive

procedure that solves for the contingent security values in each state using the characteristics

of each security (e.g., seniority, maturity, call/put option, conversion), and discounts them

back to time zero. The objective of the procedure is to measure the components of convert-

ible debt. Therefore, instead of using estimates of initial total capital and asset volatility to

calibrate the tree, I use a numerical search algorithm to solve for the parameters that mini-

mize the squared error between the observed and estimated security prices as in Barth et al.

[3].13 Implementation of the binomial model requires many inputs. These include debt issue

characteristics, market prices for debt and equity, outstanding equity shares and dividend

payout ratio, and risk-free interest rates. The resulting binomial tree enables the estimation

of the FC and PB convertible components. Appendix A contains a detailed example that

illustrates the di�erent component estimation methods.

The estimation procedure in this paper closely follows that described in Barth et al. [3],

with the following exceptions. Barth et al. [3] estimate debt component values at a single

point in time for a sample constructed using detailed information from year-end �nancial

statements. In contrast, I construct a panel dataset that spans multiple years and includes

12See Garbade [15] for a detailed analysis of contingent claims pricing for various corporate securities.13The search procedure requires starting values for initial total capital and asset volatility. I generate these

using available book and market values of debt and leverage-adjusted historical equity volatility, respectively.

11

quarterly observations. Capital structure disclosures in quarterly �nancial statements lack

some details, particularly the debt issue characteristics and the amount outstanding for in-

dividual debt issues, that are necessary to implement the estimation procedure. Therefore I

construct quarterly observations using machine-readable databases to obtain amounts out-

standing for public debt issues as well as public and private debt issue characteristics. I

restrict the estimation sample either to observations for which public debt outstanding is

within 5% of book value of debt, or to those for which public debt makes up between 50%

and 95% of book debt while the maximum amount of private debt outstanding exceeds the

di�erence between book and public debt. Maximum private debt is the total amount of

revolving and term loans issued prior to the observation date that have a maturity beyond

the observation date. To minimize the e�ects of estimation error from the sample selection

and estimation procedure, I adjust estimated asset volatility by leverage to obtain estimated

equity volatility. I eliminate observations that deviate most from observed equity volatil-

ity (top and bottom 5%). I also eliminate observations with extreme di�erences between

observed and estimated market values of debt (top and bottom 5%).

4.2. Creditors, leverage, and credit risk

Embedded within the Merton [23] model is the probability that the �rm defaults on its

debt. The Merton [23] default probability depends heavily on leverage, and has been shown

to explain cross-sectional variation in both actual default probability and bond yield spreads

(Hillegeist et al. [17], Bharath and Shumway [5]). I rely on this link between leverage

and credit risk to determine which method of estimating convertible components is most

consistent with that used by credit market participants. While bond yield spreads are widely

available for �rms with public debt, prior research has shown that signi�cant portions of the

spread can be attributed to illiquidity and di�erential state taxes (Longsta� et al. [22],

Elton et al. [13]). Therefore I examine the relationship between leverage components and

�rm credit risk, using various methods to separate the components of convertible debt, and

measuring �rm credit risk by Credit Default Swap (CDS) spreads.

12

A CDS can be viewed as an insurance contract that compensates the buyer for losses that

result from default. The buyer of protection pays the seller a periodic �xed premium until

either the contract expires or the issuer defaults. If default occurs, the seller of protection

buys back from the purchaser the defaulted bond (or another bond that satis�es the contract)

at par value.14 Because a CDS is a contract and not a security, it is less susceptible to liquidity

e�ects. Das et al. [10] develop a cross-sectional model of CDS spreads that incorporates both

accounting and market-based metrics. They �nd that the accounting-based variables are as

e�ective as market-based variables at explaining cross-sectional variation in CDS spreads. A

related study by Ericsson et al. [14] �nds that equity return volatility and leverage explain

a signi�cant portion of the variation in CDS spreads. To examine the distinct relationships

between leverage components and credit risk, I estimate the following least-squares regression

for �rms with convertible debt (each �rm-quarter can have multiple CDS spreads, each with

di�erent maturity and seniority):

log(CSijt) = β0 + β1DEBTCAPit + β2V OLit + β3LASSETit + β4ROAit + β5INTCOVit + β6QUICKit

+β7CASHTAit + β8EQRETit + β9IGit + β10SAP12MOt + β11RF3MOt + β12MATURITYijt [EQ 1]

+β13SENIORijt + εijt

The explanatory variable of interest is DEBTCAP. DEBTCAP is a measure of market

leverage that is de�ned as the market value of debt divided by the market value of total

capital ( MVDMVD+MVE+PSTK

), where MVD is the market value of debt, MVE is the market

value of equity, and PSTK is the par value of preferred stock. To test which convertible debt

measurement approach is most consistent with that used by creditors, I replace DEBTCAP

with the following leverage speci�cations:

14The contract may also allow for cash settlement in which the seller delivers the di�erence between theface value and default value of the bond in cash.

13

Leverage Variable Speci�cation

1 β1aDEBTCAPNC+β1bDEBTCAPCB, where DEBTCAPNC = MVNonConvertibleMV D+MVE+PSTK

and DEBTCAPCB = MV ConvertibleMV D+MVE+PSTK

2 β1aDEBTCAPNC+β1bDEBTCAPDBPB+β1cDEBTCAPEQPB, where

DEBTCAPDBPB = MVConvertibleDebtComponentPBMVD+MVE+PSTK and DEBTCAPEQPB =

MVConvertibleEquityComponentPBMVD+MVE+PSTK

3 β1aDEBTCAPNC+β1bDEBTCAPDBFC+β1cDEBTCAPEQFC, where

DEBTCAPDBFC=MV ConvertibleDebtComponentFCMVD+MVE+PSTK and

DEBTCAPEQFC=MV ConvertibleEquityComponentFCMVD+MVE+PSTK

The accounting and market-based control variables are de�ned below:

Variable Description

CS CDS spread in basis points

VOL Annualized prior 100 trading day equity volatility

LASSET Log of total assets scaled by CPI

ROA Trailing 4Q average of net income to total assets

INTCOV Trailing 4Q average of interest coverage

QUICK Quick ratio de�ned as (current assets�inventories)/current liabilities

CASHTA Cash divided by total assets

EQRET Annualized prior 100 trading day equity return

IG Indicator variable equal to 1 if S&P rating for long-term debt is BBB- or

above

SAP12MO Prior year return on S&P 500

RF3MO 3-month T-bill from St. Louis Federal Reserve FRED database

MATURITY Maturity of the CDS contract in years

SENIOR Indicator equal to 1 when underlying debt of CDS contract is senior

I use Leverage Speci�cation 1 to test whether the relationship between debt and credit risk

di�ers across convertible and non-convertible debt. I am speci�cally interested in whether

β1a di�ers signi�cantly from β1b. Speci�cation 2 (3) tests the degree to which the convertible

debt components measured using the PB (FC) method are consistent with those used by

credit market participants. A positive relationship between debt/leverage and credit risk

implies that equity component coe�cients should be both signi�cantly less than the debt

component coe�cient (β1c<β1b) and non-positive (β1c≤0). If either the PB or FC methods

yield equity estimates that satisfy these criteria, then I can conclude that creditors do not

use the FV method. I use non-nested hypotheses tests to assess the validity of the PB and

14

FC model alternatives.

4.3. Shareholders, leverage, and systematic equity risk

Positive relationships have been well established in the �nance literature (Hamada [16],

Bowman [6]) between operating risk and systematic equity risk and between leverage and

systematic equity risk . By examining how a particular security a�ects systematic equity risk,

one can assess the degree to which shareholders view the security as debt or equity. Several

accounting studies use this framework to assess the economic substance of unfunded pension

obligations (Dhaliwal [11]), redeemable and non-redeemable preferred stock (Kimmel and

War�eld [20], Cheng et al. [7]), and minority interest (Cheng et al. [7]). I use convertible

component estimates to adjust leverage by reclassifying the convertible equity component

as equity. I then relate the various convertible-adjusted leverage measures to equity risk to

determine how shareholders perceive of the economic substance of convertible debt.

If shareholders believe that the full market value of convertible debt is a liability, then

the di�erence between unadjusted and convertible-adjusted leverage should be positively

associated with systematic equity risk. I refer to that di�erence as leverage error. On the

other hand, if shareholders recognize debt and equity components of convertibles in a manner

consistent with a particular estimation method, then the resulting leverage error should be

non-positively associated with systematic equity risk. To test the estimation methods, I

estimate the following least-squares regression using quarterly observations for �rms with

convertible debt:

EQBETAit = β0 + β1ABETAit + β2ABETAit ∗DECDit + β3ABETAit ∗ (DEit −DECDit) [EQ 2]

+ΣINDDUM + ΣY EARDUM + εit

15

Variable Description

EQBETA Equity beta estimated from a one-factor market model using weekly returns over

the prior year

ABETA Firm asset beta calculated each December using time-series regressions of �rm

asset returns (value-weighted equity and debt returns) on market asset returns for

the prior 12 months, lagged by a minimum of 12 months prior to the quarterly

observation

DEBV Debt/equity ratio using book value of debt BVD/(MVE+PSTK), where BVD is

the book value of debt, MVE is the market value of equity, PSTK is the par value

of preferred stock, and with all D/E ratios measured using a trailing 4-quarter

average

DE Debt/equity ratio using market value of debt MVD/(MVE+PSTK), where MVD is

the estimated market value of debt

DECD Convertible-adjusted debt/equity ratio. Either:

1) DEPB for convertible equity component measured using PB method classi�ed as

equity (DEPB=(MVD=EQPB)/(MVE+PSTK+EQPB), where EQPB is the

equity component of convertible measured using PB method), or

2) DEFC for convertible equity component measured using FC method classi�ed as

equity (DEFC=(MVD=EQFC)/(MVE+PSTK+EQFC), where EQFC is the equity

component of convertible measured using FC method)

INDDUM

Fama-French 17 industry dummy variables

If either the FC or PB methods yield a leverage error that is more weakly related to equity

risk than is convertible-adjusted leverage (β3<β2), then I can conclude that the FV method

is not used by shareholders to measure leverage. To compare the FC and PB approaches, I

again use non-nested hypotheses tests.

5. Data and sample selection

5.1. Data

To estimate convertible debt components, I obtain annual and quarterly �nancial data

from Compustat for all �rms with convertible debt (excluding �nancial and utility �rms,

4-digit SIC 6000�6799 and 4900�4999, respectively). I obtain issue characteristics for all

outstanding public debt issues from Mergent FISD from 1995 to 2008. For private debt,

16

I use Securities Data Company (SDC) loan data to identify all loans issued by the �rms

starting from 1990. I obtain daily equity prices and dividend history from CRSP, daily bond

prices from either TRACE or Datastream, and risk-free rates from the St. Louis Federal

Reserve FRED database.15

Credit risk tests use daily CDS spreads from both ValuSpread and Datastream that span

2003�2007 (see Appendix B for details). CDS spread regressions include �nancial controls

from Compustat, market controls from CRSP, and the 3-month treasury rate from the St.

Louis Federal Reserve FRED database. I use the 17-industry de�nition �le from Ken French's

website to create industry controls.

I calculate equity betas, which are the dependent variable in the equity risk tests, using

weekly equity returns generated using CRSP daily data from 1994 to 2008. The measure of

operating risk, asset beta, is the beta from a regression of monthly �rm returns on monthly

market returns, where both �rm and market returns are based on value-weighted debt and

equity returns (Choi [8]).16

5.2. Sample selection

I �rst generate convertible component estimates for �rms that report convertible debt

outstanding and that have the necessary data to implement the binomial model. Table 1

shows the sample selection criteria that result in the estimation of convertible debt compo-

nents for 3,763 quarterly observations for 418 �rms. To ensure the accuracy of component

estimates used in the credit and equity risk tests, I �lter the estimates by comparing model

estimated equity volatility to historical volatility, and estimated bond values to observed

market values. The resulting sample contains debt and equity component estimates for

2,927 quarterly observations for 397 �rms.

CDS spread availability is the primary determinant of the credit risk sample size. After

15I use the clean price from TRACE, adjusted for accrued interest if available. Otherwise I use the grossbond price from Datastream. I thank Jens Dick-Nielsen for providing code used to clean TRACE bondprices (Dick-Nielsen [12]).

16I thank Jaewon Choi for generously providing asset betas use in this study.

17

merging the convertible component estimates with CDS spreads as well as �rm and macro

controls, the resulting sample contains 1,706 CDS spreads associated with 351 quarterly

reporting periods for 59 unique �rms (for details see Tables B1 and B2 in Appendix B). CDS

spreads can be quoted for multiple maturities, and for both senior and subordinated issues.

As a result, multiple spreads can exist for a given quarterly observation. The less restrictive

data requirements for the equity risk tests yield a larger sample that includes 1,778 quarterly

observations for 285 �rms.

6. Results

6.1. Convertible debt component estimates

To assess how e�ectively the estimation procedure separates the components of convert-

ible debt, I examine debt and equity component sizes as they relate to both settlement

outcomes and the ratio of conversion to market value of the convertible.17 The larger the

ratio of conversion to market value, the higher the probability of conversion, and the more

equity-like the convertible. Panel A of Table 2 summarizes the convertible component es-

timates for the 3,532 convertible bonds in the sample, for quartiles of increasing CV/MV.

Both the PB and FC methods produce component estimates with an increasing fraction of

equity across quartiles. The lowest-quartile debt percentage is 90% under the PB method

and 93% under the FC method, while the highest-quartile debt percentage is 21% under the

PB method and 57% under the FC method. As anticipated, the PB method produces larger

equity component estimates than does the FC method in every quartile, with the di�erence

increasing with CV/MV. In addition, the average bond market value increases across quar-

tiles from a mean of $233.31M in the lowest quartile to $425.06M in the highest quartile.

Panel B contains summary statistics for the most recent component estimates available in

the two-year period prior to settlement.18 Both converted issues and issues called when the

17CV/MV = (EquityPrice*NumberConvertibleShares)/((BondPrice/100)*TotalFaceValue)18I identify the settlement outcome using the Mergent FISD amount outstanding history data, and include

only those bonds that are either called, converted, or matured. To determine whether the conversion optionwas in the money for bonds that have been called, I compare the conversion price to the last stock price

18

conversion option was in-the-money (likely forced conversions) have relatively small PB and

FC debt components compared to those of issues that settle as debt at maturity. In sum, the

data in Table 2 suggest that the PB and FC convertible component estimates are reliable.

I combine convertible debt component measurements for each of the 2,927 �rm quarters,

and calculate debt, equity, and leverage using the FV, FC, and PB methods. Table 3 contains

leverage-related summary statistics for the full estimate sample. Average market values of

debt and equity are large, approximately $800M and $4B, respectively. The large �rm bias

is a result of the data requirements imposed to estimate the binomial model, primarily

the requirement to have available bond prices.19 Each of the FC and PB approaches yields

estimates with signi�cant variation in the debt and equity proportions. The PB (FC) method

produces component estimates with 25% (45%) of the market value of convertible debt

assigned to debt for the observation at the 25% percentile, and 84% (96%) percent of the

fair value at the 75% percentile. Classi�cation of the full market value of convertibles as debt

results in an average debt-to-total-capital ratio of 0.22 (median 0.19), approximately three

quarters of which, on average, consists of convertible debt. Reclassi�cation of the equity

component, measured using the PB method, reduces the average debt-to-total-capital ratio

over 30% to 0.15 (median 0.11). The reduction is less than 25% when the equity component is

measured using the FC method (mean 0.17 and median 0.14). Overall, Table 3 indicates that

the three convertible measurement methods produce signi�cantly di�erent leverage estimates.

6.2. Convertible debt and credit risk: creditors' perspective

Table 4 contains descriptive statistics for the 351 �rm-quarters in the CDS sample. The

average debt-to-total-capitalization ratio is 0.19, with roughly 40% consisting of convertible

debt. The large inter-quartile ranges of DEBTPCTPB and DEBTPCTFC indicate a sig-

ni�cant amount of variation in the debt and equity component measurements. However,

available prior to the date on which the debt is extinguished.19Prior to October 1, 2004, TRACE prices are only available for issues with initial issuance values of

$100M and above. Similarly, Datastream bond prices are only available for issues of $100M or more prior to2008.

19

variation in overall �rm credit risk may be limited, as indicated by the low leverage and the

large percentage of observations with investment grade long-term debt ratings.

Table 5 reports regression results for the credit risk sample using only a subset of theoret-

ical determinants of default risk from Equation 1. Speci�cally, I include leverage, volatility,

and the risk-free rate along with controls for the characteristics of the underlying debt as-

sociated with the CDS. Regressions in Tables 5 and 6 also include industry controls. These

tables report t-statistics using standard errors corrected for clustering at the �rm and cal-

endar year-quarter level. From Column 1 of Table 5 we see that leverage, de�ned using

the entire market value of all debt, is positively associated with CDS spreads. In addi-

tion, volatility and risk-free rate are signi�cantly associated with default risk as predicted

by structural models, and the explanatory power of the minimal set of regressors is high

(adjusted R-squared of 0.68). In Column 2, I include DEBTCAPCB to test whether the

relationship between convertible debt and CDS spreads di�ers from that of CDS spreads

and non-convertible debt. I �nd that the di�erence is positive and signi�cant at the 5%

level. The expected coe�cient on DEBTCAPCB depends on a number of assumptions,

including whether the market value of convertible debt contains an equity-like component,

whether one expects the debt component of convertible debt to relate to credit risk in the

same way as does non-convertible debt, and the average portion of the debt component for

the sample. In Column 3 of Table 5, I use the PB method to independently measure the

e�ects for non-convertible debt and for the debt and equity components of convertible debt.

The coe�cient of the equity component is less than that of the debt component (5.794 for

DEBTCAPEQPB compared to 7.636 for DEBTCAPDBPB), although the di�erence is not

signi�cant. In addition, the equity component is positively and signi�cantly associated with

CDS spreads. Therefore I cannot conclude from Column 3 that credit market participants

separate the market value of debt using the PB method. Results in Column 4 indicate that

the FC method produces an equity component coe�cient that is both signi�cantly less than

that of the debt component, and not signi�cantly greater than zero. This suggests that

20

the FC method produces equity components not positively associated with credit risk, thus

rejecting the hypothesis that credit market participants view the full market value of debt

as a liability. Separation of convertible market value into components using the FC method

also provides a modest increase in R-squared over that of the PB method. However, results

from the J -test used to compare the validity of the non-nested models are inconclusive.

The large coe�cients on the debt component of the convertible in Table 5, relative to

those of non-convertible debt, suggests the convertible debt component is riskier. Com-

ponent estimation is linked directly to stock price performance from the time of issuance

to the measurement date, which could cause the component estimates to proxy for market

performance. It is possible that correlated omitted variables that capture other aspects of

�rm solvency and pro�tability are also a�ecting the results in Table 5. Therefore I include

additional controls for �rm pro�tability, solvency, and market performance in Table 6 to

better isolate the e�ects of the debt and equity component measurements. After including

the additional controls, the di�erence between the coe�cient on the debt component of the

convertible and the non-convertible debt reduces signi�cantly, but it is still positive. The

results in Columns 3 and 4 indicate that, after controlling for other �rm characteristics re-

lated to credit risk, both the PB and FC methods produce equity components that are more

weakly associated with CDS spreads than the debt components, and that are non-positively

related to CDS spreads. However, the J -test rejects the PB model in favor of the FC model

at the 1% level. In sum, the results in Tables 5 and 6 reject the hypothesis that creditors

recognize the market value of convertible debt as a liability, and indicate that the FC method

is most consistent with the method used by the credit market. 20

6.3. Convertible debt and equity risk: shareholders' perspective

Table 7 contains descriptive statistics for the debt/equity ratios and beta estimates used

in the equity beta regressions. I trim the top and bottom 1% of the of the observations

20Restricting the sample to a single observation per �rm-quarter yields consistent results (sample limitedto CDS contracts for senior debt and 5-year maturity). Also, the results in Table 6 are unchanged when Iuse prior 1/2/4-year �rm returns for FIRMEQRET.

21

based on the D/E ratio, and winsorize ABETA at the top and bottom 1%. Reclassi�cation

of the equity measured with PB and FC reduces the average D/E ratio by 32% and 21%,

respectively.

Table 8 reports results for Equation 2 regressions of systematic equity risk on operat-

ing risk and leverage measures. Each regression includes industry and year controls, and

reports t-statistics using standard errors corrected for clustering at the �rm level. To create

convertible-adjusted D/E ratios, I subtract the equity component value from the market

value of debt in the numerator, and add it to the market value of equity plus preferred

stock in the denominator. I average all D/E ratios over the trailing four quarters to account

for changes over the equity beta estimation period. I use asset betas from the year prior

to the start of the observation year in order to avoid any overlap between the asset beta

and equity beta measurement periods. Column 1 of Table 8 includes book value of debt

in the leverage measure, and it con�rms the positive relationship between operating risk,

leverage, and equity risk found in prior studies. In Column 2, I replace the book value with

the market value of debt, resulting in a larger coe�cient on the leverage interaction term

(0.109 for ABETA*DEBV compared to 0.127 for ABETA*DE). The improved performance

of the model using the market value of debt is not surprising given that the underlying the-

ory applies to market leverage. However, if we assume that a portion of the market value

of the convertible should not be positively associated with equity risk, then adjusting the

D/E ratio using the FC and PB methods should provide further improvements. Results in

Column 3 con�rm that adjusting the D/E ratio by reclassifying the equity component mea-

sured using the PB method strengthens the relationship between leverage and systematic

equity risk. The leverage error coe�cient of -0.133 is negative and the di�erence between the

PB�adjusted D/E ratio and the leverage error is signi�cant at the 1% level. In addition, the

coe�cient on convertible-adjusted D/E increases to 0.135 from 0.127 for unadjusted D/E.

Adjusting leverage using the FC�measured equity also yields an improvement, though it is

weaker. The leverage error coe�cient is -0.109, which is signi�cantly di�erent from that of

22

the FC�adjusted D/E at the 5% level. Though signi�cance levels indicate the PB method

is more consistent with that used by shareholders, the J -test of the PB and FC non-nested

models yields inconclusive results.

Changes in �rm stock price link the probability that stock options are exercised and

increase equity, to the equity components measured using both the PB and FC methods.

To ensure that the results in Table 8 are not driven by the correlation between component

estimates and stock option value, I run the equity risk regression using low and high con-

vertible intensity sub-samples. I de�ne high convertible intensity as observations with ratios

of convertible shares to common shares outstanding above 0.10. The low convertible inten-

sity results (unreported) show that neither the PB or FC methods yield improved leverage

measures. However, Column 3 of Table 9 indicates that the PB equity improves leverage

measurement for the high convertible intensity sample. Assuming convertible intensity is

not related to stock option issuance, the results suggest that the improvement in leverage

measurement is due to reclassi�cation of PB measured equity, and not to potential stock

option�related equity increases. Together, the equity risk results indicate that shareholders

adjust the market value of convertible debt when measuring leverage, and that they recognize

equity in a manner consistent with the PB method.

7. Conclusion

In this study I examine how creditors and shareholders perceive the economic substance

of convertible debt. Prior research presents alternative methods to measure the debt and

equity components of convertible debt, with di�erences among the alternatives arising from

the de�nitions of liability they assume, and whether the approach adopts a more creditor-

or shareholder-focused perspective. Using market measures of credit and equity risk, I �nd

that creditors and shareholders recognize separately the debt and equity components of

convertibles in a manner consistent with the use of option-pricing�based procedures. For a

sample of �rms with convertible debt, I �nd that cross-sectional variation in CDS spreads,

which is a measure of credit risk, is best explained by leverage that separates the market

23

value of convertible debt into a debt component valued as an identical issue without the

conversion option. In contrast, when separating the convertible into a debt component that

incorporates the probability that the issue settles as debt, I �nd measures of leverage most

consistent with theory that links leverage to systematic equity risk. These results suggest

that neither shareholders nor creditors view the entire market value of convertible debt as a

liability, and that each investor group adopts di�erent liability assumptions when measuring

the debt and equity components.

E�orts to improve accounting guidelines for hybrid �nancing instruments such as con-

vertible debt are currently part of the FASB/IASB project for �nancial instruments with

characteristics of equity (formerly the liabilities and equity project). The groups have re-

cently decided that convertible debt should be treated as a liability in its entirety. The

supporting argument for the decision, also shared by supporters of the FV method, is that

payment with either shares or cash is a cost to the �rm, and therefore should be classi�ed as

a liability. Further decisions regarding accounting for convertibles will fall under the project

for �nancial instruments, which currently does not clearly specify whether fair-value report-

ing for convertible debt will be required. The �ndings of this study suggest that fair-value

reporting of convertible debt, without additional information to help investors adjust fair

value accurately and e�ciently, will be of limited use to investors. While this paper focuses

on the balance sheet e�ects of convertible debt accounting, I acknowledge that any poten-

tial improvements must also be judged on their ability to adequately facilitate performance

measurement.

An investor interested in measuring the debt and equity characteristics of convertible

debt can choose from a number of con�icting methods, each with its own merits. Despite the

numerous alternatives, and their di�erences in assumptions and outcomes, I am not aware of

any studies that examine which methods are actually used by investors. By taking a market

perspective, this study provides insight into the way creditors and shareholders perceive

the economic substance of convertible debt and the degree to which their perceptions are

24

consistent with proposed accounting methods.

25

Appendix A: Convertible debt component estimates

I use the non-callable convertible debt example from Barth et al. [3] to illustrate the

three di�erent approaches to convertible component measurement. The example uses the

binomial model to value a convertible debt issue for a �rm with a single share of equity and

a single outstanding convertible bond. The $60 face-value bond matures at the end of two

binomial periods. This bond can be converted into a single share of common stock. It pays

interest of $6 in Periods 1 and 2 if neither default nor conversion occurs. The initial total

capital value of the �rm is $100. The model parameters are u=1.5 (up transition), d=0.5

(down transition) and r=0.05 (risk-free rate). Therefore (π = 1+r−du−d = 1.05−0.5

1.5−0.5= 0.55) is the

risk-neutral probability of an up transition. When the conversion value exceeds the value

of holding the bond, the debt holder optimally exercises the conversion option. The hold

value is the expected next-period payo�, calculated using the risk-neutral probabilities, and

discounted by the risk-free rate. The resulting contingent value function that determines

debt value in each state is DEBT = min(max(0.5∗FirmV al, DebtPmt), F irmV al), where

FirmVal equals total capital value in each state, and DebtPmt is either face value plus interest

at end of period 2, hold value plus interest at end of period 1, or hold value at time zero.

Equity value is the di�erence between �rm value and debt value in each state. I use the

notation Si,j to refer to states of the tree where i equals the time period and j equals the

number of up transitions that have occurred.

Table A1 shows the recombining binomial tree used to value the convertible bond and

common share. At t=2, we see that the bond is converted in S2,2, the principal and interest

is paid in S2,1, and default occurs in S2,0. The resulting fair value of the convertible at t=0

is $70.26, and this is the debt value used in the FV method (FV equity equal to 0). The PB

method requires one to identify and allocate the components that make up the convertible

fair value to debt or equity outcomes. I specify conversion as an equity outcome, and all

others as debt outcomes (e.g., principal payments, interest payments, default). We see from

Table A1 that the equity conversion component value is $30.87 (π2∗112.50(1+r)2

= 30.87). Table A2

26

uses the same model parameters to value an identical non-convertible issue. The resulting

debt value of $57.50 is the FC debt component, and the di�erence between FC debt and fair

value is the FC equity component ($12.76). For each method, the fair value of the convertible

is equal to the sum of the debt and equity components. The actual implementation of the

model accommodates multiple debt issues, and takes into account other debt features that

a�ect pricing (e.g., call, put, sinking fund, seniority).

27

TableA1:

Estimationof

FVandPBConvertibleDebt/EquityCom

ponents

ModelParameters

t=0

t=1

t=2

u1.50

d0.50

Hold

0.00

r0.05

Convert

112.50

pi

0.55

Debt

112.50

CF

60.00

Equity

112.50

int

0.10

Total

225.00

convshr

1.00

Hold

87.21

Convert

75.00

Method

Component

Value

Debt

93.21

HFV

Debt

70.26

Equity

56.79

Equity

0.00

Total

150.00

Total

70.26

Hold

70.26

Hold

0.00

PB

Debt

39.39

Convert

50.00

Convert

37.50

Equity

30.87

Debt

70.26

HDebt

66.00

FTotal

70.26

Equity

29.74

Equity

9.00

Total

100.00

Total

75.00

ConvertibleOutcome

Value

Hold

45.29

Conversion

30.87

Convert

25.00

PrincipalPmt.

13.47

Debt

50.00

DInterestPmt.

4.49

Equity

0.00

Default

21.43

Total

50.00

Total

70.26

Hold

0.00

Convert

12.50

Debt

25.00

DEquity

0.00

Total

25.00

Description:Example

ofestimationof

convertible

debtcomponents

usingbinomialmodel.Letters

nextto

thedebtvaluein

each

state

indicate

whether

theconvertiblewasheld(H

),converted

(C),defaulted

(D),ortheface

valuewaspaid

infull(F).

28

TableA2:

Estimationof

FCConvertibleDebt/EquityCom

ponents

ModelParameters

t=0

t=1

t=2

u1.50

d0.50

Hold

0.00

r0.05

Convert

0.00

pi

0.55

Debt

66.00

FF

60.00

Equity

159.00

int

0.10

Total

225.00

convshr

0.00

Hold

62.86

Convert

0.00

Method

Component

Value

Debt

68.86

HFC

Debt

57.50

Equity

81.14

Equity

12.76

Total

150.00

Total

70.26

Hold

57.50

Hold

0.00

Convert

0.00

Convert

0.00

Debt

57.50

HDebt

66.00

FEquity

42.50

Equity

9.00

Total

100.00

Total

75.00

Hold

45.29

Convert

0.00

Debt

50.00

DEquity

0.00

Total

50.00

Hold

0.00

Convert

0.00

Debt

25.00

DEquity

0.00

Total

25.00

Description:Example

ofestimationof

convertible

debtcomponents

usingbinomialmodel.Letters

nextto

thedebtvaluein

each

state

indicate

whether

theconvertiblewasheld(H

),converted

(C),defaulted

(D),ortheface

valuewaspaid

infull(F).

29

Appendix B: Credit Default Swap (CDS) data

I obtain CDS spreads for U.S. �rms for the period from 2003 to 2007 from both ValuS-

pread and Datastream. Each source contains spreads for single-name CDS contracts, the

seniority and currency of the underlying debt, and the maturity used in the contract. Only

ValuSpread speci�es the restructuring clause for the CDS for the full sample period, while

Datastream speci�es restructuring starting in May 2008. To maintain comparability across

sources, I restrict ValuSpread observations to only those with modi�ed restructuring.21

If multiple spreads are available for a given �rm observation and seniority/maturity, I

use the one that is most reliable as determined by the standard deviation of the mid-market

spread (Valuspread) or veracity index (Datastream). I de�ne spread reliability as follows

(from highest to lowest reliability) :

1. Datastream veracity index=1 (observed market spread).

2. ValuSpread standard deviation of mid-market spread between 0% and 20% of mean

spread (standard deviation of 0 could indicate a small number of available quotes).

3. ValuSpread standard deviation of mid-market spread of 0% or greater than 20% of

mean spread.

4. Datastream veracity index=2 (derived spread).

Tables B1 and B2 contain descriptive statistics for the CDS spreads that correspond to

the quarterly observations used in the �nal convertible sample. As expected, CDS spreads

increase monotonically with maturity, and spreads for senior issues are much lower than

those of subordinated. Also, CDS spreads exhibit a gradual decrease over the sample period.

21Modi�ed restructuring is the most common clause for U.S. �rms (Berndt et al. [4]), and is assumed inthe absence of a speci�ed restructuring type by Datastream.

30

Table B1: CDS Spreads by Seniority/Maturity

Maturity1YR 3YR 5YR 7YR 10YR ALL

Senior mean 46.29 64.90 82.69 88.93 99.37 76.63median 13.45 28.42 43.15 49.89 60.41 39.27N 313 330 344 320 323 1630

Subord. mean 73.30 87.37 105.62 121.42 129.48 104.61median 46.05 58.24 67.42 104.08 106.13 75.45N 12 16 18 14 16 76

Total mean 47.28 65.94 83.83 90.29 100.79 77.87median 13.65 29.86 44.24 52.42 62.75 40.50N 325 346 362 334 339 1706

Description: CDS descriptive statistics by seniority/maturity for convertible component regression sample.

CDS data obtained from ValuSpread and Datastream (2003�2007). CDS spreads in basis points.

Table B2: CDS Spreads by Year

Year2003 2004 2005 2006 2007 ALL

Spread mean 159.31 80.44 63.01 75.81 55.31 77.87median 66.00 47.61 39.65 32.95 31.90 40.50N 182 344 428 372 380 1706

Firm-Quarters N 36 70 94 76 75 351Firms (Unique) N 18 31 40 28 28 59

Description: CDS descriptive statistics by year for convertible component regression sample. CDS data

obtained from ValuSpread and Datastream (2003�2007). CDS spreads in basis points.

31

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34

Table 1: Convertible Component Estimation, Sample Selection

No. Selection Criterion Source Obs. Firms1 Annual observations with convertible debt

outstanding anytime between 1995 and2008

Compustat Annual 10047 3066

2 Number of quarters for convertible debt�rms from 1995 to 2008

Compustat Quarterly 114792 3062

3 Quarterly observations with CRSP priceavailable for single equity issue

CRSP Daily 75025 2534

4 Public debt only (w/in 5% of �ndebt), orpublic + private > �ndebt

Mergent FISD / SDC 8032 662

5 At least one bond price following earningsreport

TRACE / Datastream 6148 539

6 Convertible component estimates(convertible debt / total debt > 10% ,total debt / total capital > 5%, publicdebt / total debt > 50%)

3763 418

7 Convertible component estimates �lteredby estimated equity volatility and bondvaluation error

2927 397

Sources: Compustat North America Fundamental Annual/Quarterly Files, CRSP Daily Stock File, Mergent

FISD, Securities Data Co. (SDC) Syndicated Loan Data, TRACE Historical Time and Sales Data, Thomson

Reuters Datastream, St. Louis Federal Reserve Economic Data (STL FRED).

35

Table 2: Convertible Bond Component Estimates

Panel A: Estimates by Conversion/Market Value QuartileConversion/Market Val. Variable mean sd 25th pct median 75th pct

Q1 MVERRPCT 1.03 3.94 -0.00 0.00 0.48(N=883) MVCD 233.31 211.93 105.88 168.38 300.72

DEBTPCTPB 0.90 0.15 0.82 0.99 1.00DEBTPCTFC 0.93 0.11 0.91 1.00 1.00

Q2 MVERRPCT 1.34 4.50 -0.00 0.00 0.83(N=883) MVCD 294.58 290.15 126.04 194.66 353.63

DEBTPCTPB 0.63 0.27 0.39 0.57 0.94DEBTPCTFC 0.71 0.25 0.49 0.71 0.98

Q3 MVERRPCT 0.70 3.43 -0.00 0.00 0.00(N=883) MVCD 323.61 339.49 139.94 213.84 367.66

DEBTPCTPB 0.43 0.27 0.21 0.31 0.62DEBTPCTFC 0.59 0.32 0.28 0.62 0.93

Q4 MVERRPCT 0.20 2.49 -0.32 0.00 0.56(N=883) MVCD 425.06 448.27 162.74 284.39 530.63

DEBTPCTPB 0.21 0.24 0.03 0.12 0.32DEBTPCTFC 0.57 0.30 0.30 0.64 0.83

Panel B: Estimates Prior To SettlementSettlement Variable mean sd 25th pct median 75th pctConverted DEBTPCTPB 0.20 0.31 0.00 0.09 0.20(N=26) DEBTPCTFC 0.41 0.28 0.15 0.41 0.64

Called (in-the-money) DEBTPCTPB 0.23 0.36 0.00 0.01 0.33(N=46) DEBTPCTFC 0.60 0.31 0.36 0.62 0.91

Called (at/out-of-the-money) DEBTPCTPB 0.87 0.28 0.95 1.00 1.00(N=84) DEBTPCTFC 0.95 0.14 0.98 1.00 1.00Matured DEBTPCTPB 0.84 0.32 0.92 1.00 1.00(N=65) DEBTPCTFC 0.94 0.13 0.97 1.00 1.00

Description: Convertible bond component estimates by conversion/market value quartile ((equityprice*convertible shares)/market value) in Panel A, and by settlement type in Panel B. Component es-timates in Panel B are the most current available in the two year period prior to settlement for bonds thatcan be identi�ed as called, converted, or matured in the Mergent FISD database.

Variable De�nitions: MVERRPCT is the percent error between the observed and estimated market value

of convertible debt ((MV(estimated)/MV(observed)-1)*100). MVCD is the estimated market value of con-

vertible debt. DEBTPCTPB is the fraction of market value of the convertible attributable to the debt

component and is computed as CBDEBTPB/(CBDEBTPB+CBEQPB), where CBDEBTPB (CBEQPB)

is the estimated amount of the debt (equity) component of the convertible using the probability-weighted

method in millions USD. DEBTPCTFC is the fraction of market value of the convertible attributable to the

debt component and is computed as CBDEBTFC/(CBDEBTFC+CBEQFC), where CBDEBTFC (CBE-

QFC) is the estimated amount of debt (equity) component of convertible using the fundamental components

method in millions USD.

36

Table 3: Convertible Debt Components and Leverage, Full Estimate Sample

Variable mean (N=2927) sd 25th pct median 75th pctMVE 3964.33 8681.87 656.49 1318.21 3184.53BVD 749.72 1308.57 175.00 316.26 638.17MVD 798.84 1411.79 173.92 314.46 709.03CBDEBTPB 207.55 292.82 49.10 114.68 244.03CBEQPB 212.62 347.00 29.47 111.99 233.90DEBTPCTPB 0.53 0.32 0.25 0.49 0.84CBDEBTFC 293.47 431.66 79.07 160.05 345.78CBEQFC 126.70 202.79 10.20 65.63 149.58DEBTPCTFC 0.68 0.29 0.45 0.76 0.96DEBTCAP 0.22 0.13 0.13 0.19 0.29DEBTCAPCB 0.17 0.10 0.10 0.15 0.21DEBTCAPNPB 0.15 0.14 0.06 0.11 0.21DEBTCAPNFC 0.17 0.14 0.08 0.14 0.24

Description: Summary statistics for convertible debt components and leverage related variables, full estimatesample.

Variable De�nitions: MVE is the market value of equity. BVD is the book value of debt. MVD

is the estimated market value of debt. CBDEBTPB (CBEQPB) is the estimated amount in mil-

lions USD of the debt (equity) component of the convertible using a probability-weighted method.

DEBTPCTPB is the fraction of market value of the convertible attributable to the debt compo-

nent (CBDEBTPB/(CBDEBTPB+CBEQPB)). CBDEBTFC (CBEQFC) is the estimated amount in

millions USD of the debt (equity) component of the convertible using the fundamental components

method. DEBTPCTFC is the fraction of market value of the convertible attributable to the debt

component and is computed as CBDEBTFC/(CBDEBTFC+CBEQFC). DEBTCAP is debt to total

capitalization (MVD/(MVD+MVE+PSTK)). DEBTCAPCB is the convertible debt to total capitaliza-

tion ((CBDEBTPB+CBEQPB)/(MVD+MVE+PSTK)). DEBTCAPNPB is the debt to total capital-

ization, excluding the equity component of the convertible measured using the probability-weighted

method ((MVD=CBEQPB)/(MVD+MVE+PSTK)). DEBTCAPNFC is the debt to total capitalization,

excluding the equity component of the convertible measured using the fundamental components method

((MVD=CBEQFC)/(MVD+MVE+PSTK)).

37

Table 4: CDS Sample Descriptive Statistics

mean (N=351) sd 25th pct median 75th pctDEBTCAP 0.19 0.11 0.10 0.16 0.28DEBTCAPNC 0.11 0.10 0.03 0.07 0.19DEBTCAPCB 0.08 0.05 0.05 0.06 0.10DEBTCAPEQPB 0.04 0.03 0.02 0.03 0.05DEBTCAPEQFC 0.02 0.02 0.00 0.01 0.02DEBTPCTPB 0.50 0.29 0.28 0.50 0.71DEBTPCTFC 0.80 0.16 0.68 0.84 0.95VOL 0.27 0.11 0.19 0.24 0.32ASSET 9512.23 9072.05 3029.92 4864.20 14472.50ROA 0.02 0.01 0.01 0.02 0.03INTCOV 12.42 11.14 4.22 9.97 17.89QUICK 1.66 1.28 0.89 1.37 2.00CASHTA 0.13 0.11 0.05 0.10 0.19IG 0.85 0.36 1.00 1.00 1.00EQRET 0.16 0.41 -0.11 0.14 0.40

Description: Descriptive statistics for �rm characteristics for 351 quarterly observations in the CDS sample.

Variable De�nitions: DEBTCAP is debt to total capitalization and is computed as

MVD/(MVD+MVE+PSTK), where MVE is the market value of equity and MVD is the estimated

market value of debt. DEBTCAPCB is the convertible debt to total capitalization and is computed as

(CBDEBTPB+CBEQPB)/(MVD+MVE+PSTK), where CBDEBTPB (CBEQPB) is the estimated amount

of debt (equity) component of convertible using the probability-weighted method. DEBTCAPNC is debt

to total capitalization, excluding convertible debt (DEBTCAP=DEBTCAPCB). DEBTCAPEQPB is the

estimated equity component of convertible debt using the probability-weighted method to total capitalization

(CBEQPB/(MVD+MVE+PSTK)). DEBTCAPEQFC is the estimated equity component of convertible

debt using the fundamental components method to total capitalization (CBEQFC/(MVD+MVE+PSTK)).

DEBTPCTPB is the fraction of market value of the convertible attributable to the debt component

measured using the PB method (CBDEBTPB/(CBDEBTPB+CBEQPB)). DEBTPCTFC is the fraction

of market value of convertible attributable to the debt component measured using the FC method

(CBDEBTFC/(CBDEBTFC+CBEQFC)). VOL is the annualized prior 100 trading day equity volatility.

ASSET is total �rm assets. ROA is the trailing four-quarter average of net income to total assets. INTCOV

is the trailing four-quarter average of interest coverage. QUICK is the quick ratio de�ned as (current

assets=inventories)/current liabilities. CASHTA is the cash divided by total assets. IG is the indicator

variable equal to 1 if S&P rating for long-term debt is BBB- or above. EQRET is the annualized prior 100

trading day equity return.

38

Table 5: CDS Spreads and Convertible Debt Components, Structural Variables

Panel A: Regression Results(1) (2) (3) (4)

FV PB FCVARIABLES (COMBINED) (DEBT ONLY) (PROB WEIGHT) (DEBT FIRST)

DEBTCAP 3.673***(7.959)

DEBTCAPNC 3.162*** 3.133*** 3.206***(6.255) (6.066) (6.542)

DEBTCAPCB 7.216***(3.567)

DEBTCAPDBPB 7.636***(3.371)

DEBTCAPEQPB 5.794***(3.122)

DEBTCAPDBFC 8.172***(3.549)

DEBTCAPEQFC 1.787(0.998)

VOL 3.680*** 3.157*** 3.104*** 3.177***(8.990) (6.321) (5.984) (6.385)

RF3MO -0.105*** -0.0899*** -0.0875** -0.0875**(-3.242) (-2.656) (-2.577) (-2.579)

MATURITY 0.148*** 0.148*** 0.148*** 0.148***(10.40) (10.44) (10.46) (10.48)

SENIOR -0.567*** -0.469*** -0.482*** -0.519***(-6.743) (-4.135) (-4.833) (-5.962)

Constant 1.441*** 1.337*** 1.383*** 1.439***(6.802) (5.030) (5.543) (6.355)

Observations 1706 1706 1706 1706Adjusted R2 0.683 0.705 0.706 0.711

Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.10

Panel B: Hypothesis TestsPB: β1b = β1c F=1.17 p=.28FC: β1b = β1c F=5.13 p=.02

PB v. FC: J-test H0(PB) t=6.54 p=.00PB v. FC: J-test H0(FC) t=-3.46 p=.00

OLS regressions of the log of CDS spreads on structural variables, with controls for issue characteristics andindustry e�ects. CDS spreads from ValuSpread and Datastream, with controls from Compustat quarterly�les, CRSP, and St. Louis Fed (STL FRED). Standard errors are corrected for clustering at the �rm andcalendar year-quarter level.

39

Variable De�nitions: DEBTCAP is debt to total capitalization and is computed asMVD/(MVD+MVE+PSTK), where MVE is the market value of equity and MVD is the estimatedmarket value of debt. DEBTCAPCB is convertible debt to total capitalization and is computed as(CBDEBTPB+CBEQPB)/(MVD+MVE+PSTK), where CBDEBTPB (CBEQPB) is the estimatedamount of the debt (equity) component of the convertible using the probability-weighted method.DEBTCAPNC is debt to total capitalization, excluding convertible debt (DEBTCAP - DEBTCAPCB).DEBTCAPBDPB is the estimated debt component of convertible debt using the probability-weightedmethod to total capitalization (CBDEBTPB/(MVD+MVE+PSTK)). DEBTCAPEQPB is the estimatedequity component of convertible debt using the probability weighted method to total capitalization(CBEQPB/(MVD+MVE+PSTK)). DEBTCAPBDFC is the estimated debt component of convertible debtusing the fundamental components method to total capitalization (CBDEBTFC/(MVD+MVE+PSTK)).DEBTCAPEQFC is the estimated equity component of convertible debt using the fundamental componentsmethod to total capitalization (CBEQFC/(MVD+MVE+PSTK)). VOL is the annualized prior 100 tradingday equity volatility. RF3MO is the 3-month T-bill. MATURITY is the maturity of the CDS contract inyears. SENIOR is an indicator variable equal to 1 if underlying bond is senior.

40

Table 6: CDS Spreads and Convertible Debt Components, Accounting- and Market-based Controls

(1) (2) (3) (4)FV PB FC

VARIABLES (COMBINED) (DEBT ONLY) (PROB WEIGHT) (DEBT FIRST)

DEBTCAP 2.414***(5.355)

DEBTCAPNC 2.298*** 2.360*** 2.399***(4.447) (4.759) (4.847)

DEBTCAPCB 3.905***(3.350)

DEBTCAPDBPB 4.833***(3.609)

DEBTCAPEQPB 1.514(1.366)

DEBTCAPDBFC 5.000***(3.636)

DEBTCAPEQFC -0.612(-0.381)

VOL 1.948*** 1.897*** 1.743*** 1.889***(4.652) (4.687) (4.165) (4.563)

LASSET -0.321*** -0.309*** -0.321*** -0.300***(-7.290) (-7.630) (-7.828) (-7.108)

ROA -3.872 -2.208 -1.111 -1.269(-0.907) (-0.601) (-0.319) (-0.347)

INTCOV -0.00582** -0.00644** -0.00642** -0.00671**(-2.314) (-2.278) (-2.221) (-2.267)

QUICK -0.0245 -0.0548** -0.0617*** -0.0649***(-0.871) (-2.305) (-2.594) (-2.776)

CASHTA -0.507 -0.427 -0.290 -0.281(-1.422) (-1.289) (-0.902) (-0.866)

EQRET -0.130* -0.117 -0.0698 -0.0755(-1.653) (-1.492) (-0.899) (-0.992)

IG -0.982*** -0.945*** -0.973*** -0.958***(-5.571) (-5.854) (-6.525) (-6.747)

SAP12MO 0.00781 0.0574 0.0192 0.0299(0.0260) (0.199) (0.0728) (0.108)

RF3MO -0.0950*** -0.0910*** -0.0857*** -0.0891***(-3.488) (-3.201) (-2.958) (-3.113)

MATURITY 0.148*** 0.148*** 0.149*** 0.149***(10.44) (10.45) (10.53) (10.51)

SENIOR -0.452*** -0.435*** -0.461*** -0.487***(-5.016) (-4.284) (-4.706) (-5.570)

Constant 4.776*** 4.597*** 4.719*** 4.628***(19.26) (19.55) (21.78) (18.99)

Observations 1706 1706 1706 1706Adjusted R2 0.791 0.793 0.797 0.797

Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.10

41

Panel B: Hypothesis Tests

PB: β1b = β1c F=7.24 p=0.01

FC: β1b = β1c F=6.07 p=0.01

PB v. FC: J -test H0(PB) t=2.87 p=0.00

PB v. FC: J -test H0(FC) t=1.18 p=0.24

OLS regressions of the log of CDS spreads on leverage measures, with controls for accounting- and market-based variables. CDS spreads from ValuSpread and Datastream, with controls from Compustat quarterly�les, CRSP, and St. Louis Fed (STL FRED). Standard errors are corrected for clustering at the �rm andcalendar year-quarter level.

Variable De�nitions: DEBTCAP is debt to total capitalization and is computed as

MVD/(MVD+MVE+PSTK), where MVE is the market value of equity and MVD is the estimated

market value of debt. DEBTCAPCB is convertible debt to total capitalization and is computed as

(CBDEBTPB+CBEQPB)/(MVD+MVE+PSTK), where CBDEBTPB (CBEQPB) is the estimated

amount of the debt (equity) component of the convertible using the probability-weighted method.

DEBTCAPNC is debt to total capitalization, excluding convertible debt (DEBTCAP=DEBTCAPCB).

DEBTCAPBDPB is the estimated debt component of convertible debt using the probability-weighted

method to total capitalization (CBDEBTPB/(MVD+MVE+PSTK)). DEBTCAPEQPB is the estimated

equity component of convertible debt using the probability-weighted method to total capitalization

(CBEQPB/(MVD+MVE+PSTK)). DEBTCAPBDFC is the estimated debt component of convertible debt

using the fundamental components method to total capitalization (CBDEBTFC/(MVD+MVE+PSTK)).

DEBTCAPEQFC is the estimated equity component of convertible debt using the fundamental components

method to total capitalization (CBEQFC/(MVD+MVE+PSTK)). VOL is the annualized prior 100 trading

day equity volatility. LASSET is the log of total assets scaled by CPI. ROA is the trailing four-quarter

average of net income to total assets. INTCOV is the trailing four-quarter average of interest coverage.

QUICK is the quick ratio (current assets=inventories)/current liabilities. CASHTA is cash divided by total

assets. EQRET is the annualized prior 100 trading day equity return. IG is an indicator variable equal to 1

if S&P rating for long-term debt is BBB- or above. SAP12MO is the prior 12-month value return on the

S&P 500. RF3MO is the 3-month T-bill. MATURITY is the maturity in years of CDS contract. SENIOR

is an indicator variable equal to 1 if underlying bond is senior.

42

Table 7: Equity Beta Sample Descriptive Statistics

mean (N=1778) sd 25th pct median 75th pctEQBETA 1.55 0.82 0.93 1.45 2.09ABETA 1.59 1.31 0.69 1.41 2.39DEBV 0.38 0.32 0.18 0.27 0.45DE 0.37 0.27 0.19 0.28 0.44DEPB 0.25 0.29 0.08 0.17 0.31DEFC 0.29 0.29 0.11 0.20 0.36

Variable De�nitions: EQBETA is the equity beta estimated from a one-factor market model using weekly

returns over the prior year. ABETA is the �rm asset beta, calculated each December using time-series

regressions of �rm asset returns (value-weighted equity and debt returns) on market asset returns (value-

weighted asset returns) for the prior 12 months. DEBV is the debt/equity ratio calculated using the book

value of debt and is computed as BVD/(MVE+PSTK), where BVD is the book value of debt, MVE is the

market value of equity, and PSTK is the par value of preferred stock. DE is the debt/equity ratio calculated

using the market value of debt and is computed as MVD/(MVE+PSTK), where MVD is the estimated

market value of debt. DEPB is the PB�adjusted debt/equity ratio calculated by classifying the equity

component of the convertible as equity and is computed as (MVD=EQPB)/(MVE+PSTK+EQPB), where

EQPB is the equity portion of convertible debt measured using PB method. DEFC is the FC�adjusted

debt/equity ratio calculated by classifying the equity component of the convertible as equity and is computed

as (MVD=EQFC)/(MVE+PSTK+EQFC), where EQFC is theequity portion of convertible debt measured

using the FC method.

43

Table 8: Regressions of systematic equity risk on operating risk and convertible adjusted leverage (D/Ecalculated using trailing 4Q averages)EQBETAit = β0+β1ABETAit+β2ABETAit∗DECDit+β3ABETAit∗(DEit−DECDit)+ΣINDDUM +ΣY EARDUM +εit

Panel A: Regression Results(1) (2) (3) (4)

FV PB FCVARIABLES (BOOK DEBT) (DEBT ONLY) (PROB WEIGHT) (DEBT FIRST)

ABETA 0.189*** 0.190*** 0.217*** 0.210***(7.785) (7.013) (7.555) (7.490)

ABETA*DEBV 0.109**(2.174)

ABETA*DE 0.127*(1.859)

ABETA*DEPB 0.135**(2.463)

ABETA*(DE-DEPB) -0.133(-1.034)

ABETA*DEFC 0.131**(2.277)

ABETA*(DE-DEFC) -0.109(-0.793)

Constant 1.072*** 1.062*** 1.083*** 1.093***(4.334) (4.310) (4.507) (4.446)

Observations 1778 1778 1778 1778Adjusted R2 0.388 0.386 0.393 0.391

Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.10

Panel B: Hypothesis TestsPB: β2 = β3 F=6.51 p=.01FC: β2 = β3 F=4.41 p=.04

PB v. FC: J-test H0(PB) t=-2.83 p=.00PB v. FC: J-test H0(FC) t=3.94 p=.00

Description: Cross-sectional regressions of quarterly observations of systematic equity risk on operating riskand convertible adjusted leverage. Standard errors adjusted for �rm-level clustering.Variable De�nitions: EQBETA is the equity beta estimated from a one-factor market model using weeklyreturns over the prior year. ABETA is the �rm asset beta, calculated each December using time-seriesregressions of �rm asset returns (value-weighted equity and debt returns) on market asset returns (value-weighted asset returns) for the prior 12 months. DEBV is the debt/equity ratio calculated using the bookvalue of debt and is computed as BVD/(MVE+PSTK), where BVD is the book value of debt, MVE isthe market value of equity, and PSTK is the par value of preferred stock. DE is the debt/equity ratiocalculated using the market value of debt and is computed as MVD/(MVE+PSTK), where MVD is theestimated market value of debt. DEPB is the PB-adjusted debt/equity ratio calculated by classifying theequity component of the convertible as equity and is computed as (MVD - EQPB)/(MVE+PSTK+EQPB),where EQPB is the equity portion of convertible debt measured using PB method. DEFC is the FC-adjusteddebt/equity ratio calculated by classifying the equity component of the convertible as equity and is computedas (MVD - EQFC)/(MVE+PSTK+EQFC), where EQFC is the equity portion of convertible debt measuredusing the FC method.

44

Table 9: Regressions of systematic equity risk on operating risk and convertible adjusted leverage (D/Ecalculated using trailing 4Q averages), high convertible intensityEQBETAit = β0+β1ABETAit+β2ABETAit∗DECDit+β3ABETAit∗(DEit−DECDit)+ΣINDDUM +ΣY EARDUM +εit

Panel A: Regression Results(1) (2) (3) (4)

FV PB FCVARIABLES (BOOK DEBT) (DEBT ONLY) (PROB WEIGHT) (DEBT FIRST)

ABETA 0.161*** 0.156*** 0.198*** 0.182***(4.794) (4.422) (4.948) (4.770)

ABETA*DEBV 0.139(1.587)

ABETA*DE 0.170*(1.833)

ABETA*DEPB 0.245***(3.898)

ABETA*(DE-DEPB) -0.135(-0.770)

ABETA*DEFC 0.221***(3.070)

ABETA*(DE-DEFC) -0.0834(-0.426)

Constant 1.177*** 1.158*** 1.098*** 1.132***(3.968) (3.946) (3.832) (3.874)

Observations 1065 1065 1065 1065Adjusted R2 0.369 0.368 0.378 0.373

Robust t-statistics in parentheses *** p<0.01, ** p<0.05, * p<0.10

Panel B: Hypothesis TestsPB: β2 = β3 F=5.89 p=.02FC: β2 = β3 F=2.66 p=.10

PB v. FC: J-test H0(PB) t=-2.14 p=.03PB v. FC: J-test H0(FC) t=3.52 p=.00

Description: Cross-sectional regressions of quarterly observations of systematic equity risk on operating riskand convertible adjusted leverage. Standard errors adjusted for �rm-level clustering.Variable De�nitions: EQBETA is the equity beta estimated from a one-factor market model using weeklyreturns over the prior year. ABETA is the �rm asset beta, calculated each December using time-seriesregressions of �rm asset returns (value-weighted equity and debt returns) on market asset returns (value-weighted asset returns) for the prior 12 months. DEBV is the debt/equity ratio calculated using the bookvalue of debt and is computed as BVD/(MVE+PSTK), where BVD is the book value of debt, MVE isthe market value of equity, and PSTK is the par value of preferred stock. DE is the debt/equity ratiocalculated using the market value of debt and is computed as MVD/(MVE+PSTK), where MVD is theestimated market value of debt. DEPB is the PB-adjusted debt/equity ratio calculated by classifying theequity component of the convertible as equity and is computed as (MVD - EQPB)/(MVE+PSTK+EQPB),where EQPB is the equity portion of convertible debt measured using PB method. DEFC is the FC-adjusteddebt/equity ratio calculated by classifying the equity component of the convertible as equity and is computedas (MVD - EQFC)/(MVE+PSTK+EQFC), where EQFC is the equity portion of convertible debt measuredusing the FC method.

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