20101027 why do convertible issuers simultaneously repurchase stock

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Journal of Financial Economics

Journal of Financial Economics 100 (2011) 113–129

0304-40

doi:10.1

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Arturo B

Rudi Fa

Lewis,

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Rosenth

Thomas

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journal homepage: www.elsevier.com/locate/jfec

Why do convertible issuers simultaneously repurchase stock?An arbitrage-based explanation$

Abe de Jong a,b,n, Marie Dutordoir c, Patrick Verwijmeren d

a Rotterdam School of Management, Erasmus University, the Netherlandsb University of Groningen, the Netherlandsc Manchester Business School, UKd University of Melbourne, Australia

a r t i c l e i n f o

Article history:

Received 15 December 2008

Received in revised form

22 January 2010

Accepted 17 February 2010Available online 27 October 2010

JEL classification:

G32

Keywords:

Convertible debt

Convertible arbitrage

Short selling

Stock repurchase

5X/$ - see front matter & 2010 Elsevier B.V. A

016/j.jfineco.2010.10.016

thank an anonymous referee, Geert Bekaert,

ris, Hans Dewachter, Nico Dewaelheyns, Amy

hlenbrach, Mila Getmansky, Bruce Grundy, An

Igor Loncarski, Hanno Lustig, Sophie Mani

a, Ronald Masulis, Ser-Huang Poon, Mig

al, Anil Shivdasani, Norman Strong, Marta Szy

, Linda van de Gucht, Mathijs van Dijk, Chris V

and seminar participants at Universitat Aut �o

University of Louvain, Maastricht Universit

University of Melbourne, Rotterdam Schoo

s University, University of Stirling, Universit

ustralasian Finance and Banking Conference,

ment Association Conference, and the 2009

tion Conference for their useful comments. Par

while Patrick Verwijmeren was visiting Owe

ilt University.

esponding author at: Rotterdam School of Ma

ity, the Netherlands.

ail addresses: [email protected] (A. de Jong),

[email protected] (M. Dutordoir),

@unimelb.edu.au (P. Verwijmeren).

a b s t r a c t

Over recent years, a substantial fraction of US convertible bond issues have been

combined with a stock repurchase. This paper explores the motivations for these

combined transactions. We argue that convertible debt issuers repurchase their stock

to facilitate arbitrage-related short selling. In line with this prediction, we show that

convertibles combined with a stock repurchase are associated with lower offering

discounts, lower stock price pressure, higher expected hedging demand, and lower issue-

date short selling than uncombined issues. We also find that convertible arbitrage

strategies explain both the size and the speed of execution of the stock repurchases.

& 2010 Elsevier B.V. All rights reserved.

ll rights reserved.

Ekkehart Boehmer,

Dittmar, Eric Duca,

drew Karolyi, Craig

gart, Maria-Teresa

uel Rosellon, Len

manowska, Randall

eld, Kathleen Weiss

noma de Barcelona,

y, Manchester Uni-

l of Management,

y of Warwick, the

the 2008 Financial

European Finance

t of this article was

n Graduate School,

nagement, Erasmus

1. Introduction

Convertible bond issuance by US corporations hasincreased dramatically from $15.1 billion in 1993 to$61.6 billion in 2007. Over recent years, a substantialpercentage of US convertible debt issuers have announceda stock repurchase simultaneously with their convertibleoffering. Over the period 2005 to 2007, 23.7% of convertibleissues were combined with a stock repurchase. On average,the stock buybacks account for 41.1% of the proceeds of theconvertible bond issue.

The combinations of convertible debt offerings withstock repurchases (combined offerings) are intriguing.Why would a firm, on the one hand, issue an equity-linkedsecurity and, on the other hand, reduce its equity base byrepurchasing shares?

Our goal in this paper is to obtain more insight into whatmotivates firms to combine convertible debt offerings withstock repurchases. Based on informal talks with investment

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dx.doi.org/10.1016/j.jfineco.2010.10.016

1 Next to the relatively limited number of papers on arbitrage-

induced short selling, a broad stream of literature also exists on short

selling by fundamental traders (see, e.g., Diamond and Verrecchia, 1987;

Senchack and Starks, 1993; Aitken, Frino, McCorry, and Swan, 1998;

Cohen, Diether, and Malloy, 2007; and Diether, Lee, and Werner, 2009).

A. de Jong et al. / Journal of Financial Economics 100 (2011) 113–129114

bankers and chief financial officers of companies thatexecuted a combined offering, we hypothesize that therecent surge in combined convertible debt offerings andstock repurchases can be explained by the influence ofconvertible debt arbitrageurs. To exploit underpriced con-vertible issues, these funds buy the convertibles and shortthe underlying common stock. The resulting open-marketshort selling creates downward pressure on the stock priceof the convertible debt issuer (Arshanapalli, Fabozzi,Switzer, and Gosselin, 2005; Loncarski, ter Horst, andVeld, 2009).

We hypothesize that the combinations of convertibledebt offerings with stock repurchases result from aninterplay between the issuing firm and the arbitrageur.In a first step, the issuer sells the convertible to a con-vertible debt arbitrageur via an underwriter. Subsequently,the arbitrageur borrows issuer shares and sells them to theunderwriter at a pre-agreed price. The underwriter thensells the shares back to the issuing firm, thereby complet-ing the stock repurchase. The arbitrageur benefits from thistransaction because he does not have to short stock at anuncertain price in a market that is crowded by other shortsellers. The issuer benefits from the combination because,in return for acting as a counterparty in the short-sellingtransaction of the arbitrageur, he can charge a higher pricefor the convertible offering. Moreover, by privately crossingthe arbitrageur’s trades, the issuer avoids concentratedopen-market short sales and their negative stock priceeffect. Given its associated benefits for both issuers andbuyers, investment bankers refer to the combination of aconvertible issue and a stock repurchase as a Happy Meal.In the academic literature, this popular transaction hasthus far been ignored, however.

We use a sample of uncombined convertible offerings,uncombined stock repurchases, and combined convertibledebt-stock repurchase offerings made by US firms between2003 and 2007 and obtain the following six pieces ofempirical evidence consistent with the arbitrage explana-tion for combined offerings. First, combined offerings areapproximately 20% less underpriced upon issuance thanotherwise similar uncombined convertible offerings. Thisresult is consistent with the notion that firms are able tonegotiate more beneficial offering terms in exchange forfacilitating arbitrageurs in setting up their short positions.Second, issue-date abnormal stock returns for uncombinedofferings are significantly negative, while issue-date abnor-mal stock returns for combined offerings are close to zero.This pattern is consistent with lower issue-date pricepressure associated with combined convertible offerings.Third, the expected hedging demand from convertiblearbitrageurs is significantly higher for combined conver-tible issues than for uncombined issues. Fourth, observedissue-date open-market short sales are significantly lowerfor combined offerings. This finding is in line with theprediction that the short positions associated with com-bined convertibles are established in a privately negotiatedtransaction. Fifth, the number of shares that the convertibleissuers announce to repurchase is highly correlated withthe number of shares expected to be shorted by arbitra-geurs. Sixth, the typical firm engaged in a combinedoffering repurchases 86.6% of the announced number of

shares in the first quarter after the announcement,whereas for uncombined stock repurchases this percen-tage is much lower (2.6%). The immediate execution ofstock repurchases is consistent with arbitrageurs setting uptheir positions.

We also examine potential alternative explanations forcombined offerings. We analyse whether firms engage incombined offerings to signal their true value to the market,to reduce earnings per share dilution, to optimize capitalstructure, or to finance a stock repurchase program.Collectively, our results indicate that combinations areprimarily motivated by the issuers’ wish to cater to thehedging needs of convertible bond arbitrageurs.

Our main contributions to the literature are the follow-ing. First, our findings add new insights into the impact ofarbitrage-driven short selling on corporate actions. Priorstudies have focused on the impact of arbitrage-drivenshort selling on stock prices (Mitchell, Pulvino, andStafford, 2004; Arshanapalli, Fabozzi, Switzer, andGosselin, 2005) and on its implications for liquidity andmarket efficiency (Agarwal, Fung, Loon, and Naik, 2007;Choi, Getmansky, and Tookes, 2009).1 Lamont (2004)documents various mechanisms used by firms to reduceshort-selling activity, e.g., stock splits, lawsuits, or lettersencouraging stockholders not to lend out their shares. Weshow that, instead of remaining passive or trying to impedeshort selling, firms can also adjust their corporate financeactions to cater to the specific needs of arbitrageurs.

Second, our paper provides new insights into the stock-holder wealth effects of convertible debt offerings. It is welldocumented that announcements of convertible bondofferings induce a significant negative average stock pricereaction. While studies published in the 1980s and 1990sregister convertible debt announcement effects in theorder of �2% (see Eckbo, Masulis, and Norli, 2007, for areview of the literature), Marquardt and Wiedman (2005)find that recent convertible debt announcements areaccompanied by stock returns that are more than twiceas negative. Our results suggest that a substantial part ofthe announcement-date stock price effects associated withrecent convertible debt issues can be attributed to hedging-induced price pressure. In line with the arbitrage explana-tion, we find that, for uncombined convertible bondofferings, a significant stock price reversal occurs overthe weeks following the offering. For combined convertiblebond issues, we find no negative stock price reaction and nostock price drift over subsequent weeks. Also consistentwith the arbitrage explanation, we find that the differencein stock price reactions to combined and uncombinedofferings is no longer significant after controlling fordifferences in hedging-induced price pressure. Our findingshighlight the need to control for downward price pressureresulting from uninformed arbitrage-related short sellingin an analysis of the wealth effects associated with recentconvertible bond offerings. If not, estimates of the

3 It could be questioned why a firm would want to issue an under-

valued security in the first place. A potential explanation lies in the profile

of the typical US convertible debt issuer described earlier, i.e., a firm that

has difficulties attracting standard (debt or equity) financing instruments.4 Combinations of security offerings and stock repurchases were

prohibited under Rule 10b-6 of the Securities Act of 1934 (Lowenfels,

1973). Regulation M, which has replaced Rule 10b-6 since December

A. de Jong et al. / Journal of Financial Economics 100 (2011) 113–129 115

information content of convertible debt offerings are likelyto suffer from a downward bias.

Third, our paper adds to a number of recent studies thatexamine innovations in the design of convertible bondofferings. Hillion and Vermaelen (2004) describe the use offloating conversion prices, Korkeamaki (2005) analyzes theinclusion of soft and hard call features, Marquardt andWiedman (2005) examine the use of a contingent conver-sion feature, and Lewis and Verwijmeren (2009) study cashsettlement features.2 The combinations of convertible debtissues and stock repurchases are yet another illustration ofthe creativity with which convertible debt issuers deal withtheir changing environment, notably with the widespreadpresence of convertible debt arbitrageurs over recent years.

Fourth, we contribute to the literature on stockrepurchases. Traditional motivations for stock repurchasesinclude signaling (Bhattacharya, 1979; Vermaelen, 1984;Louis and White, 2007), free cash flow reduction (Jensen,1986), capital structure optimization (Dittmar, 2000), andtakeover deterrence (Billett and Xue, 2007). Our resultssuggest another important motivation for repurchasing stock,namely the provision of a short position to arbitrageurs.

The remainder of this paper is organized as follows.Section 2 discusses the arbitrage explanation together withthe related literature and constructs our testable predic-tions. Section 3 describes the data set. Section 4 presentsour empirical tests related to the arbitrage explanation, andSection 5 investigates alternative explanations. Section 6concludes.

2. Theoretical background

This section provides the theoretical background for ouranalysis and derives testable predictions.

2.1. The arbitrage explanation for combined offerings

Prior literature provides several rationales for issuingconvertible debt. These include mitigating asset substitu-tion problems (Green, 1984), resolving the disagreementbetween managers and bondholders regarding the risk of afirm’s activities (Brennan and Kraus, 1987; Brennan andSchwartz, 1988), providing backdoor-equity financingwhen conventional equity issuance is difficult due toasymmetric information (Stein, 1992), and reducing theissuance costs of sequential financing while at the sametime mitigating overinvestment (Mayers, 1998). Together,these rationales imply that convertibles are a suitablefinancing tool for firms with high costs of attractingstandard financing instruments. Empirical studies find thatconvertible debt issuers tend to be small, high-growth,unrated companies with high debt- and equity-relatedfinancing costs (Kang and Lee, 1996; Lewis, Rogalski, andSeward, 1999, 2003).

Our key research question is: Why, over recent years,have many convertible debt issuers combined their offer-ing with a stock repurchase? Based on exploratory talks

2 Investment Dealers’ Digest (2006) states that ‘‘convertibles are

reinvented more times than Madonna’’.

with advisers and CFOs of companies that engaged incombinations, we argue that the explanation for thesecombinations can be found on the buyers’ side of theconvertible debt market, notably in the widespread pre-sence of convertible debt arbitrageurs over recent years.While convertible arbitrageurs have been active since theearly 1990s, Choi, Getmansky, and Tookes (2009) report asharp increase in their importance since the beginning ofthe 21st century. Choi, Getmansky, Henderson, and Tookes(2010) show that aggregate convertible debt issuancevolumes measured over the period 1995 to 2006 increasefollowing positive shocks in the funds available to con-vertible debt arbitrageurs. Brown, Grundy, Lewis, andVerwijmeren (2010) show that convertible arbitrage fundspurchase 73.4% of the primary issues of convertible debtduring the period 2000–2008.

Convertible arbitrage opportunities arise either whenconvertibles are underpriced or when arbitrageurs canexploit superior technology in managing convertible risk(Agarwal, Fung, Loon, and Naik, 2007). Potential reasons forconvertible debt underpricing include illiquidity and com-plexities associated with the valuation of hybrid securities(Lhabitant, 2002).3 Because convertibles embed a calloption on the underlying stock, convertible debt arbitra-geurs generally buy the (underpriced) convertibles andshort the common stock of the issuing firm to hedge theirpositions. Brent, Morse, and Stice (1990) and Ackert andAthanassakos (2005) show that convertible debt issuersreport substantially higher monthly short equity positionsthan other companies.

We argue that the combined transactions result fromthe convertible debt issuers’ anticipation of this scenario.That is, the issuer is aware of the arbitrageur’s need to shortsell shares and, therefore, sets up the following mechanism.In a first step, the issuer sells the bond to an underwriter ina private Rule 144A offering.4 The underwriter subse-quently resells the 144A security for a spread to qualifiedinstitutional buyers (QIBs). In a second step, these QIBs(henceforth, arbitrageurs) hedge their position by borrow-ing shares of the issuer and selling them to the underwriterat a pre-agreed price. Fig. 1 summarises the combinedpackage, which can be executed as rapidly as overnight.

To the arbitrageur, the transaction offers the advantagethat he instantaneously obtains a hedged position withouthaving to engage in open-market short sales at uncertainprices. From the issuer’s viewpoint, the transaction has theadvantage that he can negotiate a better price for theconvertible offering in return for acting as a counterparty inthe arbitrageur’s short-selling transaction. The issuer alsomitigates the negative issue-date price pressure caused by

1996, allows the combination of convertible issues and stock repurchases

for Rule 144A issues. Thus, by construction, all combined issues are

privately placed Rule 144A offerings. The percentage of Rule 144A

offerings among the uncombined issues is also very high (94.55%).

Step 1: The convertible debt issuer sells a convertible debt offering, structured as a private Rule 144A offering, to an arbitrageur via an underwriter.

Step 2: The arbitrageur borrows a specific portion of the shares of the issuer and sells them to the underwriter at a pre-agreed price, thus obtaining a hedge against stock price movements. The underwriter then sells shares to the issuer, thereby completing the stock repurchase.

Issuer Underwriter Arbitrageur

Convertible Convertible

Cash Cash

Arbitrageur

Stock

CashCash

Stock

UnderwriterIssuer

Fig. 1. Mechanics of the ‘‘Happy Meal’’ transaction. This flow diagram provides an overview of the hypothesized steps in the package consisting of a

convertible debt offering and a stock repurchase.


an increase in the supply of stock due to arbitrage-relatedshort selling. The extent to which price pressure caused bythe short-selling actions of convertible debt arbitrageurs isshort-lived or (partly) permanent is an empirical questionthat we address further in this paper. Previous studies havefound mixed evidence on the impact of various otheruninformed demand or supply shocks on stock prices.Some authors report a complete price reversal within daysafter the shock, which is consistent with the notion thatdemand curves for stock are inelastic only in the short run(Harris and Gurel, 1986; Bechmann, 2004). Other authorsfind that part of the price pressure effect is permanent(Dhillon and Johnson, 1991; Mazzeo and Moore, 1992;Lynch and Mendenhall, 1997), which is consistent withlong-run downward-sloping demand curves (Shleifer,1986). If convertible issuers attach a positive probabilityto a long-lived price drop caused by short selling, this couldprovide another motivation for them to add a stockrepurchase to their convertible offering.

2.2. Testable predictions

Convertible debt arbitrageurs are not required to reporttheir transactions. Similar to other studies (Choi, Getmansky,and Tookes, 2009; Edwards and Weiss Hanley, 2009;Loncarski, ter Horst, and Veld, 2009), we thus have to relyon indirect evidence on arbitrageurs’ activities. From ourmain hypothesis regarding the motivation for combinedofferings, we derive six empirically testable predictions.

The first four predictions pertain to differences betweencombined and uncombined convertibles. First, while con-vertibles are traditionally underpriced at issuance, offeringdiscounts should be lower for combined convertibles thanfor uncombined convertibles, ceteris paribus. The under-lying rationale is that issuers of combinations should be ableto negotiate a higher convertible bond price in exchange forsetting up the short position for the convertible bond buyers.Second, issue-date stock returns should be more negative foruncombined offerings than for combined offerings, due tolower levels of hedging-induced price pressure for the latter

offerings. Third, combined offerings should appeal most tofirms with a high expected shorting demand from conver-tible debt arbitrageurs. For such offerings, arbitrageursshould be more eager to reach an agreement with the firmin return for not having to go to the open market to obtaintheir short positions. We thus predict a higher expectedhedging demand for combined convertibles than for uncom-bined issues. Fourth, combined offerings should be asso-ciated with lower issue-date open-market short sales thanuncombined convertibles. The reason is that, in combinedofferings, the short position is established through a pri-vately negotiated transaction and, as such, is not recorded inopen-market short sales records.

The last two predictions pertain to the stock repurchaseaccompanying the convertible offering. First, if the arbitrageexplanation for combined offerings holds, then the numberof shares that a convertible debt issuer announces torepurchase should closely match the number of sharesexpected to be shorted by arbitrageurs. Second, whereasnormal stock repurchases often take a very long time to beexecuted (Stephens and Weisbach, 1998), combined con-vertible debt issuers should repurchase their stock almostimmediately after the repurchase announcement, to allowconvertible debt arbitrageurs to obtain their short positions.

3. Data

We acquire information on convertible issues and sharerepurchases made by US firms over the period from 1997 to2007. We start in 1997 because Regulation M, which madecombined offerings legal, was introduced in December1996. We obtain a sample of nonmandatory convertibledebt offerings from the Securities Data Corporation (SDC)Global New Issues Database and a sample of stock repurch-ase announcements from SDC’s Mergers and AcquisitionsDatabase. We exclude stock repurchases that SDC classifiesas Dutch auctions or self-tender offers. We use Factiva todetermine the announcement dates of the convertible debtofferings and the stock repurchases. We mark a convertibleas a combined offering if the firm announces that it uses the

Table 1Descriptive statistics for (combined) convertible issues and stock repurchases.

This table presents summary statistics. Panel A reports the number of convertible issues, stock repurchases, and combined offerings of convertible issues

and stock repurchases per year. N indicates the number of transactions. The column ‘‘% combinations’’ indicates the number of combined transactions as a

percentage of the total number of convertible offerings. Panel B compares the proceeds of the convertible issue with the size of the announced stock

repurchase. We also compare the announced size of the repurchase with firms’ market values, calculated by multiplying Compustat item #25 with #199

(both measured at the fiscal year-end prior to the issue date). In Panel C, we show the distribution of convertible issues over Fama-French 12-industry

classifications. The sample period in Panel A is 1997–2007, the sample period in Panels B and C is 2003–2007.

Panel A: Intertemporal dispersion

Year N convertibles N repurchases N combinations % combinations

1997 237 1,286 0 0.0

1998 145 1,934 0 0.0

1999 108 1,515 0 0.0

2000 153 806 1 0.7

2001 207 659 3 1.4

2002 117 469 2 1.7

2003 256 470 10 3.9

2004 181 563 9 5.0

2005 105 638 13 12.4

2006 142 586 47 33.1

2007 162 972 37 22.8

Panel B: Value of the announced stock repurchases compared with the proceeds of the convertible issue and firms’ market values

Mean Median Minimum Maximum Standard deviation

Value repurchase/proceeds 0.411 0.348 0.050 1.111 0.253

Value repurchase/market value 0.069 0.053 0.004 0.489 0.062

Panel C: Industry classification

Fama-French 12 industry classification Combined issues Uncombined issues

N Percent N Percent

Consumer nondurables 1 0.9 13 1.8

Consumer durables 2 1.7 9 1.2

Manufacturing 4 3.5 48 6.6

Energy 0 0.0 49 6.7

Chemicals 0 0.0 12 1.6

Business equipment 32 27.6 151 20.7

Telephone 3 2.6 30 4.1

Utility 1 0.9 22 3.0

Wholesale 14 12.1 51 7.0

Health care 20 17.2 128 17.5

Financial 22 19.0 121 16.6

Other 17 14.7 96 13.2

Total 116 100.0 730 100.0


proceeds to repurchase stock or if both transactions areannounced separately on the same date. We also searchthe window [�5, +5] relative to the convertible debtannouncement date for stock repurchases, but this opera-tion yields no additional observations.5 Panel A of Table 1shows the number of convertible issues, stock repurchases,and combined offerings over the sample period.

The number of convertible debt issues fluctuates overtime, whereas the number of stock repurchases has beenfairly constant since 2000. Combined offerings are virtually

5 A substantial number of combined stock repurchases (77 out of 122)

are not covered by SDC. The majority of the stock repurchases registered in

SDC (29 out of 45) are marked as Privately Negotiated Offers, which is

consistent with our main hypothesis that these repurchases are nego-

tiated with convertible debt buying institutions.

nonexistent prior to 2003 but make up a substantial fractionof convertible debt issuance from 2005 onward. In 2006,almost one-third of all US convertibles are combined with astock repurchase. In 2007, the combinations remain verypopular as well (22.8% of all convertible offerings).6 Giventhe very low number of combined offerings prior to 2003, welimit our research window to the period 2003 to 2007 insubsequent analyses. This operation results in a sampleof 730 uncombined convertible offerings, 3,229 uncombinedstock repurchases, and 116 combined offerings.

6 We checked whether the exponential increase in combined offer-

ings is driven by the presence of a few financial advisers that push the

combinations. We did not find a significant overrepresentation of any

advisory firm in combined offerings, compared with the advisory firms

involved in uncombined issues.

7 Detailed offering discount estimates and test results obtained using

these alternative volatility measures are available upon request.


We gather the information necessary for constructingthe explanatory variables for the empirical tests from thefollowing sources. Deal-specific information is obtainedfrom SDC and cross-checked by means of the offeringprospectuses retrieved through the Edgar 10K Wizard. Incase of disagreement between both sources, we take thevalue obtained from the offering prospectus. Companyaccounts variables are obtained from Compustat andmeasured at the fiscal year-end before the convertibledebt issue date (in the variables description, # refers to aCompustat item number). Data related to stock prices (i.e.,prices, volatility, trading volumes, and other liquiditymeasures) are retrieved from the Center for Research inSecurity Prices (CRSP). Trading days are measured relativeto the convertible debt issuance date. We define eachexplanatory variable only upon its first occurrence inthe paper.

Panel B of Table 1 shows that the offering proceeds ofconvertible issues tend to be substantially larger than thefunds used to repurchase shares. On average, the stockrepurchase represents 41.1% of the convertible issue pro-ceeds and 6.9% of the issuer’s equity market value (calcu-lated as #199 multiplied by #25). There are only four firmsfor which the value of the announced repurchase exceedsthe convertible issue proceeds. The minimum percentageof proceeds used to repurchase shares is 5.0%.

Panel C of Table 1 provides Fama-French 12-industryclassifications for the two subsamples of convertibleissuers. Most convertibles are issued by firms in thebusiness equipment, financial, and health care industry.Firms engaging in combined offerings are spread over tenof the 12 industries, although the wholesale, financial, andhealth care industries are slightly overrepresented.

4. Empirical evidence related to the arbitrageexplanation

In this section, we test the six predictions derived fromthe arbitrage explanation for combinations of convertiblesand stock repurchases.

4.1. Offering discounts

The arbitrage explanation predicts that, after control-ling for other potential determinants of underpricing,combined offerings should exhibit lower offering discountsthan uncombined convertibles. The reason is that com-bined issuers should be able to obtain a stronger bargainingposition (and hence, a better convertible price) by offeringthe short position to arbitrageurs. In line with Chan andChen (2007), we define the Offering Discount (OD) for aconvertible debt offering as

OD¼ ðTheoretical Price-Offer PriceÞ=Theoretical Price ð1Þ

We obtain convertible debt offer prices from the Mer-gent Fixed Income Securities Database. In line with mostother recent studies on convertible debt underpricing(Ammann, Kind, and Wilde, 2003; Chan and Chen, 2007;Loncarski, ter Horst, and Veld, 2009), we use the Tsiveriotisand Fernandes (1998) model to calculate the theoreticalvalue of convertibles. According to Zabolotnyuk, Jones, and

Veld (2009), this convertible bond valuation model is verypopular among practitioners. Tsiveriotis and Fernandes(1998) essentially use a binomial-tree approach to modelthe stock price process and decompose the total value of aconvertible bond into an equity component and a straightdebt component. We use the following input variables inthe algorithm: risk-free interest rate (the yield on USTreasury bills with a maturity as close as possible to thematurity of the convertible bond, obtained from Data-stream); stock price (measured five trading days prior tothe issue date to abstract from the price drop resulting fromshort-selling activity); stock return volatility; coupon rateand coupon payment frequency; issue, settlement, andmaturity date; dividend yield; call schedule; and creditspread. The call schedule is obtained from Mergent, and allother security-related information is obtained from SDC(supplemented with information from the issue prospec-tuses). The credit spread is based on Standard and Poor’s(S&P) ratings for corporate industrial bonds with a maturityas close as possible to that of the convertible bond. Weobtain the convertibles’ ratings from Mergent and the creditspreads from Datastream. A substantial part (68.76%) of oursample offerings does not have an S&P (or Moody’s) ratingat issuance. This observation can be explained by the factthat convertibles tend to be issued by small, unratedcompanies. In line with Loncarski, ter Horst, and Veld(2009), we assign a BBB rating to unrated bonds. The stockreturn volatility is defined as the annualized volatilityestimated from daily stock returns over trading days�240 to �40 (as in Lewis, Rogalski, and Seward, 1999).In total, there are 361 convertibles for which we havesufficient information to calculate the offering discount.Our findings with respect to convertible debt offeringdiscounts are robust to the use of the following alternativevolatility measures: historical volatility estimated fromdaily stock returns over trading days �520 to �1, as inAmmann, Kind, and Wilde (2003) (337 usable observa-tions); historical volatility estimated from monthly stockreturns over the five years preceding the issue date, as inKing (1986) (301 usable observations); GARCH(1,1) volati-lity predicted over the five years post-issuance estimatedwith daily stock returns over trading days �1,300 to �40,as in Figlewski (1997) (273 usable observations); andimplied volatility on the issuer’s nearest-the-money calloption with the longest remaining maturity outstanding onthe issue date, obtained from OptionMetrics (269 usableobservations).7 Panel A of Table 2 provides the average andmedian offering discounts for combined and uncombinedconvertible offerings.

The average (median) OD for the entire sample of con-vertibles (untabulated) is 17.06% (17.29%). This percentage iscomparable to initial underpricing levels reported by otherrecent studies (e.g., Zabolotnyuk, Jones, and Veld, 2009). Wefind that convertibles combined with a stock repurchase are,on average, 23.23% less underpriced than uncombined con-vertibles [(17.61�13.52)/17.61]. In median terms, the dif-ference in ODs is even larger [(17.54�11.60)/17.54, or

Table 2Difference in offering discounts between combined and uncombined issues.

Panel A reports a univariate analysis of the Offering Discount (OD),

calculated as (Theoretical Price�Offer Price)/Theoretical Price for conver-

tibles combined with a stock repurchase and single convertibles. The

theoretical convertible debt price is obtained using the model of

Tsiveriotis and Fernandes (1998). t-statistics and Wilcoxon test statistics

are for the differences between combined and uncombined convertibles.

Panel B reports a cross-sectional analysis of the determinants of OD.

Combined Offering is equal to one for combined offerings and equal to zero

otherwise. Delta is the convertible’s sensitivity to small stock price changes

calculated according to Eq. (2). Log(Assets) is the natural logarithm of

Compustat item #6, measured at the fiscal year-end preceding the issue date.

Proceeds/MV is offering proceeds divided by the market value of equity

(measured as #25 multiplied by #199). Amihud is the Amihud (2002)

measure for illiquidity (multiplied by 106). Volatility is the daily stock return

volatility calculated from stock returns over trading days �240 to �40. We

also include year dummy variables (not reported for space reasons).

t-statistics (calculated with White heteroskedasticity-consistent standard

errors) are in parentheses. The sample period is 2003 to 2007. *, **, and

*** indicate significance at the 10%, 5%, and 1% level, respectively.

Panel A: Univariate analysis of offering discounts

Combined Uncombined t-statistic (Wilcoxon

test statistic)

Average

(median) OD

13.52%

(11.60%)

17.61%

(17.54%)

�2.21** (�2.32**)

Number 49 312

Panel B: Regression analysis of offering discounts

OD

Intercept 0.194 (3.62***)

Combined offering �0.039 (�2.26**)

Delta 0.028 (0.95)

Log(Assets) �0.019 (�3.11***)

Proceeds/MV 0.097 (1.91*)

Amihud�106 3.383 (4.38***)

Volatility 1.426 (3.60***)

Number 318

R2 33.17%

8 All callable convertibles have a call protection period of at least one

year. The average call protection period length for these convertibles is 5.37

years, and their average stated maturity is substantially longer (16.71 years).

Other factors (next to the presence of a call feature) that could influence the

lifetime of a convertible are the presence of a soft call feature (which is the

case for 1.47% of the sample offerings), the presence of a put feature (which

is the case for 58.68% of the sample offerings), delays in calling the bond, and

(delays in) voluntary conversion of the bonds (Dunn and Eades, 1989).9 To check whether the coefficient of the Combined Offering dummy

variable could be affected by an endogeneity bias, we also estimate the

regression using a two-step Heckman (1979) regression procedure. The

first step consists of estimating a probit regression with a dummy variable

equal to one for combined offerings and equal to zero for uncombined

offerings as a dependent variable, and with the same explanatory

variables as those in Panel B of Table 2 on the right-hand side. In the

second step, we estimate the same model as that represented in Panel B,

except that we include the inverse Mills ratio obtained from the first-step

analysis as an additional explanatory variable. This operation does not

materially change the coefficient of the Combined Offering dummy

variable (coefficient is �0.038, significant at less than 5%). The inverse

Mills ratio is insignificant (z-value equals �1.41).


33.87%]. The difference in ODs between combined anduncombined offerings is significant at the 5% level.

The literature has shown that underpricing tends to behigher for more equity-like convertibles, for smaller firms,for larger offer sizes, for less liquid firms, and for firms withmore volatile stock returns (Corwin, 2003; Cai, Helwege,and Warga, 2007; Loncarski, ter Horst, and Veld, 2009). Totest whether the difference between combined and uncom-bined convertibles remains significant after controlling forthese determinants, we regress the ODs on a CombinedOffering dummy variable equal to one for combinedofferings as well as on Delta, Log(Assets) (#6), Proceeds/MV (offering proceeds normalized by the market value ofequity), the Amihud (2002) illiquidity measure (calculatedusing daily stock returns and trading volumes averagedover the window [�120, �20]); and Volatility. We calcu-late the convertible debt delta as

Delta¼ e�dT Nðd1Þ ¼ e�dT NlnðS=XÞþðr�dþðs2=2ÞÞT

sffiffiffiTp

� �, ð2Þ

where d is the continuously compounded dividend yieldcalculated as #21 divided by the market value of equity,

N(.) is the cumulative probability under a standard normaldistribution, S is the price of the underlying stock measuredat day �5, X is the conversion price, r is the yield on a ten-year US Treasury bond (obtained from Datastream), ands is the annualized stock return volatility. T represents anestimate of the effective lifetime of the convertible as of itsissuance date. The stated maturity of convertibles is likelyto overstate T, because convertibles can be terminatedprematurely for a number of reasons. Lewis, Rogalski, andSeward (1998) and Marquardt and Wiedman (2005) arguethat the bulk of premature conversions of convertibleshappen through conversion-forcing calls, which could takeplace as soon as the call protection period of the con-vertibles expires. For the callable convertibles in our dataset, we therefore use the length of the call protection periodas an estimate of their effective maturity.8 For noncallableconvertibles (which constitute only 8.43% of the sample),we use the stated maturity. We also include year dummyvariables (not reported for space reasons). The number ofobservations that can be included in the regression is 318.

Panel B of Table 2 shows the regression results. Con-sistent with our prediction that combined issuers benefitfrom the transactions by providing lower offering dis-counts, we observe a significant negative coefficient for theCombined Offering dummy variable.9 The combined con-vertibles are still substantially underpriced at issuance,however (average OD of 13.52%), implying that arbitra-geurs can still realize substantial profits from buying theseinstruments. As expected, ODs are significantly positivelyinfluenced by Proceeds/MV, Amihud, and Volatility andsignificantly negatively influenced by Log(Assets).

4.2. Abnormal stock returns at convertible debt issue dates

To test whether combined offerings induce lower pricepressure, we calculate cumulative abnormal stock returns(ARs) at the convertible debt issue date by means of standardevent study methodology as described in Brown and Warner(1985). We use the period [�200, �30] as the estimationwindow and the CRSP equally weighted market index as amarket proxy. Panel A of Table 3 presents the event studyresults.

Table 3Differences in issue-date stock returns between combined and uncombined issues.

Panel A presents issue-date abnormal stock returns (ARs) for (un)combined convertible debt offerings. ARs are calculated using standard event study

methodology (market model regressions). t-statistics and Wilcoxon test statistics are for the differences between combined and uncombined convertibles.

The sample period in Panel A is 2003 to 2007. Panel B presents a regression analysis of issue-date ARs on a number of potential determinants. Combined

Offering is a dummy variable equal to one for convertibles combined with a stock repurchase and equal to zero otherwise. All firm-specific variables are

measured at the fiscal year-end preceding the issue date, unless noted otherwise. Delta is the convertible’s sensitivity to small stock price changes calculated

according to Eq. (2). Stock Run-up is the raw stock return measured over the window [�76, �2]. Log(Assets) is the natural logarithm of the book value of

total assets (Compustat item #6). Volatility is the daily stock return volatility calculated from stock returns over trading days �240 to �40. Leverage is the

ratio of long-term debt (#9) to total assets. Market to Book is calculated as (#25�#199�#60+#6)/#6). Short Sales is the sum of all open-market short sales

for each firm on the issue date. SO are shares outstanding, measured as of trading day �20. Amihud is the Amihud (2002) measure for illiquidity (multiplied

by 106). Analyst Dispersion is the standardized standard deviation of analysts’ forecasts for one-year-ahead EPS. t-statistics (calculated with White

heteroskedasticity consistent standard errors) are in parentheses. The sample period in Panel B is January 2005 to July 2007. *, **, and *** indicate significance

at the 10%, 5%, and 1% level, respectively.

Panel A: Issue-date ARs for combined and uncombined offerings

Combined Uncombined t-stat. (Wilcoxon test stat.)

Average (median) AR 0.32% (0.22%) �3.37% (�2.74%) 9.84*** (7.89***)

Patell Z (rank test) statistic 2.60*** (1.75**) �32.29*** (�11.55***)

Number 108 633

Panel B: Regression analysis of issue-date ARs

Issue-date AR

(1) (2)

Intercept �0.065 (�1.84*) 0.008 (0.23)

Combined offering 0.024 (2.87***) 0.012 (1.56)

Delta �0.068 (�2.36**) �0.046 (�2.07**)

Stock run-up 3.922 (1.32) 2.034 (1.07)

Log(Assets) 0.008 (2.43**) 0.000 (0.01)

Volatility 0.042 (0.05) 0.496 (0.81)

Leverage 0.031 (1.77*) 0.041 (2.17**)

Market to book 0.011 (2.36**) 0.006 (1.82*)

Short sales/SO �1.473 (�3.11***)

Amihud�106�663.96 (�1.44)

Analyst dispersion �0.000 (�0.08)

Analyst dispersion� Short sales/SO �0.086 (�0.45)

Number 100 100

R2 24.88% 40.24%


We find that the issue-date AR is significantly negative(�3.37% on average) for uncombined convertible issues.ARs for combined issues are significantly positive (0.32% onaverage). The difference in issue-period returns betweencombined and uncombined issues is significant at the 1%level. We thus obtain evidence consistent with our pre-diction that issuers of combined offerings are able tomitigate downward stock price pressure by reducingopen-market short sales.

One problem associated with the interpretation of theresults in Panel A is that for 92.58% of the convertible debtofferings the announcement date falls in the window [�1, 0]relative to the issue date. This observation can be explainedby the very fast placement of recent convertible debtofferings (Mitchell, Pedersen, and Pulvino, 2007). As a result,the observed AR differences between combined and uncom-bined convertible offerings could also be caused by differ-ences in the information content of both offerings. Followingthe logic of the Myers and Majluf (1984) model, announcingan equity-linked security offering could signal that the firmis overvalued. Convertible debt announcements shouldtherefore have a negative impact on stock prices, which isconfirmed by findings of Davidson, Glascock, and Schwarz

(1995), Lewis, Rogalski, and Seward (2003), and Marquardtand Wiedman (2005). Repurchasing stock, in turn, generallyresults in a positive stock price reaction, because firms aremore likely to buy back stock when they are undervalued(Asquith and Mullins, 1986; Comment and Jarrell, 1991;Ikenberry, Lakonishok, and Vermaelen, 1995). Thus, theobserved differences in Panel A could also be caused bythe fact that the addition of a stock repurchase mitigates thenegative information content of the convertible offering.Constantinides and Grundy (1989) develop a model thatexplicitly predicts that firms issue a combination of aconvertible and a stock repurchase for signaling purposes.

To establish the extent to which the findings in Panel A areattributable to differences in price pressure for combined anduncombined convertibles (as would be predicted by thearbitrage explanation) as opposed to differences in theirinformation content (as would be predicted by a signalingscenario), we conduct a regression analysis with the issue-dateAR as dependent variable. In a first regression model, weinclude the Combined Offering dummy variable as well asa number of explanatory variables that are traditionallyincorporated in cross-sectional regressions of convertible debtannouncement effects, i.e., Delta, Stock Run-up [the stock

Table 4Analysis of stock price reversals after convertible debt issues.

This table reports (post-) issue-date cumulative average abnormal stock returns (CAARs) for three subsamples of convertible debt issues. The separate-

date sample consists of uncombined convertibles for which the announcement date differs by more than one trading day from the issue date. The similar-

date sample incorporates all other uncombined convertibles. The sample period is 2003 to 2007. *, **, and *** indicate significance at the 10%, 5%, and 1% level,

respectively.

Separate-date sample (1) Similar-date sample (2) Combined offerings (3)

CAAR [0,0] �1.40% �3.53% 0.32%

Patell Z �5.03*** �32.13*** 2.60***

Percent positive returns 23.40 21.33 56.48

CAAR [+1, +6] 2.10% 1.07% 0.68%

Patell Z 2.51** 3.08** 0.86


CAAR [+1, +20] 2.04% 1.20% �0.22%

Patell Z 2.10* 1.27 �0.23


Number 47 586 108

10 We check whether the change in impact of Log(Assets) could be

driven by a multicollinearity problem by calculating condition numbers

for the matrices of explanatory variables (see Marquardt and Wiedman,

2005, for a similar approach). Condition numbers between 30 and 100

indicate moderate to strong multicollinearity. The highest condition

number for the regression in Column 2 is 34.96. Log(Assets) has, by far,

the highest impact on multicollinearity levels. When Log(Assets) is

omitted from the regression, the highest condition number drops to

20.86, with the main conclusions remaining unchanged.


return over trading days �76 to �2], Log(Assets), Volatility,Leverage [the ratio of long-term debt (#9) to total assets], andMarket to Book (market value minus book value of equity(#60) plus total assets, divided by total assets) (see, e.g., Lewis,Rogalski, and Seward, 2003; Dutordoir and Van de Gucht,2007). We limit the regression to those 100 observations forwhich we have price pressure proxies available, because weinclude these proxies in the next step of the analysis. Resultsare presented in Column 1 of Panel B of Table 3. As expected,we find a significant positive regression parameter for theCombined Offering dummy variable. We also find a significantnegative impact for Delta, which is consistent with the notionthat more equity-like securities are perceived as a morenegative signal about firm value (Myers and Majluf, 1984).Log(Assets), Leverage, and Market to Book have a significantlypositive influence.

In a second regression analysis presented in Column 2,we add explanatory variables measuring the magnitudeof hedging-induced price pressure. We use the ratio ofissue-date short sales to shares outstanding (Short Sales/SO) as a proxy for the magnitude of the supply shock. Weretrieve daily open-market short sales data from the NYSETrade and Quote database’s Regulation SHO (REG SHO) file,which covers short-selling transactions from January 2005to July 2007. We measure shares outstanding on tradingday �20. We also include the Amihud (2002) illiquiditymeasure, because price pressure effects should be strongerfor more illiquid stocks (Bagwell, 1992). As argued byBaker, Coval, and Stein (2007), stocks with a larger disper-sion in analyst opinions about their value are likely to havesteeper demand curves, which should result in a largerprice impact of a given supply shock. In line with theseauthors, we therefore control for the level of AnalystDispersion (both separate and interacted with the ShortSales/SO ratio), measured as the standardized standarddeviation of one-year analyst forecasts of earnings pershares (EPS) obtained from the Institutional Brokers’Estimate System (I/B/E/S).

After controlling for price pressure proxies, the Com-bined Offering dummy variable is no longer significant. Itscoefficient drops to half the size of the coefficient reported

in Column 1. This result suggests that the significantdifferences in issue-date ARs for combined and uncom-bined offerings are largely attributable to hedging-relatedprice pressure, as would be expected under an arbitragescenario. As predicted, Short Sales/SO has a significantlynegative impact. The other price pressure-related variableshave insignificant effects. Findings with respect to deal-and firm-specific financing costs proxies are similar tothose in Column 1, except for the fact that the effect ofLog(Assets) is now insignificant.10

To further disentangle the arbitrage explanation for com-bined offerings from a signaling interpretation, we examinecumulative average abnormal stock returns (CAARs) over theextended window [0, +20]. If demand curves for stock are notperfectly elastic, a large increase in the supply of stock due toarbitrage-related short selling is expected to cause a stock pricedecrease. Once the market has absorbed the excess supply,however, prices should reverse to their fundamental levelsunder the assumption that demand curves are inelastic only inthe short run. The observation of a quick stock price reversalwould thus be consistent with the arbitrage explanation, whilethe observation of a permanent price effect would be con-sistent with a signaling explanation or with the existence oflong-run downward-sloping demand curves. We initiallyperform the price reversal analysis for the 47 uncombinedconvertibles for which the announcement happens more thanone trading day prior to the issue date (labeled ‘‘separate-datesample’’), because this subset is most likely to yield clean pricepressure estimates. Table 4 presents the results.

Consistent with the arbitrage explanation, we find that thenegative average issue-date effect of �1.40% quickly and fully


reverses after the issuance (significant positive CAAR of 2.10%over window [+1, +6]). CAARs over the window [+1, +20] aresimilar to those over the window [+1, +6].

The separate-date subsample also provides a good labora-tory for obtaining clean estimates of convertible debtannouncement effects. The average announcement-date ARfor the 47 convertibles in this subsample (obtained throughstandard event study methodology) is �2.61% (untabulated).This estimate is very similar in size to the announcementeffects registered by early studies on convertible bonds (seeEckbo, Masulis, and Norli, 2007, for a review of the literature).Remarkably, Marquardt and Wiedman (2005) report a muchmore negative stock price reaction of �5.50% for convertibledebt offerings made over the period 2000 to 2002. Our resultssuggest that this more negative return could be explained byarbitrage-related short selling surrounding recent convertibledebt offerings. Our findings highlight the need to control forthis price pressure effect when estimating the informationcontent of convertible offerings. Mitchell, Pulvino, and Stafford(2004) obtain a similar conclusion with respect to the influenceof merger arbitrage on acquiring-firm stock price reactions.

In Column 2, we report stock price reversal calculations forthe 586 convertibles for which the announcement date falls inthe window [�1, 0] relative to the issue date (labeled similar-date sample). Consistent with the arbitrage explanation, weagain find that the stock price changes direction immediatelyafter the issue date. Over the window [+1, +6], we register asignificant positive stock return of 1.07%. This reversal effectmight seem small relative to the average issue-date AR of�3.53%. However, as this issue-date return simultaneouslyincorporates the effect of the convertible debt announcement,the true percentage reversal of the price pressure effect is likelyto be considerably larger.11

To conclude, we find evidence of a (partial) reversal of theissue-date AR for uncombined convertibles, which suggeststhat (at least a component of) the issue-date effect is attribu-table to hedging-induced price pressure. To the extent thatmanagers attach a positive probability to a long-lived drop intheir firms’ stock price resulting from open-market shortselling (due to long-run downward-sloping demand curves),this provides an additional motivation for them to combinetheir convertible offering with a stock repurchase.

For completeness, Column 3 of Table 4 presents reversalcalculations for convertibles combined with a stockrepurchase. Consistent with the arbitrage explanation,we find no evidence of significant post-issuance stock pricemovements for these offerings.

12 Our motivation for using issue-date short sales instead of changes

in monthly short interest is that the former data provide a cleaner

laboratory for testing our prediction. Monthly short interest data repre-

sent cumulative outstanding short positions at a given date during the

month. This date overlaps with the convertible debt issuance date only by

4.3. Expected hedging demand

To examine our prediction that combined issues shouldbe associated with a higher expected hedging demand(EHD) from convertible arbitrageurs, we first modelissue-date short sales of the uncombined subsample(scaled by SO, as outlined earlier) as a function of potentialdeterminants of convertible arbitrageurs’ shorting demand

11 Assuming a similar average price pressure effect as for the

separate-date subsample (i.e., �1.40%), for example, we find that

85.71% (1.20/1.40) of the issue-date effect has evaporated by day +20.

for the stock. There are 149 observations for which we canobtain issue-date short sales information from NYSE TAQ’SREG SHO file, of which 42 are combinations.12 We then usethe coefficients obtained from this regression to calculatethe EHD for combined issuers had they opted for anoncombined offering instead. We include the followinghedging demand determinants in our analysis.

�

coin

affe

also

Too

inte

Amihud: the Amihud (2002) measure for illiquidity.According to Calamos (2003), it is easier for arbitrageursto dynamically hedge more liquid stocks.
� Institutional Ownership: the number of shares held by
13F institutions (obtained from Thomson Reuters)divided by the number of shares outstanding (bothmeasured at the fiscal year-end preceding the issuedate). In line with Asquith, Pathak, and Ritter (2005), weuse this variable as a proxy for the availability of sharesto be borrowed.
� Dividend-Paying: a dummy variable equal to one if the
firm has paid a dividend in the fiscal year preceding theconvertible issue date (which can be establishedthrough #21) and equal to zero otherwise. Calamos(2003) argues that short sellers have a preference forstocks that pay no dividends, because the dividendrepresents a cash outflow for them.
� Volatility: the annualized volatility estimated from
daily stock returns over trading days �240 to �40.Convertible debt arbitrageurs can potentially realizehigher trading profits on convertibles issued by morevolatile firms due to the embedded option in the bond(Choi, Getmansky, and Tookes, 2009).
� Fundflow: net inflows in convertible arbitrage hedge
funds (in millions of US dollars) measured over thethree months preceding the issue month (obtained fromthe TASS Live and Graveyard hedge fund databases).Fundflow serves as a proxy for intertemporal fluctua-tions in the availability of funds for convertible debtarbitrage activities.
� Normal Short Sales/SO: average short sales over the
window [�10, �4], scaled by shares outstanding. Inline with Christophe, Ferri, and Angel (2004), we use thisvariable to control for each firm’s typical ratio of shortedshares during the nonissuance period. We obtain simi-lar findings when we measure Normal Short Sales overalternative windows, e.g., [�20, �2].
� Delta: ceteris paribus, arbitrageurs have to short-sell
more shares for convertibles with a higher delta,because these convertibles have a larger equity expo-sure. Moreover, as shown by Loncarski, ter Horst, andVeld (2009), relatively more equity-like convertibles aremore likely to be underpriced at issuance.

cidence. Monthly short interest data are therefore more likely to be

cted by short selling unrelated to the convertible debt offering. See

Mitchell, Pulvino, and Stafford (2004) and Choi, Getmansky, and

kes (2009) for a description of the noise associated with monthly short

rest data.

Table 5Difference in expected hedging demand between combined and uncombined issues.

Panel A presents a univariate analysis of the differences in potential hedging demand determinants for combined and uncombined convertible debt issues.

Amihud is the Amihud (2002) measure for illiquidity. For expositional purposes, we multiply this measure by 1012 in the univariate analysis and by 106 in the

regression analysis. Institutional Ownership is the number of shares held by 13F institutions at fiscal year-end preceding the issue date divided by the

number of shares outstanding. Dividend-Paying is a dummy variable equal to one when the firm pays dividends over the year preceding the issue date

(which can be established by looking at Compustat item #21). Volatility is the daily stock return volatility calculated from stock returns over trading days

�240 to �40. Fundflow equals net inflows in convertible arbitrage hedge funds (in millions of US dollars) measured over the three months preceding the

issue month. Normal Short Sales are average short sales over trading days �10 to �4. Delta is the convertible’s sensitivity to small stock price changes

calculated according to Eq. (2). Log(Proceeds) is the natural logarithm of the offering proceeds. R�arb=SO is the number of shares that need to be repurchased to

obtain a delta-neutral hedge as of the issuance date [calculated according to Eq. (3)], divided by the number of shares outstanding as of trading day �20.

Panel B reports a cross-sectional regression analysis of the hedging demand for uncombined convertibles. Short Sales is the sum of all open-market short

sales for each firm on the issue date, as reported in NYSE Trade and Quote database’s Regulation SHO file. Panel C reports the results of a univariate

comparison of Expected Hedging Demand (EHD) for combined and uncombined convertibles. EHD is the predicted value of the Short Sales/SO ratio obtained

from the regressions in Panel B. In the univariate results, t-statistics and Wilcoxon test statistics are for the differences between combined and uncombined

convertibles. In the regression results, t-statistics (calculated with White heteroskedasticity-consistent standard errors) are in parentheses. The sample

period is January 2005 to July 2007. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Panel A: Univariate analysis of potential hedging demand determinants

Average (median)

Combined Uncombined t-statistic (Wilcoxon statistic)

Amihud�1012 9.21 (6.48) 21.91 (8.90) �1.58 (�0.96)

Institutional Ownership 83.10% (86.83%) 74.28% (78.31%) 2.43** (2.29**)

Dividend-Paying 45.24% (0.00%) 63.55% (100.00%) �2.02** (�2.03**)

Volatility 1.86% (1.57%) 1.83% (1.64%) 0.05 (0.05)

Fundflow 249.42 (42.47) 54.86 (42.47) 1.03 (1.25)

Normal Short Sales/SO 0.21% (0.18%) 0.20% (0.16%) 0.16 (0.65)

Delta 0.67 (0.71) 0.57 (0.63) 1.70* (1.35)

Log(Proceeds) 5.68 (5.52) 5.66 (5.56) 0.13 (�0.27)

R�arb=SO 6.66% (5.87%) 6.29% (4.57%) 0.33 (1.50)

Panel B: Regression analysis of hedging demand for uncombined convertibles

Short Sales/SO

(1) (2)

Intercept �0.003 (�0.33) �0.002 (�0.16)

Amihud�106�86.221 (�1.49) �104.464 (�0.95)

Institutional Ownership 0.009 (2.45**) 0.009 (2.32**)

Dividend-Paying 0.000 (0.12) 0.000 (0.11)

Volatility �0.161 (�1.14) �0.159 (�1.11)

Fundflow 0.000 (1.68*) 0.000 (1.62)

Normal Short Sales/SO 2.369 (2.17**) 0.023 (2.14**)

Delta 0.006 (1.78*) 0.006 (1.75*)

Log(Proceeds) �0.001 (�0.59) �0.001 (�0.60)

R�arb=SO 0.088 (3.24***) 0.087 (2.99***)

R�arb=SO� ðAmihud� 106Þ 69.617 (0.19)

Number 82 82

R2 41.91% 41.93%

F-statistic 5.05*** 4.48***

Panel C: Analysis of expected hedging demand (EHD)

Combined Uncombined t-statistic (Wilcoxon test statistic)

(1) Average (median) EHD 1.55% (1.48%) 1.28% (1.10%) 2.05** (2.38**)

Number 35 82 117

(2) Average (median) EHD 1.56% (1.47) 1.28% (1.10%) 2.08** (2.24**)

Number 35 82 117


�
Log(Proceeds): the natural logarithm of theoffering proceeds. Ceteris paribus, arbitrageurs haveto short-sell more shares for larger convertibleofferings. � R�arb=SO: the number of shares that needs to be
shorted to obtain a delta-neutral hedge), which

can be determined by means of the formula(Calamos, 2003)

R�arb ¼number of convertibles issued� face value� delta

conversion price:

ð3Þ


We scale R�arb by shares outstanding. We expect thisvariable to have a positive impact on the issue-datehedging demand of arbitrageurs.

Panel A of Table 5 provides a comparison of thesepotential hedging demand determinants for combinedand uncombined convertibles. We find that combinedofferings have a significantly higher percentage of institu-tional ownership (83.10% on average versus 74.28% onaverage) and a significantly lower portion of dividend-paying firms (45.24% versus 63.55%). We also find thatcombined convertible issues are more equity-like in naturethan uncombined offerings (average Delta of 0.67 versus0.57). Together, these findings suggest that combinedconvertible debt issues are likely to attract higher hedgingdemand than uncombined convertible debt issues. Theother variables do not significantly differ between bothsubsamples.13

Column 1 in Panel B of Table 5 presents the results of aregression of the Short Sales/SO ratio of uncombinedconvertibles on its potential determinants. There are 82uncombined convertibles for which we have sufficientinformation to estimate the regression model. All t-statis-tics are calculated with White heteroskedasticity-consis-tent standard errors. In line with our expectations, we findthat daily short sales are significantly positively influencedby Institutional Ownership, Fundflow, Normal Short Sales/SO, Delta, and the R�arb=SO ratio. The regression has a highexplanatory power (R2 of 41.91%, F-statistic significant atthe 1% level). In Column 2, we add an interaction termbetween the R�arb=SO ratio and the Amihud illiquiditymeasure. We expect a negative impact for this variable,because it should be easier for arbitrageurs to reach theiroptimal hedging levels for relatively less illiquid shares. Wefind no significant impact for the interaction term, how-ever. All other regression results remain similar.

Subsequently, we use the coefficients of the regressionsestimated for uncombined offerings to calculate theexpected hedging demand (EHD) for combined convertibleofferings. Using the regression specification in Column 1,we find an average (median) EHD of 1.55% (1.48%) forcombined issues, while the average EHD for uncombinedissues is only 1.28% (1.10%). The difference between bothratios is statistically significant at the 5% level, bothaccording to a t-test and a Wilcoxon test. We obtain similarfindings when we use the regression specification inColumn 2 to calculate the EHD. Overall, we can concludethat our results are consistent with the prediction thatcombined offerings are associated with higher expectedshorting demand from arbitrageurs.14

13 It is remarkable that the offering proceeds of combined and

uncombined convertible debt issues are not significantly different. In

other words, combined issuers do not seem to compensate for the

repurchase by raising more convertible financing.14 To assess whether the results could be affected by an endogeneity

bias caused by the fact that firms self-select into issuing combined

convertibles, we also estimate the regression using a two-step

Heckman (1979) procedure. The first step consists of estimating a probit

regression with a dummy variable equal to one for combined offerings and

equal to zero for uncombined offerings as a dependent variable, and with

the same explanatory variables as those in Panel B of Table 5 on the right-

hand side. In the second step, we estimate the same model as that

4.4. Issue-date open-market short sales

The arbitrage explanation predicts a higher expectedhedging demand but lower observed issue-date open-market short sales for combined offerings. Table 6 presentsseveral issue-date short sales measures for combined anduncombined convertibles. Short Sales and SO are calculatedas outlined earlier. D Short Sales is the difference betweenissue-date short sales and Normal Short Sales. TV is theaverage daily trading volume. In line with Choi, Getmansky,and Tookes (2009), we measure TV over the window[�120, �20].

We find that the average Short Sales/SO ratio forcombined issues is 0.71%. For uncombined issues this ratiois almost twice as large (1.32%). The difference betweencombined and uncombined offerings is significant at lessthan 1%. We obtain similar results when we use D ShortSales in the numerator and when we use TV in thedenominator. The findings in Table 6 are consistent withthe notion that the short sales associated with combinedissues happen largely outside of the open market, and areas such not recorded on open-market daily shortsales tapes.

4.5. Number of shares announced to be repurchased

If the arbitrage explanation holds, we expect to find aclose correspondence between the number of shares thatshould be repurchased to hedge the arbitrageurs’ position[labeled ‘‘R�arb’’, see Eq. (3)] and the number of shares thefirm effectively announces to repurchase (labeled ‘‘R’’). Weassume that convertible arbitrageurs follow a so-calleddelta-neutral hedging technique that makes their positionsinvariant to small stock price movements.15

We calculate delta using the call protection length as ameasure for the convertible’s effective maturity. Becausewe are unsure about the maturity measure that is effec-tively used by arbitrageurs, we also calculate the deltausing the stated maturity. Not surprisingly, this approachyields a much higher delta (0.87 on average, versus 0.60 onaverage when using the call protection length).

For 77 of the firms engaging in a combined offering, wehave sufficient information to calculate R�arb. Using the deltameasure based on the call protection length, we find thatthe Pearson correlation coefficient between R�arb and R is ashigh as 0.83. The ratio of R to R�arb has an average value closeto one (1.19). Using the delta measure based on the stated

(footnote continued)

represented in Panel B, except that we include the inverse Mills ratio

obtained from the first-step analysis as an additional explanatory vari-

able. This operation leaves the results virtually unaltered. The inverse

Mills ratio is insignificant (z-value equals �0.44).15 The comments accompanying the convertible bond issues

retrieved from SDC contain several references to the use of the delta-

neutral hedging technique, e.g.: ‘‘Proceeds from the offering were used y

to repurchase $150m of stock on the deal; y the delta hedge is a common

application to mitigate the impact of short selling’’ (convertible issue of

Medimmune, June 24, 2006). Arguably, arbitrageurs could take other

Greeks into account when deciding on their hedging positions. Still, most

of the convertible arbitrage strategies build on the delta-neutral techni-

que (Calamos, 2003).

Table 6Difference in observed daily short sales between combined and uncombined issues.

This table presents a univariate analysis of the differences in observed daily short sales measures for combined and uncombined convertible debt issues.

Short Sales is the sum of all open-market short sales for each firm on the issue date, as reported in NYSE Trade and Quote database’s Regulation SHO file. SO is

the number of shares outstanding measured at trading day �20 relative to the issue date. D Short Sales is the difference between Short Sales and Normal

Short Sales, which are average daily short sales measured over trading days �10 to �4. TV is the average daily trading volume measured over trading days

�120 to �20. t-statistics and Wilcoxon test statistics are for the differences between combined and uncombined convertibles. The sample period is January

2005 to July 2007. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Average (median)

Combined Uncombined t-statistic (Wilcoxon statisitc)

Short Sales (N shares) 702,387 (395,350) 1,740,084 (699,050) �2.62*** (�3.60***)

Short Sales/SO 0.71% (0.48%) 1.32% (1.11%) �2.98*** (�3.46***)

D Short Sales/SO 0.51% (0.30%) 1.12% (0.95%) �3.24*** (�3.53***)

Short Sales/TV 0.77 (0.54) 1.88 (1.51) �4.25*** (�3.28***)

D Short Sales/TV 0.55 (0.33) 1.66 (1.29) �4.46***(�3.45***)

Number 42 107

Fig. 2. Percentages of actual repurchases in the first quarter after the stock repurchase announcement. This figure shows the percentages of announced stock

repurchases that are actually repurchased within the first quarter after the announcement. The black bars represent stock repurchases announced in

combination with convertible bond issues. The grey bars represent stock repurchases announced without a simultaneous convertible bond issue. The sample

period is 2003–2007.


maturity, we also find a close correspondence between R�arb

and R (correlation coefficient of 0.89, and an average R toR�arb ratio of 0.86).16 These findings are consistent with thenotion that the stock repurchases are added to fulfil thehedging needs of convertible bond arbitrageurs.

4.6. Speed with which common stock is repurchased

An announcement of a stock repurchase does notprecommit firms to acquire a specified number of shares.If convertible debt issuers buy back shares to help

16 Our findings on the correspondence between R�arb and R are robust

to using the equity component size produced by the convertible bond

valuation model of Tsiveriotis and Fernandes (1998) (estimated using the

input parameters described in Section 4.1) and to using the probability of

conversion of the convertible bonds (estimated following the simulation

procedure outlined in Lewis and Verwijmeren, 2009) instead of the delta

in Eq. (2). Our findings are also robust to using a maturity estimate

obtained from the Lewis and Verwijmeren (2009) simulation algorithm in

the calculation of the delta.

arbitrageurs obtain their arbitrage positions, however,we expect the stock repurchases to be executed veryquickly after their announcement. Stephens andWeisbach (1998) study a sample of 450 repurchase pro-grams from 1981 to 1990. They find that firms on averageacquire only 6.3% of the number of stocks announced to berepurchased in the quarter of the repurchase announce-ment. Similar to these authors, we examine changes inshares outstanding obtained from CRSP. Among the com-bined issues, we have 72 observations with sufficient datato determine the changes in shares outstanding for the firstquarter. We also estimate the percentage of shares that isrepurchased for normal (uncombined) stock repurchasesover our research window. We have 2,281 stock repurchaseobservations with sufficient data. In line with Stephens andWeisbach, we reset observations in which the number ofshares increases to zero, because we are only interested indecreases.

Fig. 2 shows the actual shares repurchased in normalstock repurchases and in combined offerings during thefirst quarter after the announcement date.


The white bars represent the percentage of stockrepurchased in uncombined stock repurchases. More than70% of the firms repurchase less than 20% of the announcednumber of shares in the first quarter. To calculate the averagepercentage of shares repurchased, we reset observations inwhich the number of shares repurchased exceeds theannounced number to 100%. For normal, uncombined stockrepurchases, we find that on average 18.8% of the announcedshares are repurchased in the first quarter (the median valueequals 2.6%). The black bars represent the percentage of stockrepurchased in combined offerings. A relatively large num-ber of firms (42 or 58.3%) perform more than 80% of theannounced stock repurchase in the first quarter after theannouncement. The average (median) percentage of sharesrepurchased in the first quarter is 66.1% (86.6%). Due topotential simultaneous increases in shares outstanding(e.g., caused by stock option exercises), the real percentagesthat are repurchased are expected to be even higher.Apparently, firms in a combined offering repurchase sharesmuch faster than in normal repurchases, which is consistentwith arbitrageurs obtaining their positions.

5. Alternative explanations

A number of other potential alternative explanationsexists for the occurrence of combinations of convertibleofferings and stock repurchases. In this section, we exam-ine the validity of these explanations.

5.1. Signal firm value

In Section 4.2, we disentangle the arbitrage explanationfrom a signaling interpretation by showing that the differ-ences in stock price effects between combined and uncom-bined offerings are no longer significant after controllingfor differences in hedging-induced price pressure, and thatnegative stock price reactions for uncombined convertibles(partially) reverse post-issuance. In this subsection, wefurther assess the validity of the signaling explanation forcombined offerings by comparing firm characteristics ofcombined issuers with those of uncombined issuers. If thesignaling explanation for combinations holds, then weshould observe that firms with stronger incentives forsignaling are more likely to add a stock repurchase to theirconvertible offering. We include four proxies for a firm’sneed for signaling in the analysis. The first proxy is theStock Run-up variable defined earlier. When a firm has ahigh stock price run-up prior to an equity(-linked) offeringannouncement, the market is more likely to think that theoffering is inspired by firm overvaluation. For such com-panies, repurchasing stock might be a way to signal thattheir stock is in fact not overvalued. Three other proxyvariables, PPE, Psi, and SDaccruals, relate to the level ofinformation asymmetry regarding the firm. High informa-tion asymmetry increases the need to reveal the firm’s truevalue to the market. The variables are calculated as follows.

�
PPE: plant, property, and equipment (#7) divided bytotal assets. Firms with a higher proportion of tangibleassets are expected to have a lower level of asymmetricinformation regarding their value.
�
Psi: firm-specific return variability in a given year relativeto the total return variability, as in Durnev, Morck, Yeung,and Zarowin (2003). The underlying intuition is that alarger firm-specific variation in stock returns reflects moreinformation getting into the stock price, and thus lessinformation asymmetry. The firm-specific stock returnvariation is obtained from the regression
Firm returnt ¼ b0þb1 market returnt

þb2 industry returntþe, ð4Þ

which is estimated for each firm using monthly returnsmeasured over the previous calendar year. Industryreturns are based on two-digit standard industrial classi-fication (SIC) codes. Market and industry returns are value-weighted averages excluding the firm for which theregression is estimated. The variance of e is scaled bythe total variance of the dependent variables in theregression.
� SDaccruals: Lee and Masulis (2009) suggest that poor
accounting quality, as proxied by a high standard deviationof estimation errors of accounting accruals, results in a highlevel of asymmetric information with regard to the firm’svalue. We use the McNichols (2002) modification of theDechow and Dichev (2002) model, which is

CAt ¼ g0þg1 CFOtþg2 CFOtþ1þg3 CFOt�1

þg4 DSalestþg5 PPEtþn ð5Þ

In line with Lee and Masulis (2009), we calculate CA(current accruals) asD current assets (#4) minusD currentliabilities (#5) minus D cash (#1) plus D debt in currentliabilities (#34), withD representing changes from year t toyear t�1. CFO is cash flows from operations, calculated asnet income before extraordinary items (#18) minus totalaccruals, with total accruals equal to CA minus deprecia-tion and amortization expenses (#14). Sales are defined astotal revenue (#12). All variables are scaled by the averageof total assets between year t�1 and year t. We take thestandard deviation of the estimation error n, with aminimum number of observations of four consecutiveyears and a maximum of 15.

We test the effects of these four proxy variables on thedecision to combine a convertible debt offering with a stockrepurchase by means of a probit analysis with the Com-bined Offering dummy variable as dependent variable. Wealso control for a number of other firm-specific character-istics that could affect the decision to add a stock repurch-ase, i.e., Log(Assets), Leverage, and Market to Book. Weinclude year dummy variables to control for the increasein popularity of the combinations over the sample period(not reported for space reasons).

The probit results presented in Column 1 of Table 7 showthat the SDaccruals variable has a significant negative impacton the decision to add a stock repurchase, which is exactlyopposite to the prediction derived under the signalinginterpretation. The other three signaling proxies have insig-nificant effects. With the exception of Market to Book, whichis significantly higher for combined offerings, the effects ofthe control variables are not significant either. Togetherwith the evidence presented in Table 5 on the differencesin expected hedging demand between combined and

Table 7Impact of firm characteristics on the decision to combine a convertible issue with a stock repurchase.

This table presents the results of a probit model estimating the impact of firm characteristics on the decision to combine a convertible with a stock

repurchase. The dependent variable is a dummy variable equal to one for convertibles combined with a stock repurchase and equal to zero otherwise. All

firm-specific variables are measured at the fiscal year-end preceding the issue date, unless noted otherwise. Stock Run-up is the stock return measured over

the window [�76, �2]. PPE is the ratio of plant, property and equipment (Compustat item #7) to total assets (#6). Psi measures firm-specific return

variability as in Durnev, Morck, Yeung, and Zarowin, 2003). SDaccruals measures the standard deviation of errors in estimations of accruals [accruals are

estimated with Eq. (5)]. Log(Assets) is the natural logarithm of the book value of total assets. Leverage is the ratio of long-term debt (#9) to total assets.

Market to Book is calculated as (#25�#199�#60+#6)/#6). Decrease EPS is the change in diluted earnings per share that would occur without a stock

repurchase. Bonus is the correlation between the change in annual chief executive officer cash bonus (reported in Execucomp) and the change in diluted EPS

by two-digit standard industrial classification code for the year before the offering. Deviation from Target captures the difference between firms’ leverage

and the industry median leverage, in which the industries are based on the Fama-French 12-industry classification. Marginal Tax Rate measures the marginal

tax rate before interest expenses. This variable is downloaded from John Graham’s website (www.duke.edu/� jgraham/). We also include year dummies (not

reported for space reasons). z-statistics (calculated with Huber-White heteroskedasticity-consistent standard errors) are in parentheses. The sample period

is 2003–2007. *, **, and *** indicate significance at the 10%, 5%, and 1% level, respectively.

Combined offering

(1) (2) (3)

Intercept �2.439 (�3.94***) �2.438 (�3.31***) �1.954 (�2.15**)

Stock Run-up 0.301 (1.13) 0.191 (0.69) 0.202 (0.58)

PPE �0.317 (�0.74) �0.300 (�0.62) 0.103 (0.18)

Psi �0.171 (�0.48) �0.140 (�0.36) 0.222 (0.44)

SDaccruals �3.667 (�2.70***) �3.310 (�2.29**) �6.342 (�1.92*)

Log(Assets) �0.008 (�0.08) �0.031 (�0.28) 0.040 (0.27)

Leverage 0.256 (0.64) 0.405 (0.96)

Market to Book 0.206 (2.67***) 0.223 (2.73***) 0.286 (1.70*)

Decrease EPS 0.043 (0.02)

Bonus 0.202 (0.40)

Deviation from Target 0.391 (0.68)

Marginal Tax Rate 0.914 (0.77)

Number 394 344 181

McFadden R2 24.57% 24.50% 28.08%


uncombined offerings, the results in Table 7 suggest thatcombined and uncombined issuers differ in their attractive-ness to arbitrageurs, not in their need for signaling.

5.2. Reduce EPS dilution

Combining convertible issues and stock repurchasesreduces the short-term EPS dilution caused by the con-vertible issue. Under the ‘‘if-converted’’ method, thedenominator of diluted EPS needs to incorporate the sharesthat can be issued upon conversion of the convertiblebonds, even though these convertibles are not (yet) con-verted into stock. When stock is repurchased, the numberof outstanding shares decreases and EPS dilution is miti-gated. To test the validity of the EPS dilution explanation,we augment the probit model reported in Column 1 ofTable 7 with the following two variables.

�
Decrease EPS: the change in diluted earnings per sharethat would occur without a stock repurchase. In linewith Marquardt and Wiedman (2005), we calculate thisvariable as
Decrease EPS¼ 1�EPSPOST�CB

EPSPRE�CB

� �ð6Þ

with EPSPOST�CB, earnings adjusted for the convertibleoffering (labeled Eadj) divided by SHARESadj, which is thesum of shares outstanding and the potentially dilutiveshares resulting from the offering; and EPSPRE�CB, earn-ings unadjusted for the convertible offering (labeledEunadj) divided by shares outstanding (SHARESunadj).

�
Bonus: the correlation between the change in theannual chief executive officer cash bonus (obtainedfrom ExecuComp) and the change in diluted EPS bytwo-digit SIC code for the fiscal year before the offering(only if the number of observations for each industry-year is larger than five). We expect that managers aremore concerned with diluted EPS when their bonusplans relate to this measure, i.e., when Bonus is high.
As can be seen in Column 2 of Table 7, the effects ofDecrease EPS and Bonus are both insignificant. As anadditional test for the validity of the EPS dilution explana-tion, we calculate the correspondence between the numberof shares that managers would have to repurchase tocompletely neutralize the decrease in EPS due to theconvertible offering (labeled R�EPS) and the number of sharesthey announce to repurchase (labeled R). Using the nota-tion adopted earlier, we obtain the equation

1�ðEadj=ðSHARESadj�R�EPSÞÞ

ðEunadj=SHARESunadjÞ¼ 0 or

R�EPS ¼ SHARESadj�Eadj � Eunadj

SHARESunadj

� �: ð7Þ

We find that the average ratio of R to R�EPS is 0.56. This valuedeviates much more strongly from one than the correspondingratio calculated using R�arb, which varied between 0.86 and1.19. For 71 of the 77 observations for which we can calculateboth R�EPS and R�arb, we find that the distance between R�arb and R

is smaller than the distance between R�EPS and R. Together withthe probit results in Table 7, this finding suggests that the

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www.duke.edu/&sim;jgraham/


share repurchase decision is motivated by the presence ofarbitrageurs, not by EPS dilution considerations.

5.3. Optimize capital structure

The combined transactions could also be motivated by theissuers’ wish to move closer to their target debt ratios. If thisexplanation holds, then issuers of combinations should bemore underlevered than other convertible issuers, asrepurchasing stock increases the debt ratio (ceteris paribus).To examine whether combinations are driven by static trade-off considerations, we extend the probit analysis reported inColumn 1 of Table 7 (excluding Leverage) with the variableDeviation from Target, which measures the differencebetween the firms’ actual Leverage and the median industryleverage (industries are based on the Fama-French12-industry classification). We also include the MarginalTax Rate (before interest expenses) downloaded fromJohn Graham’s website (http://www.duke.edu/� jgraham).According to the static trade-off theory, firms with higher taxrates have a higher optimal debt ratio due to the taxdeductibility of interest rates. We thus expect a negativeimpact of Deviation from Target and a positive impact ofMarginal Tax Rate on the decision to add a stock repurchase.As can be seen in Column 3 of Table 7, these two additionalvariables have insignificant effects. Thus, the decision tocombine a convertible debt offering with a stock repurchasedoes not seem to be driven by static trade-off considerations.

5.4. Finance a stock repurchase

Throughout the paper, we have assumed that firmsengaging in a combined offering add a stock repurchase to aconvertible issue. However, the possibility exists thatthe initial decision is to repurchase stock and that theconvertible issue is added simply to obtain funds for therepurchase. One argument against this reasoning is that, asshown in Table 1, the convertible issue tends to be abouttwice the size of the stock repurchase. Moreover, if themain motivation for the combined offerings is to obtainfinancing to repurchase stock, we would predict that firmsengaging in combined offerings have less financial slackthan normal (separate) stock repurchasers, which is not thecase (t-statistic for difference in average Cash to TotalAssets ratios equals �0.49). We also check whether firmsengaging in a combined offering regularly announce stockrepurchases and are therefore expected to do so again. Wefind that, for the combined issuers, the number of stockrepurchases announced over the five years preceding theconvertible debt announcement does not significantlydiffer from the numbers announced by separate stockrepurchasers or by uncombined convertible issuers.17

6. Conclusion

We examine why convertible debt issuers add a stockrepurchase to their offering. We argue that the stock

17 Detailed results regarding the comparisons between combined

issues and uncombined stock repurchases can be obtained upon request.

repurchase serves to provide a short position to convertibledebt arbitrageurs. In return for acting as counterparty inthe short-selling transaction, the issuer can negotiate alower offering discount. Moreover, he avoids negative pricepressure around the convertible debt issuance date, whichcould be partly permanent.

We present six pieces of empirical evidence consistentwith the arbitrage explanation. First, combined offeringsare offered at lower discounts than otherwise similaruncombined convertibles, suggesting that combinedissuers benefit from the transaction by obtaining a betterprice for their convertible. Second, issue-date stock returnsare significantly less negative for combined issues than foruncombined offerings. Consistent with the arbitrage expla-nation, a substantial part of the negative stock price reactionfor uncombined offerings reverses in the weeks followingthe offering, while no significant stock price drift exists forcombined offerings. Third, combined offerings are issued byfirms with high expected hedging demand from convertiblebond arbitrageurs. Fourth, observed issue-date open-mar-ket short sales are significantly lower for combined offer-ings. Fifth, the number of shares that a firm announces torepurchase correlates strongly with the expected shortpositions of convertible arbitrageurs. Sixth, the speed withwhich stock is repurchased is substantially higher in thecombined transactions than in pure stock repurchases.

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20101027 why do convertible issuers simultaneously repurchase stock

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