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英文 Convertible bond arbitrage, liquidity externalities, and stock prices

Convertible bond arbitrage,liquidity externalities,and stock prices $

Darwin Choi a,1,Mila Getmansky b,2,Heather Tookes a,?

a Yale School of Management,P.O.Box 208000,New Haven,CT 06520-8000,USA

Isenberg School of Management,University of Massachusetts,121Presidents Drive,Room 308C,Amherst,MA 01003,USA

a r t i c l e i n f o

Article history:

Received 19March 2007Received in revised form 23January 2008

Accepted 25February 2008

Available online 25November 2008JEL classi?cation:G12G14

Keywords:

Convertible bond arbitrage Liquidity

Market ef?ciency Hedge funds

a b s t r a c t

In the context of convertible bond issuance,we examine the impact of arbitrage activity on underlying equity markets.In particular,we use changes in equity short interest following convertible bond issuance to identify convertible bond arbitrage activity and analyze its impact on stock market liquidity and prices for the period 1993to 2006.There is considerable evidence of arbitrage-induced short selling resulting from issuance.Moreover,we ?nd strong evidence that this activity is systematically related to liquidity improvements in the stock.These results are robust to controlling for the potential endogeneity of arbitrage activity.

1.Introduction

Does arbitrage activity impact market quality?Although this question is not new,the proliferation of

hedge funds in recent years has brought increasing attention to important questions regarding their impact on both liquidity and market ef?ciency (see,e.g.,Secu-rities and Exchange Commission (SEC)Staff Report,2003).In this paper,we focus on one particular strategy:convertible bond arbitrage.The growth in the issuance of the equity-linked debt securities can be attributed,at least in part,to the growing supply of capital provided by hedging strategies.Convertible bond issuance has in-creased more than sixfold in the past 15years,from $7.8billion in 1992to $50.2billion in 2006(Securities Data Corporation (SDC),Global New Issues database).In fact,the widespread belief among Wall Street practitioners is that convertible bond arbitrage hedge funds purchase 70%to 80%of the convertible debt offered in primary markets.1

Contents lists available at ScienceDirect

journal homepage:https://www.wendangku.net/doc/1613861249.html,/locate/jfec

Journal of Financial Economics

We would like to thank Vikas Agarwal,Nick Bollen,Ben Branch,John Burke,Michael Epstein,Richard Evans,Shuang Feng,Laura Frieder,William Fung,Paul Gao,William Goetzmann,Robin Greenwood,Jennifer Jeurgens,Charles Jones,Nikunj Kapadia,Hossein Kazemi,Camelia Kuhnen,Owen Lamont,Laura Lindsay,David Modest,Sanjay Nawalkha,Thomas Schneeweis,Matthew Spiegel,Norman Wechsler,Rebecca Zarutskie,and seminar participants at Yale University,the Batten Young Finance Scholars Conference,UMASS-Amherst,the NBER Microstructure working group,and the FDIC/JFSR Bank Research Conference on Liquidity and Liquidity Risk for helpful discussions.We are extremely grateful to Paul Bennett and the NYSE for providing the short-interest data.We also thank Eric So for his assistance with the Nasdaq data and Scott Zhu for excellent research assistance.We are grateful to an anonymous referee for suggestions that greatly improved the paper.We thank the International Center of Finance at the Yale School of Management for its ?nancial support.Any errors are our own.?Corresponding author.Tel.:+12034360785.

E-mail addresses:darwin.choi@https://www.wendangku.net/doc/1613861249.html, (D.Choi),msherman@https://www.wendangku.net/doc/1613861249.html, (M.Getmansky),heather.tookes@https://www.wendangku.net/doc/1613861249.html, (H.Tookes).

Tel.:+12034325661.2

Tel.:+14135773308;fax:14135453858.1

While they do not constitute the entire universe of convertible bond arbitrageurs,hedge funds are an important subset.Mitchell,Pedersen,and Pulvino (2007),report that convertible arbitrage funds account for 75%of the market.Similar estimates can be found in the popular press.See,e.g.,a Wall Street Journal article (Pulliam,2004)on convertible bond issuance in 2004:‘‘As much as 80%of those issues were bought by hedge funds,according to brokers who work on

Journal of Financial Economics 91(2009)227–251

In order to clarify the intuition as to why convertible bond arbitrage might impact liquidity in underlying equity markets,it is useful to outline the basics of the strategy.The aim of convertible bond arbitrage is to exploit mispricing in convertible bonds,usually by buying an undervalued convertible bond(Henderson,2005)and taking a short position in the equity.2A typical convertible bond arbitrage strategy employs delta-neutral hedging,in which an arbitrageur buys the convertible bond and sells short the underlying equity at the current delta.There are two important components of the strategy(shown in Fig.1).The?rst is the initial position,which is set up so that no pro?t or loss is generated from very small movements in the underlying stock price and where cash ?ows are captured from both the convertible bond’s yield and the short position’s interest rebate.The second is dynamic hedging activity that follows the initial short position.If the price of the stock increases,the arbitrageur adds to the short position because the delta has increased. Similarly,when the stock price declines,the arbitrageur buys stock to cover part of the short position due to the decrease in delta.Aggregate equity market trading demand,in contrast,is expected to move in the opposite direction.For example,Chordia,Roll,and Subrahmanyam (2002)show a positive correlation between stock returns and order imbalances.This means that the dynamic hedging activities of convertible bond arbitrageurs,a class of investors trading against net market demand,should improve liquidity.This potentially positive role for hedge funds and other convertible bond arbitrageurs is contrary to the view of a destabilizing role for arbitrageurs in markets(see Mayhew,2000,for a survey of this literature).

Although we do not have direct data on convertible bond arbitrage activity in individual stocks,we are able to identify?rms and dates on which we know that initial arbitrage positions are taken:convertible bond issuance dates.We use these initial positions as a proxy for the presence of convertible bond arbitrageurs in the market for the stock(i.e.,their future dynamic hedging).For the period1993to2006,we calculate changes in short interest at issuance.Our approach is simple,yet it captures the strategy,as we observe large increases in short interest near convertible debt offerings.The meth-odology allows us to use aggregate data to identify the presence of a particular type of trader in equity markets.

Our proxy for arbitrage activity(initial change in short interest of issuing?rms)has several advantages over using hedge fund databases to estimate convertible bond arbitrage activity.First,this provides a measure of positions taken by arbitrageurs in individual securities. Fund?ows data in hedge fund databases are self-reported and therefore provide an incomplete measure of con-vertible bond arbitrage activity.The databases only partially represent the hedge fund universe,with many large funds choosing not to participate.Second,there can be style misclassi?cation and funds reporting multiple strategies to hedge fund databases.Third,even if we measured the assets of the funds perfectly,the positions would still be unobservable due to the use of leverage.

We?nd considerable evidence of arbitrage activity (i.e.,short selling in the stock at the date of bond issuance).We also?nd increased equity market liquidity following bond issuance.Moreover,these liquidity im-provements are positively and signi?cantly related to our proxy for convertible bond arbitrage activity.We also observe changes in stock return volatility.Following convertible debt issuance there is an average decrease in total return volatility as well as the idiosyncratic compo-nent of volatility.However,we do not?nd evidence of a systematic relationship between convertible bond arbit-rage activity and these changes.We measure price ef?ciency using return autocorrelation and variance ratios (as in Lo and MacKinlay,1988),to capture the extent to which stock prices follow a random walk.We do not observe signi?cant changes in either of these measures following issuance.Taken together,we interpret the ?ndings as evidence that convertible bond arbitrage activity tends to positively affect equity markets;however, this is primarily through liquidity improvements,not through stock prices.

A critical aspect of the analysis is that we do not observe arbitrage activity directly.Instead,we infer it based on changes in short interest at bond issuance.We conduct several tests to examine the validity of this important assumption.3First,we rule out the possibility that changes that we observe are due to changes in market-wide variables or to factors impacting?rms with similar characteristics.We do this by conducting all analyses based on changes relative to a set of control ?rms(matched on industry,exchange,size,book-to-market,and turnover).Second,it could be that the short selling that we observe is due to valuation shorting resulting from news of the convertible bond issue,not due to classic convertible bond arbitrage.In order to address this issue,we hand-collect announcement dates for our sample of issues.The announcement and issue dates allow us to separate the impact of announcement period shorting versus issue period shorting,which we interpret as valuation shorting versus convertible bond arbitrage,respectively.In all of these tests,we?nd evidence consistent with the view that the short selling that we observe near convertible bond issues is due to convertible bond arbitrage.We also conduct robustness tests,in which we explicitly control for other potential sources of volume that can be associated with the

(footnote continued)

convertible-bond trading desks.’’The Financial Times(Skorecki,2004) reports that hedge funds bought70%of new issues in2003and that95% of trades in converts are made by hedge funds.The evidence presented in this study of large increases in short selling near issuance is consistent with that view.

2A convertible bond is a hybrid debt instrument:it is a bond that may,at the option of the holder,be converted into stock at a speci?ed price for a given time period.Due to the conversion option,convertible bond purchasers may pro?t from equity price gains,but they also have

downside protection since they are guaranteed bond payments(and,in the event of bankruptcy,are senior to equity holders).

3We thank an anonymous referee for encouraging this line of inquiry.

D.Choi et al./Journal of Financial Economics91(2009)227–251 228

convertible bond issue.In addition,we control for potential endogeneity of arbitrage activity and?nd similar results.

The main contribution of this paper is that we identify arbitrage activity and are able to estimate its impact on market quality(we use changes in equity market liquidity and price ef?ciency as measures of quality).By identifying a particular trader type,our methodology allows us to shed additional light on the mechanisms through which quality changes following issuance occur.The primary ?ndings suggest that changes in liquidity vary system-atically with the positions taken by arbitrageurs.The ?ndings in this paper may be of interest to managers of issuing?rms concerned about liquidity and ef?ciency spillovers in their stock as a result of their capital structure decisions.

This paper is organized as follows.Section2contains a brief review of related literature.Section3constructs the main hypotheses.Section4describes the data and sample. Section5presents the analysis of arbitrage activity, liquidity,and prices.Several robustness checks are also presented.Finally,Section6concludes.

2.Related literature

The notions of liquidity and ef?ciency‘‘externalities’’underlie much of the analysis in this paper.The idea in Ross(1976)and subsequent theoretical works(e.g.,Easley, O’Hara,and Srinivas,1998;Biais and Hillion,1994; Grossman,1988)that the introduction of options markets can enhance ef?ciency by making markets less incomplete or by positively impacting informativeness of stock prices has been followed by empirical investigations of the impact of derivatives markets on the market for the underlying asset(e.g.,Kumar,Sarin,and Shastri,1998; DeTemple and Jorion,1990).4Mayhew(2000)provides an excellent survey of this literature.The main?ndings indicate that derivatives markets have a positive impact on liquidity and no negative impact on price ef?ciency. Most authors report a decrease in total volatility and an increase in trading volume following the introduction of options.We consider our study of the liquidity and ef?ciency externalities of convertible bond markets to be an extension of this line of research.Because of the embedded option in the convertible bond,the issuance of convertible bonds is analogous to the introduction of options.5Our identi?cation(based on short selling)allows us to provide a more direct test of the impact of arbitrageurs.While prior work has provided evidence that new securities markets can impact equity market quality on average,we identify the mechanisms through which quality changes occur.

Our basic empirical strategy uses increases in short interest near debt issuance to identify arbitrage activity. In that way,it is closely related to the growing empirical literature on short selling activity.There has been considerable focus on the relationship between future stock returns and both observed short sales and short-sales constraints(see, e.g.,Diether,Lee,and Werner, 2008;Boehme,Danielsen,and Sorescu,2006;Asquith, Pathak,and Ritter,2005;Jones and Lamont,2002; Dechow,Hutton,Meulbroek,and Sloan,2001;Asquith and Meulbroek,1996).The information content of short sales in event settings has also received attention in the recent empirical literature(e.g.,Christophe,Ferri,and Angel,2004).All of these papers provide evidence that short selling and short-sales constraints impact stock prices,suggesting that short sellers help to incorporate negative information into prices.

Although short sellers can help facilitate the incor-poration of negative information into prices,many are uninformed.They use short sales to hedge other positions. Little has been done to distinguish this type of short seller.6This is an important distinction because the impact of short selling on market quality will obviously depend largely on who is engaging in the short sale. Uninformed short sellers are likely to add liquidity to markets(rather than reduce it as a result of potential adverse selection).Asquith,Pathak,and Ritter(2005, p.270)note that,‘‘Of course,a?rm might have a high short-interest ratio because there is both valuation short-ing,and arbitrage shorting taking place simultaneously. Unfortunately,we cannot identify these situations pre-cisely.’’Our event-based approach takes us further towards identifying this specialized investment strategy from the aggregate data and distinguishing this activity from valuation shorting.

Three recent papers use changes in short interest near events to infer the impact of a particular type of trader. Arnold et al.(2005)use the Tax Payer Relief Act of1997, which made selling short against the box more costly,as a laboratory for testing hypotheses regarding changes in the information content of short interest when tax-motivated short sellers(i.e.,uninformed sellers)no longer have incentives to short.This event-driven approach to trader identi?cation is similar in spirit to ours;however,we examine not only average changes,but also cross-sectional implications of the introduction of a particular trader type.That is,we examine the sensitivity of subsequent changes in liquidity and ef?ciency to the magnitude of the increase in short selling due to arbitrage. Mitchell,Pulvino,and Stafford(2004)use short interest in acquirers near merger announcements to identify activ-ities by risk arbitrageurs and estimate their impact on prices.Bechmann(2004)provides evidence that short selling induced by hedging activities explains part of the stock price decline following convertible bond calls.

4More recently,Basak and Croitoru(2006)show how the presence of arbitrageurs improves market quality and risk sharing in the context of rational markets with heterogeneous risk-averse investors and short-

sales constraints.

5In fact,in unreported analysis,we?nd that the absence of put or call options on a particular stock is associated with greater convertible bond arbitrage activity.This con?rms the idea that the existence of substitute markets is critical in any trading decision.

6Boehmer,Jones,and Zhang(2008)use proprietary order-level data from the NYSE to quantify the information content of the?ow of shorting activity by the type of account initiating the sale.Their focus is on characterizing the information content of short sales,by size and trader(account type).

D.Choi et al./Journal of Financial Economics91(2009)227–251229

In both Bechmann(2004)and Mitchell,Pulvino,and Stafford(2004),the focus is mainly on price pressure induced by short selling activity while our focus is on the impact of arbitrage on stock market liquidity and prices.

Although they do not constitute the entire universe of convertible bond arbitrageurs,convertible bond arbitrage hedge funds do play a role in primary issues of convertible debt and can impact stock market quality.Henderson (2005)studies the underpricing of convertible bonds at issue,as well as the risk and returns of the convertible bond arbitrage strategy.7He?nds that new issues of convertible bonds are underpriced at issue but that excess returns occur soon after issuance(mainly in the?rst six months).This can decrease the presence of convertible bond arbitrageurs over longer horizons.8Mitchell,Pedersen, and Pulvino(2007)analyze the impact of capital out?ows in hedge funds on convertible bond prices.Finally,Choi, Getmansky,Henderson,and Tookes(2008)examine supply and demand in the convertible bond market.They map the measure of arbitrage activity used in this paper to fund?ows and returns in convertible bond arbitrage hedge funds.Overall,?ndings in these papers suggest a signi?cant role for hedge funds in convertible bond and related markets.

3.Arbitrage,liquidity,and stock prices:predictions

This section outlines the main predictions.We measure changes in short interest near convertible bond issuance and relate this to changes in liquidity and stock price ef?ciency.We test the following two null hypotheses: H0(LiquidityT:Convertible bond arbitrage activity, proxied by increased short interest near issuance,is uncorrelated with changes in liquidity.

H0(Efficiency):Convertible bond arbitrage activity is uncorrelated with changes in ef?ciency.

The typical convertible bond arbitrage strategy(delta hedging)implies that arbitrageurs engaged in dynamic hedging are likely to trade in the opposite direction of the rest of the market:they increase their short positions as stock prices increase,and decrease them when stock prices decrease.This should result in improved market liquidity(the alternative hypothesis).

The expected improvement in liquidity described above assumes that convertible bond arbitrageurs have no special knowledge about the value of the underlying shares.If they are instead privately informed about future stock values,adverse selection costs can increase,and equity market liquidity can decrease.While it is an empirical question,we do not expect to observe evidence of this because convertible bond arbitrageurs typically act to exploit perceived underpricing in the bond,not equity.

In addition to liquidity changes,convertible bond arbitrageurs can also impact the ef?ciency of equity prices.In theory,if the short selling that we identify in the data is due to an informational advantage about equity market valuation,price ef?ciency would increase follow-ing issuance.9Even if these short sellers are not privately informed but are trading to exploit a known inef?ciency such as autocorrelation,ef?ciency will also increase following issuance.10On the other hand,if short sellers are taking equity market positions primarily to hedge their positions in the bonds,then their presence would not directly impact ef?ciency of stock prices.We con-jecture that although convertible bond arbitrageurs are sophisticated traders,they are relatively uninformed.That is,they have no private information about the value of the equity that they short.They are trading to manage equity risk exposure,not to exploit mispricing.11If this is the case,we predict:

P1:Convertible bond arbitrage activity,proxied by the increase in short interest near issuance,will be associated with improved market liquidity.This occurs via dynamic hedging strategies,in which arbitrageurs’trading activity tends to be in the opposite direction of the market.

P2:Convertible bond arbitrage activity will not impact the ef?ciency of prices.

For a more precise interpretation of prediction P2,the analysis will make a distinction between convertible bond arbitrage and other arbitrage activity(e.g.,valuation shorts or exploitation of known autocorrelation).It may be reasonable to expect short selling due to general arbitrage activity to improve price ef?ciency;however, convertible bond arbitrageurs typically take their posi-tions to hedge their bond positions and thus,stock price ef?ciency should not be affected.

In the empirical analysis,we use a variety of proxies for both liquidity and price ef?ciency.For liquidity,we examine:turnover,number of trades,the Amihud(2002) illiquidity measure,order imbalance(the absolute value of the difference between the number of buyer-and seller-initiated trades,classi?ed based on Lee and Ready,1991), quoted spread,quoted depth,and the ratio of spread to depth.High values for turnover,number of trades,and depth are interpreted as high liquidity.Low values of the Amihud(2002)measure,order imbalance,spread,and spread=depth are interpreted as high liquidity.The spread=depth measure is of interest because it re?ects both the price(spread)and quantity(depth)aspects of stock quotes and can provide more insight than examining these measures separately.The ratio of spread to depth has also been used in prior work examining the impact of a derivatives market for the quality of the underlying stock market(see Kumar,Sarin,and Shastri,1998).For stock price ef?ciency,we use:(1)the variance ratio,which compares stock price variances over different frequencies, where smaller deviations from one imply greater ef?-ciency12;and(2)autocorrelation,where smaller magni-tude of return autocorrelation is interpreted as greater

7The risks and rewards of liquidity provision by convertible bond arbitrage hedge funds are studied in Agarwal,Fung,Loon,and Naik (2007).

8This?nding aids in de?ning windows used in our main analysis of the potential impact of convertible bond activity.

9For example,see Diamond and Verrecchia(1987).

10We thank the referee for suggesting this possibility.

11Chakraborty and Yilmaz(2006)suggest convertible bonds as a solution to adverse selection problems in the market for new securities when investors are uninformed.

12See Lo and MacKinlay(1988).

D.Choi et al./Journal of Financial Economics91(2009)227–251 230

ef?ciency.13We also examine long-run stock returns following bond issue.The latter is a test of ef?ciency in that it asks whether the short-sales positions that we observe in the data would make money over various horizons.

4.Data and sample selection

4.1.Short interest and convertible debt issues

The initial sample consists of all convertible debt issues(public,private,and Rule144a)by U.S.publicly traded?rms for the period July1993through May2006.14 Issue dates and other characteristics of the issues are from the SDC Global New Issues database and the Mergent Fixed Income Securities Database(FISD).We obtain monthly short-interest data directly from the NYSE and Nasdaq and match the short-interest data with the SDC data using ticker and date identi?ers.Because the monthly short-interest?les re?ect short sales through three trading days(?ve for the?rst years of the sample) prior to the15th of each month,we calculate a trade date for each?le and use that date to match to the SDC data.15 We then match these data to the Center for Research in Security Prices(CRSP)/Compustat tapes and NYSE TAQ Database.We also obtain data on institutional holdings from the Thomson Financial Institutional(13f)Holdings and analyst opinion from Institutional Brokers Estimate System(I/B/E/S).For inclusion in the?nal sample,we require non-missing data on short interest,all liquidity and ef?ciency measures,and all control variables such as institutional holdings,analyst opinion,and historical return volatility.This results in a?nal sample of846 convertible bond issues.

Table1contains summary statistics.The issuing?rms have a mean(median)market capitalization of$4.7($1.2) billion.The convertible bond issue sizes constitute signi?cant proportion of equity value,with the mean (median)dollar value of proceeds equal to18.0%(14.9%)of equity market capitalization.The?rms for which we observe credit ratings are typically rated‘‘junk,’’with median Standard&Poor’s(S&P)rating of BB-.In addition,

Table1

Issuing?rms and characteristics.

This table presents summary statistics for the sample of convertible bond issues between July1993and May2006.Market cap is the issuing?rm’s equity market capitalization.NYSE and Nasdaq are dummy variables,indicating where the issuing?rm is listed.Debt/equity is the ratio of long-term debt to equity market capitalization in the?scal year prior to issuance.Daily dollar volume is the average daily dollar volume of the stock.Beta is the coef?cient estimate of the regression of daily stock excess returns on CRSP value-weighted market excess return.Issue size is the face value of the convertible bond times its offer price.Short interest is the average monthly short interest.Institutional holdings/shares outstanding is the institutional holdings(by13f institutions)divided by shares outstanding in the calendar year end prior to issuance.Credit rating is the bond rating issued by S&P.a All daily and monthly measures are calculated using data from the six months ending one month prior to announcement of the issue.

Number of observations?846.

Mean Median Standard deviation

Market cap($million)4,6871,17913,457 NYSE0.4900.50 Nasdaq0.5110.50

Debt/equity0.600.18 1.58

Daily dollar volume($million)42.5812.67103.10

Beta 1.34 1.270.75

Issue size($million)291.20175.50368.92 Issue size/market cap(%)17.9714.9013.38

Short interest(000shares)5,4972,15214,753

Short interest/shares outstanding(%) 4.47 3.05 4.75 Institutional holdings/shares outstanding(%)65.0068.3722.45 Credit rating BB BB-

a If the bond is not rated by S&P,Moody’s or Fitch rating is used,in that order,as available.Of846bonds444are rated by at least one of the three agencies. For calculating the mean and median credit rating,a number is assigned to each rating:best(AAA or Aaa)?1,second best?2,https://www.wendangku.net/doc/1613861249.html,ing this system, mean rating?12:29,which lies between BB and BB-for S&P and Fitch(or Ba2and Ba3for Moody’s),median?13(BB-or Ba3),standard deviation?3:85.Only rated issues are included in the calculation.

13In unreported tests,we examined two additional ef?ciency measures:idiosyncratic volatility and R-squared.Results using these two measures are similar to the other ef?ciency measures.The distinction between idiosyncratic and systematic volatility is motivated by Bris et al.(2007).They interpret an observed low R-squared as evidence of ef?ciency.Similarly,we interpret an increase in idiosyncratic volatility as evidence of improved price ef?ciency because it suggests that more?rm-speci?c information is incorporated into prices.

14We begin the analysis in1993because NYSE Trade and Quote (TAQ)data are used to construct some of the liquidity and price-ef?ciency measures.

15It is critical to correctly match the short-interest dates to the issue dates.The monthly short-interest data are based on short interest as of trade dates that occur during the middle of the month at non-constant days across months(due to settlement).Following the documentation from the short-interest?les that we received from Nasdaq and the NYSE, we de?ne the cutoff trade date for a given month as:?ve trading days before the15th(or the preceding trading day if the15th is not a trading day),through June1995;and three trading days before the15th after June1995.If a bond is issued before the cutoff trade date of a given month,the short-interest data?le for that month is matched to the issue month.Otherwise,the short-interest data for the following month is matched to the issue month.This algorithm is consistent with Bechmann (2004).

D.Choi et al./Journal of Financial Economics91(2009)227–251231

the sample consists of about the same number of NYSE and Nasdaq issuers.We do observe some short selling in these stocks prior to issuance and announcement,with mean (median)short interest during the six months prior to announcement equal to 4.5%(3.1%)of shares out-standing.This is relevant,as arbitrageurs are likely to be attracted to stocks for which a relatively liquid short selling market exists.

4.2.Proxy for the presence of the convertible bond arbitrage strategy

Our proxy for the presence of the convertible bond arbitrageurs is the change in short-interest intensity (‘‘D SI ’’)during the month of the convertible bond issue.As discussed in Section 1,the typical convertible bond arbitrage strategy employs delta-neutral hedging,and consists of two parts.The arbitrageur initially buys the convertible bond and sells short the underlying equity at the current delta.Next,if the price of the stock increases,the arbitrageur adds to the short position because the delta has increased.Similarly,when the stock price declines,the arbitrageur buys stock due to the decrease in delta.Fig.1provides a timeline.Importantly,dynamic hedging is expected to improve liquidity because aggregate equity market trading demand is expected to move in the opposite direction (see Chordia,Roll,and Subrahmanyam,2002).We do not directly observe arbitrageurs’dynamic shorting and covering transactions.Fortunately,their initial arbitrage positions can be reasonably captured since it is straightforward to identify the dates on which they are established.We expect the shares initially shorted by convertible bond arbitrageurs to be a good proxy for post-issue dynamic hedging activity because it measures the presence of arbitrageurs in the equity market.We initially de?ne two measures to proxy for arbitrage activity:

D SI _%Shrout t is the change in short interest (number of

shares)during period t ,scaled by total shares out-standing in period t à1.The change in short interest is the difference between short interest in month t and short interest during month t à1.

D SI _%Issue t is the dollar value change in short interest during the period t ,divided by issue proceeds.

The ?rst measure,D SI _%Shrout t provides a measure of the relative importance of the new arbitrageurs in the

market for the stock.The second measure,D SI _%Issue t ,is related to issue characteristics —namely,the amount of short selling activity as a fraction of the issue size (which can be directly linked to hedging activity).

We do not expect convertible bond arbitrageurs to short before the bond issue due to the risk associated with having an unhedged stock position.Similarly,we do not expect them to delay the initial hedge since the bond position will also give them unhedged exposure to equity risk.Fig.2reports means and medians of the D SI measures during months à6to t6relative to the issue date.Consistent with our ex ante expectation,the ?gures show that we are capturing an increase in short interest related to the issue.The median increase in short interest relative to shares outstanding at issue month 0(D SI _%Shrout t Tis 1.7%.The median dollar value increase in short interest relative to issue size at issue month 0(D SI _%Issue t T,is 13.1%.

As shown in the Fig.2,both D SI _%Shrout t and D SI _%Issue t capture similar variation in short selling activity.The main analysis uses D SI _%Shrout t as a proxy for convertible bond arbitrage activity due to our interest in the implications of convertible bond arbitrage for the market for the underlying stock.16In addition,we focus on the issue month 0,given the large increase in short interest that occurs at that time.For notational convenience,we denote the proxy for convertible bond arbitrage activity as D SI (i.e.,we drop both _%Shrout and the t subscript).17

Fig.3provides a description of the time series of convertible bond issuance and the size of convertible bond arbitrage hedge funds.Issuance has steadily in-creased over time.We have also seen growth in the total assets managed by convertible bond arbitrage hedge funds,which is consistent with a role for hedge funds as suppliers of capital as discussed in Section 1.We also examined the time series of changes in short interest during the sample period and,not surprisingly,observe

Initial hedge:

buy bond and short stock

Adjust short positions according to Issue date

Time

Fig.1.Convertible bond arbitrage delta-neutral hedging.This ?gure presents the timing of a delta-neutral hedge,in which the convertible bond arbitrageur buys a convertible bond and shorts the underlying stock according to the delta of the option embedded in the bond.As stock price changes over time,the position must also be adjusted in order to maintain a delta-neutral hedge.The arbitrageur will sell short additional stock when the stock price increases and buy/cover the short position as stock price declines.

However (in unreported tests)we have replicated the analysis

using D SI _%Issue t .All liquidity results are qualitatively similar (but weaker).The ef?ciency results are almost identical.

Though it is true that short sellers can also short due to private

information (see,e.g.,Christophe et al.,2004,for short selling prior to earnings announcements)or other types of arbitrage activity,the fact that we capture the increase in shorting over a relatively short horizon relative to the bond issue date suggests that our D SI measures are,in large part,capturing convertible bond arbitrage.We explicitly distin-guish valuation shorting from arbitrage shorting in an analysis of short selling near announcement of the issue versus the actual issue date (see the discussion in Sections 5.4).

signi?cant time-series variation in the data.Given this observation and ?ndings in the literature of distinct time-series patterns in short interest (see, e.g.,Lamont and Stein,2004),we include year and month ?xed effects in all cross-sectional regression speci?cations.

In the main analysis of changes in liquidity and stock price ef?ciency we examine a relatively short time

horizon in order to isolate the impact of the convertible bond arbitrage strategy.18Speci?cally,we examine

2.5%

25%

MEAN CHANGE IN SHORT INTEREST

DURING EVENT WINDOW

2.5%

25%

MEDIAN CHANGE IN SHORT INTEREST

DURING EVENT WINDOW

1.5%

2.0%15%20% 1.5%

2.0%

15%20%1.0%10%ΔS I _%I S S U E t

1.0%

10%ΔS I _%I S S U E t

0.0%0.5%0%

ΔS I _%S H R O U T t

0.0%

0.5%

5%ΔS I _%S H R O U T t

-0.5%-5%

MONTH RELATIVE TO ISSUE

-0.5%

-5%

MONTH RELATIVE TO ISSUE

Fig.2.Mean and median change in short interest enumber of observations ?846T.The charts show the mean and median change in short interest during the event window (months à6to t6).D SI _%Issue t is the dollar value of the change in short interest during month t ,divided by issue size.That is:difference between short interest in month t and short interest in month t à1,times the closing stock price in month t ,divided by issue size (face value of the convertible bond times offer price).D SI _%Shrout t is the change in short interest during month t divided by the number of shares outstanding in month t à1.The sample period is from July 1993to May 2006.

DOLLAR VALUE OF PROCEEDS

NUMBER OF ISSUES

15204050

P R O C E E D S ($ B I L L I O N )

N U M B E R O F I S S U E S

1994Q 1995Q 1996Q 1997Q 1998Q 1999Q 2000Q 2001Q 2002Q 2003Q 2004Q 2005Q 2006Q

1994Q 1995Q 1996Q 1997Q 1998Q 1999Q 2000Q 2001Q 2002Q 2003Q 2004Q 2005Q 2006Q 50

TOTAL ASSETS OF CONVERTIBLE BOND

ARBITRAGE HEDGE FUNDS

T O T A L A S S E T S ($ B I L L I O N )

1994Q 1995Q 1996Q 1997Q 1998Q 1999Q 2000Q 2001Q 2002Q 2003Q 2004Q 2005Q 2006Q Fig.3.Dollar value of proceeds,number of issues,and hedge fund size.The charts show the total dollar value of proceeds from convertible bonds,the number of convertible bond issues,and the total assets of convertible bond arbitrage hedge funds from 1993Q3to 2006Q2.

Convertible bonds often have call provisions;however,beginning

with Ingersoll (1977)the empirical evidence has suggested that ?rms call too late.Further,callability should minimally impact our study over

changes in liquidity and ef?ciency from the pre-issue period to the post-issue period.The ‘‘post-issue’’period is de?ned as the six months (120trading days)beginning one month (20trading days)following the bond issue.The ‘‘pre-issue’’period is de?ned as the six months (120trading days)ending one month (20trading days)prior to the announcement of the bond.We skip the two months immediately surrounding announcement and issuance in calculating pre-and post-issue liquidity and stock price measures.19We do this to avoid the direct impact of traders establishing valuation and/or initial arbitrage positions.A timeline de?ning these windows of interest is given in Fig.4.

As Fig.4shows,the initial delta hedge associated with buying the bond and shorting the stock is imple-mented at issuance.After the issue,arbitrage activity associated with dynamic delta-hedging occurs.Note that valuation shorting is expected to occur near the an-nouncement (not the issuance)of the bond.Note also that the liquidity changes are expected to occur over an extended time period via the dynamic arbitrage activity following issuance.Because this hedging activity is unobservable,we capture the initial positions taken by the arbitragers (at t ?0)to proxy for their presence in the post-issue market for the stock.We relate this measure to post-issue liquidity changes.

5.Convertible bond arbitrage,liquidity,and stock prices In this section,we examine links between changes in short interest near issuance and equity market character-istics.

5.1.Summary of ?rm characteristics,by D SI portfolio Table 2provides summary statistics of all of the sample ?rms prior to issuance.20The column ‘‘All’’describes the full sample of issuers.We also divide the sample into four portfolios based on the change in short interest at issue (the D SI measure)in order to provide some insight into the types of issuers for which the convertible bond arbitrage strategy is most evident.Portfolio 1(4)corre-sponds to the smallest (largest)short-interest change.There are several relevant observations from Panel A of the table.First,Nasdaq stocks see the largest D SI following issuance.Second,small issuers and private issues experi-ence higher D SI in their underlying stocks.Third,convertible bond arbitrage activity is higher in stocks that have a high pre-issue short interest,indicating that arbitrageurs choose issues where they believe they will have the ability to short the stock.Finally,as would be expected if convertible bond arbitrageurs are shorting shares to manage equity risk,the amount of short selling at issuance is positively and signi?cantly related to the conversion ratio (number of shares into which the bond can be converted).

Panel B of Table 2reports stock market liquidity measures.The number of trades,dollar volume,the Amihud (2002)illiquidity measure,order imbalance,spread,and spread-to-depth measures all indicate that

Convertible bond arbitrage: initial hedge (buy bond

Convertible bond arbitrageurs:adjust short positions

Months

X-6

X +1

X-1

0I A n n o u n c Post-issue period

Pre-issue period Fig.4.Time intervals for short interest,liquidity,and stock price variables.This ?gure illustrates the time horizons over which changes in short interest,liquidity,and stock price-ef?ciency variables are measured.The ‘‘post-issue period’’is the six-month (120trading days)period beginning one month (20trading days)after the bond issue (Day 0).The ‘‘pre-issue period’’is the six-month (120trading days)period ending one month (20trading days)prior to the announcement of the convertible bond issue (Day X).

(footnote continued )

the six-month horizon because callable bonds often have call protection periods,generally greater than six months.See,e.g.,Asquith (1995).

The bond announcement dates are hand-collected.Of 846issues,

the newswires suggest that 28are issued before announcement (23of these are private issues).For these observations,the pre-and post-periods are de?ned as:120trading days ending one month prior to issuance and beginning one month following announcement,respec-tively.Our results are not affected if we instead drop these 28issues from the sample.

All measures are calculated using daily or monthly data from the

six months (two months for Intraday AR (1))ending one month prior to announcement of the bond issue.

stocks in the smallest D SI portfolio are more liquid. However,as noted above,?rms in the high D SI portfolio tend to be smaller,making the direct comparison of the level of liquidity measures inappropriate.We therefore focus on changes in liquidity in the main analysis,and control for pre-issue liquidity level and change in?rm size in the regressions.

Panel C of Table2presents descriptive statistics on a variety of return and price-ef?ciency measures.We observe higher convertible bond arbitrage activity in stocks with higher average returns and standard deviation of returns,as well as higher betas,higher idiosyncratic volatility,and lower R-squared parameters(estimated from a market model regression).We also calculate

Table2

Issuing?rm characteristics,D SI portfolio sorts.

This table presents?rm characteristics prior to issuance.Portfolios are based on issue period change in short interesteD SIT,the proxy for convertible bond arbitrage activity.D SI is the change in short interest(from the month prior to issuance)divided by the number of shares outstanding in the month prior to issuance.

In Panel A,NYSE and Nasdaq are dummy variables,indicating where the issuing?rm is listed.Public is one if the convertible bond is a public offering, zero if private.Market cap is the equity market capitalization.Short interest/shares outstanding is the average monthly short interest divided by shares outstanding prior to issuance.Institutional holdings/shares outstanding is the institutional holdings(by13f institutions)divided by shares outstanding at calendar year end prior to issuance.Conversion ratio is the number of shares of common stock that could be obtained by converting one bond.Conversion premium is the amount(in percent)by which the conversion price exceeds the market value of the common stock at issuance.

In Panel B,Turnover is the average daily volume divided by shares outstanding.Number of trades is the average daily number of stock transactions on the ?rm’s primary exchange.Dollar volume is the average daily dollar stock volume.Amihud is the average ratio of daily absolute return to dollar volume (Amihud,2002).OIBNUM is the average daily absolute difference between the numbers of buyer-and seller-initiated trades divided by their sum.Dollar spread and Percentage spread are the difference between bid and ask quotes(time-weighted),expressed as dollars and percentage of bid–ask midpoint, respectively.Total depth/shares outstanding is the sum of bid and ask quoted depths divided by shares outstanding.Dollar spread/dollar depth is the ratio of quoted spread to quoted depth,both expressed in dollars.

In Panel C,Return and Standard deviation of return are the mean and standard deviation of daily stock return,respectively.Idiosyncratic volatility and R-squared are,respectively,the standard deviation of residuals and R-squared from the regression of daily stock excess return on CRSP value-weighted market excess return.Beta is the coef?cient estimate of the same regression.Daily AR(1)and Intraday AR(1)are the?rst-order autocorrelation of returns, calculated using daily returns and30-minute interval returns,respectively.Variance ratio(5)is the?ve-day variance ratio in Lo and MacKinlay(1988). All measures in Panels B and C are calculated using daily or monthly data from the six months(two months for Intraday AR(1))ending one month prior to announcement.The last two columns show the mean measures of Portfolio4minus Portfolio1and the corresponding industry-and time-clustered t-statistics.*,**,and***denote10%,5%,and1%signi?cance,respectively.The sample period is from July1993to May2006.

Number of observations?846.

Portfolios based on D SI

All P1P2P3P4P4àP1t-stat

(Smallest)(Largest)

Panel A:Firm and convertible bond characteristics

NYSE0.5050.6260.5520.4740.349à0.277***(à5.59) Nasdaq0.4950.3600.4480.5260.6460.286***(5.79) Public0.2520.2800.2780.2650.184à0.096**(à2.29) log Market cap21.07621.72021.40220.77920.404à1.316***(à9.54) Short interest/shares outstanding(%) 4.466 4.476 3.851 4.311 5.1850.709***(13.95) Institutional holdings/shares outstanding(%)65.00265.17165.76863.86065.2050.034(1.52) Conversion ratio43.91837.21633.68150.34854.42617.211***(2.80) Conversion premium(%)35.06234.62436.19037.04332.400à2.223(à0.61)

Panel B:Liquidity measures

log Turnoverà4.949à5.103à4.955à4.941à4.7990.304***(3.47) log Number of trades 5.987 6.220 6.135 5.849 5.744à0.476***(à3.28) log Dollar volume16.12516.61516.44615.83615.603à1.013***(à5.95) log Amihudà20.585à21.240à20.903à20.267à19.929 1.311***(9.27) OIBNUM(%)16.78915.90916.30217.20117.741 1.832**(2.37) Dollar spread0.1250.1140.1220.1240.1390.026*(1.88) Percentage spread(%)0.5380.4400.4330.6180.6620.222***(3.44) Total depth/shares outstanding(%)?10008.3667.185 6.8598.90410.512 3.327**(2.19) Dollar spread/dollar depth(%)?100050.39538.83240.91853.70868.60529.773***(4.70)

Panel C:Return and price-ef?ciency measures

Return(%)0.2380.1660.2690.2560.2610.094***(2.61) Standard deviation of return(%) 3.572 3.053 3.333 3.726 4.175 1.122***(6.27) Idiosyncratic volatility(%) 3.210 2.699 2.997 3.344 3.799 1.100***(6.81) R-squared(%)18.48221.65517.60318.53516.149à5.505***(à3.84) Beta 1.334 1.257 1.317 1.366 1.3960.139*(1.88) Daily AR(1)(%)à0.965à2.324à1.1450.174à0.567 1.757(1.56) Intraday AR(1)(%)0.048à0.528à0.1530.3360.536 1.063(1.26) Variance ratio(5) 1.035 1.022 1.014 1.060 1.0450.023(0.99)

autocorrelation of returns and variance ratios(see Lo and MacKinlay,1988),which we use as measures of the degree of price ef?ciency.Daily and intraday AR(1)parameters are calculated using daily returns and30-minute interval returns,respectively.From the table we do not observe a signi?cant relationship between changes in short interest and these ef?ciency measures.This suggests that stock price ef?ciency is not an important factor in convertible bond arbitrage(as would be expected,if equity positions are taken primarily to hedge equity risk).

5.2.Impact of convertible bond arbitrage on liquidity and prices

5.2.1.Average changes,by D SI portfolio

In Table3a,we present the changes in?rm character-istics,sorted by portfolios based on change in short interest at issuanceeD SIT.The column‘‘All’’includes data for the full sample of issuers and is presented for comparability to previous studies of changes in liquidity and stock return volatility following the introduction of derivatives markets.As in Table2,the portfolio sort groups issuers into Portfolios1through4,which corre-spond to the smallest through largest issue-month short-interest changes.All changes in liquidity and stock price variables are de?ned as the post-issue period mean minus the pre-issue period mean.Along with changes in short interest,we measure changes in the following liquidity proxies:share turnover,number of trades,dollar volume, the illiquidity measure developed by Amihud(2002), order imbalance(absolute difference between buyer-and seller-initiated trades),and time-weighted average quotes.21The Amihud(2002)measure is a proxy for Kyle’s(1985)l and is de?ned as absolute return divided by dollar volume.

We?nd strong evidence of an increase in liquidity based on all measures following issuance,with the exception of quoted depth(which indicates a decrease in liquidity).22Consistent with the predictioneP1T,these improvements increase systematically with the proxy for arbitrage activity,D SI.For example,the change in(log) turnover for the largest D SI portfolio is0.31higher than that for the smallest D SI portfolio.Importantly,because we link liquidity changes to D SI,we provide direct evidence of the impact of arbitrageurs on liquidity.Prior literature on the impact of derivatives markets on stock markets shows only average changes in these variables (see, e.g.,Mayhew,2000,for a survey)and does not examine systematic relationships with arbitrage activity.

For stock prices and ef?ciency,we examine the following measures:average daily returns,standard deviation of daily returns,idiosyncratic volatility, R-squared,beta,AR(1)parameters,and variance ratios. In regression analysis,we rely on the latter two variables to capture changes in ef?ciency.If arbitrageurs impact stock price ef?ciency,then we would expect decreases in return predictability,as captured by the AR(1)parameters. Further,the variance ratio(Lo and MacKinlay,1988) captures the extent to which stock prices follow a random walk.The standard deviation of returns is included in Table3a so that we can compare the results with the empirical regularity of decreases in volatility following the introduction of options markets.Beta and R-squared are motivated by Bris et al.(2007).

The portfolio sorts presented in Panel B of Table3a suggest that the impact of convertible bond arbitrage on stock price ef?ciency is very weak.Consistent with prior work,we do?nd an average decrease in both total return volatility and the idiosyncratic component of volatility following convertible bond issuance.However,we do not ?nd evidence that these average declines vary system-atically with short selling activity.That is,there is no evidence that arbitrage is what is driving the declines. Average returns decrease after issuance and these decreases are higher for the highest D SI portfolios,consistent with the observation that returns decrease following announcement of convertible bond issues.Beta and R-squared both increase.We do not observe signi?cant changes in the AR(1)parameters or variance ratios.Across D SI portfolios, the only systematic variation that we observe is in returns and beta.Taken together,the results in Panel B of Table3a do not indicate an impact of convertible bond arbitrage on stock price ef?ciency.Regression analysis(below)will further investigate these?ndings.

5.2.2.Control sample

It is possible that the liquidity results in Table3a are being driven by market-wide changes in liquidity,rather than convertible bond arbitrage activity.To examine this potentially important issue,we attempt to isolate changes due to the convertible bond event by analyzing the measures in Table3a for a set of control?rms.In Table 3b,we examine the possibility that the results are driven by the market-wide trends in general,rather than convertible bond arbitrage.To do this,we match?rms in the sample based on industry,exchange,size,market-to-book,and turnover before issuance.To identify the control?rms,we begin with all?rms in the CRSP/ Compustat database.From this initial sample the se-quence of identifying control?rms proceeds as follows: First,?rms that have issued any convertible debt during yearsà1tot1relative to issue are eliminated from the universe of potential control?rms.

Second,control?rms must trade on the same exchange as issuing?rms(e.g.,NYSE issuers are matched only to NYSE?rms).This is done to eliminate potential problems associated with exchange-related trends in liquidity and stock price movements.

Third,control?rms must be in the issuing?rm’s industry,based on Fama and French(1997)industry code.23

21We also examine opening quotes.Results are qualitatively similar.

22However,regression analysis(Table4)shows that quoted depth increases with arbitrage activity,after we control for other variables.

23After?ltering,the mean(median)number of valid control?rms for each issuing?rm is166(101)and there are at least two potential control?rms for each issuer.

D.Choi et al./Journal of Financial Economics91(2009)227–251237

Table3

(a)Changes in?rm characteristics.

This table presents the changes(from pre-to post-issue)in?rm characteristics,by portfolios based on issue period change in short interesteD SIT,the proxy for convertible bond arbitrage activity.D SI is the change in short interest(from the month prior to issuance)divided by the number of shares outstanding in the month prior to issuance.Changes in?rm characteristicseDTare de?ned as the average measure in post-issue period minus the pre-issue period average measure.The‘‘pre-issue period’’is de?ned as the six months(two months for Intraday AR(1))ending one month prior to announcement.The‘‘post-issue period’’is the six months(two months for Intraday AR(1))starting one month after issuance.

In Panel A,Short interest/shares outstanding is the average monthly short-interest level divided by shares outstanding.Turnover is the average daily volume divided by shares outstanding.Number of trades is the average daily number of stock transactions on the?rm’s primary exchange.Dollar volume is the average daily dollar stock volume.Amihud is the average ratio of daily absolute return to dollar volume(Amihud,2002).OIBNUM is the average daily absolute difference between the numbers of buyer-and seller-initiated trades divided by their sum.Dollar spread and Percentage spread are the difference between bid and ask quotes(time-weighted),expressed as dollars and percentage of bid–ask midpoint,respectively.Total depth/shares outstanding is the sum of bid and ask quoted depths divided by shares outstanding.Dollar spread/dollar depth is the ratio of quoted spread to quoted depth,both expressed in dollars.

In Panel B,Return and Standard deviation of return are the mean and standard deviation of daily stock return,respectively.Idiosyncratic volatility and R-squared are,respectively,the standard deviation of residuals and R-squared from the regression of daily stock excess return on CRSP value-weighted market excess return.Beta is the coef?cient estimate of the same regression.j Daily ARe1Tj and j Intraday ARe1Tj are the absolute value of?rst-order autocorrelation of returns,calculated using daily returns and30-minute interval returns,respectively.j Variance ratioe5Tà1j is the absolute deviation of the?ve-day variance ratio in Lo and MacKinlay(1988)from one.

The last column shows the mean measures of Portfolio4minus Portfolio1.Industry-and time-clustered t-statistics of the changes and differences are in parentheses.*,**,and***denote10%,5%,and1%signi?cance,respectively.The sample period is from July1993to May2006.

Number of observations?846.

Portfolios based on D SI

All P1P2P3P4P4àP1

(Smallest)(Largest)

Panel A:Changes in liquidity measures

D Short interest/shares outstanding(%) 2.371***0.181 1.233*** 2.598*** 5.465*** 5.284***

(17.90)(1.02)(8.44)(11.55)(19.27)(15.81)

D log Turnover0.239***0.079***0.217***0.272***0.387***0.308***

(15.06)(3.25)(7.27)(9.41)(11.29)(7.35)

D log Number of trades0.325***0.195***0.343***0.336***0.426***0.231***

(15.74)(6.52)(9.07)(9.67)(10.57)(4.60)

D log Dollar volume0.441***0.241***0.436***0.510***0.574***0.333***

(15.88)(6.75)(9.37)(10.77)(9.13)(4.60)

D log Amihudà0.458***à0.330***à0.475***à0.510***à0.519***à0.188**

(à17.02)(à8.55)(à11.52)(à11.20)(à8.05)(à2.51)

D OIBNUM(%)à1.041***à0.893***à0.924***à0.961***à1.385***à0.492

(à7.07)(à3.72)(à3.26)(à3.57)(à4.58)(à1.27)

D Dollar spreadà0.021***à0.022***à0.017***à0.019***à0.027***à0.006

(à7.40)(à4.30)(à3.21)(à4.42)(à4.70)(à0.77)

D Percentage spread(%)à0.134***à0.081***à0.105***à0.188***à0.160***à0.079***

(à11.48)(à5.36)(à9.36)(à5.52)(à6.57)(à2.77)

D Total depth/shares outstanding(%)?1000à0.712**à0.287à0.192à1.903à0.467à0.180

(à1.97)(à0.95)(à0.35)(à1.58)(à0.96)(à0.31)

D Dollar spread/dollar depth(%)?1000à13.970***à9.260***à11.230***à14.900***à20.470***à11.210***

(à14.06)(à5.21)(à6.18)(à7.46)(à9.61)(à4.04) Panel B:Changes in return and price-ef?ciency measures

D Return(%)à0.201***à0.128***à0.230***à0.214***à0.232***à0.105**

(à11.70)(à4.26)(à7.76)(à6.83)(à5.91)(à2.12)

D Standard deviation of return(%)à0.250***à0.341***à0.183*à0.356***à0.1230.219

(à4.20)(à3.98)(à1.94)(à3.49)(à0.96)(1.42)

D Idiosyncratic volatility(%)à0.275***à0.339***à0.209**à0.358***à0.193*0.146

(à5.37)(à4.26)(à2.55)(à3.88)(à1.66)(1.04)

D R-squared(%) 2.309*** 1.678* 1.790** 2.152** 3.612*** 1.934

(4.48)(1.88)(2.10)(2.24)(3.66)(1.45)

D Beta0.083***0.0460.0250.080*0.180***0.135**

(3.06)(1.21)(0.47)(1.67)(3.41)(2.07)

D j DailyARe1Tje%Tà0.2950.077à0.419à0.431à0.406à0.483

(à0.87)(0.11)(à0.58)(à0.66)(à0.61)(à0.50)

D j IntradayARe1Tje%T 2.5219.9730.856à0.276à0.447à10.420

(1.34)(1.34)(1.23)(à0.67)(à0.77)(à1.40)

D j Variance ratioe5Tà1je%Tà1.102à0.584à0.911à2.490à0.4280.156

(à1.43)(à0.41)(à0.60)(à1.47)(à0.28)(0.07)

(b)Control ?rm results:changes in ?rm characteristics.

This table shows the changes (from pre-to post-issue)in issuing ?rm characteristics minus the changes in control ?rm characteristics.Portfolios are based on issue period change in short interest eD SI T,the proxy for convertible bond arbitrage activity.D SI is the change in short interest (from the month prior to issuance)divided by the number of shares outstanding in the month prior to issuance.Control ?rms are matched based on size,book-to-market,and turnover before issuance,exchange,and industry.Changes in ?rm characteristics eD Tare de?ned as the average measure in post-issue period minus the pre-issue period average measure.The ‘‘pre-issue period’’is de?ned as the six months (two months for Intraday AR (1))ending one month prior to announcement.The ‘‘post-issue period’’is the six months (two months for Intraday AR (1))starting one month after issuance.

In Panel A,Short interest/shares outstanding is the average monthly short interest of the stock divided by shares outstanding.Turnover is the average daily volume divided by shares outstanding.Number of trades is the average daily number of stock transactions on the ?rm’s primary exchange.Dollar volume is the average daily dollar stock volume.Amihud is the average ratio of daily absolute return to dollar volume (Amihud,2002).OIBNUM is the average daily absolute difference between the numbers of buyer-and seller-initiated trades divided by their sum.Dollar spread and Percentage spread are the difference between bid and ask quotes (time-weighted),expressed as dollars and percentage of bid–ask midpoint,respectively.Total depth/shares outstanding is the sum of bid and ask quoted depths divided by shares outstanding.Dollar spread/dollar depth is the ratio of quoted spread to quoted depth,both expressed in dollars.

In Panel B,Return and Standard deviation of return are the mean and standard deviation of daily stock return,respectively.Idiosyncratic volatility and R-squared are,respectively,the standard deviation of residuals and R -squared from the regression of daily stock excess return on CRSP value-weighted market excess return.Beta is the coef?cient estimate of the same regression.j Daily AR e1Tj and j Intraday AR e1Tj are the absolute value of ?rst-order autocorrelation of returns,calculated using daily returns and 30-minute interval returns,respectively.j Variance ratio e5Tà1j is the absolute deviation of the ?ve-day variance ratio in Lo and MacKinlay (1988)from one.

The last column shows the mean measures of Portfolio 4minus Portfolio 1.Industry-and time-clustered t -statistics of the differences are in parentheses.*,**,and ***denote 10%,5%,and 1%signi?cance,respectively.The sample period is from July 1993to May 2006.Number of observations ?846.

Portfolios based on D SI

All

P 1P 2

P 3

P 4P 4àP 1

(Smallest)

(Largest)

Panel A:Liquidity measures (changes in issuing ?rm minus changes in control ?rm)

D Short interest/shares outstanding (%)

2.462***0.2520.875***

3.003*** 5.726*** 5.473***(12.29)(1.22)(3.17)(5.80)(16.21)(13.38)D log Turnover

0.209***0.0480.184***0.223***0.379***0.331***(10.09)(1.40)(4.44)(5.39)(8.84)(6.04)D log Number of trades

0.162***0.0410.185***0.134***0.289***0.248***(7.66)(1.13)(4.36)(3.13)(6.41)(4.30)D log Dollar volume

0.321***0.0760.319***0.356***0.531***0.455***(10.34)(1.53)(5.61)(5.46)(7.57)(5.29)D log Amihud

à0.334***à0.123**à0.317***à0.351***à0.545***à0.422***(à11.45)(à2.46)(à6.13)(à5.74)(à8.12)(à5.04)D OIBNUM (%)

à0.370*0.233à0.643à0.370à0.696*à0.929(à1.71)(0.58)(à1.48)(à0.85)(à1.65)(à1.60)D Dollar spread

0.0010.0010.0010.005à0.003à0.004(0.26)(0.18)(0.17)(0.72)(à0.47)(à0.47)D Percentage spread (%)

à0.045**0.031à0.063*à0.069à0.077*à0.107**(à2.42)(1.32)(à1.81)(à1.62)(à1.82)(à2.23)D Total depth/shares outstanding (%)?1000

0.569 1.482à0.942à0.145 1.8800.398(0.48)(0.78)(à0.26)(à0.09)(1.05)(0.15)D Dollar spread/dollar depth (%)?1000

à2.539 6.465*à1.6680.931à15.826***à22.291***(à1.30)(1.69)

(à0.62)(0.19)(à3.96)(à4.04)

Panel B:Return and price-ef?ciency measures (changes in issuing ?rm minus changes in control ?rm)

D Return (%)

à0.102***à0.032à0.067à0.152***

à0.155***à0.124**(à4.65)(à0.93)(à1.30)(à4.17)(à3.41)(à2.17)D Standard deviation of return (%)

à0.130*à0.0790.032à0.358***à0.118à0.039(à1.77)(à0.90)(0.19)(à3.48)(à0.64)(à0.19)D Idiosyncratic volatility (%)

à0.142*à0.0850.012à0.354***à0.142à0.057(à1.94)(à0.94)(0.07)(à3.23)(à0.76)(à0.28)D R -squared (%)

0.7570.1650.588 1.014 1.259 1.094(1.42)(0.16)(0.61)(1.00)(1.09)(0.71)D Beta

0.002à0.0430.006à0.0580.1040.147*(0.07)(à1.03)(0.09)(à1.10)(1.60)(1.90)D j Daily AR(1)j (%)

à0.020 1.108à0.671à0.418à0.097à1.206(à0.04)(1.16)(à0.66)(à0.46)(à0.09)(à0.86)D j Intraday AR(1)j (%)

4.152 2.691 6.6518.521à1.240à3.930(1.40)(0.32)(1.22)(1.35)(à1.52)(à0.46)D j Variance ratio (5)à1j (%)

0.026 1.652à0.302à1.5060.259à1.392(0.02)(0.89)(à0.15)

(à0.63)(0.11)(à0.45)

Table 3(continued )

D.Choi et al./Journal of Financial Economics 91(2009)227–251

238

Finally,for the remaining sample of potential control ?rms,we assign a score based on turnover,market capitalization,and book-to-market during year tà1, where t is the issue year.For each potential control ?rm we calculate a

score?abs

turnover tà1

tà1à1

tabs

market cap tà1

issuer market cap tà1

à1

tabs

book-to-market tà1

tà1à1

The?rm with the lowest score(i.e.,average distance along these three dimensions from the issuing?rm)is chosen as the control?rm.24

Results from the control sample are reported in Table 3b.All results in Table3b are presented as differences between the issuers and control?rms.From the table,it is clear that the liquidity results are robust to measuring the changes relative to control?rms.For stock price-ef?ciency measures we do not observe signi?cant differences between the issuing?rms and control?rms,suggesting little or no role in stock price ef?ciency for convertible bond arbitrageurs.If convertible bond arbitrageurs take positions mainly to exploit mispricing in the bond (and not the stock),then this would be expected.Because it is important to control for market-wide effects,the change variables in the analysis henceforth are presented as deviations from control?rms.

5.2.3.Regression analysis

We use an event study methodology to further characterize the relationships among convertible bond arbitrage,liquidity,and stock prices.These tests are more restrictive than the tests based on portfolio sorts in Tables 3a and b;however,we would like to explicitly control for factors other than D SI,issue period change in short-interest intensity.We use regression analysis to estimate the impact of convertible bond arbitrage and other stock characteristics of issuing?rm i on changes in liquidity and price-ef?ciency measures.

D Liquidity i or D Efficiency i

?atb1D SI itb2D Market Cap itb3D Volatility i

tb4D Institutional Holdings itb5Pre-Issue Price i

tb6NYSE itb7Public itb8D PrePost i

2006Apr

t?1993Jul

YearMonthDum i;tt i.(1)

Explanatory variables are de?ned below.All change variables are calculated as deviations from control?rms.

D SI is change in short interest(number of shares)

divided by total shares outstanding.The change in

short interest is the difference between short interest in the issue month and short interest in the previous month.This measure is a proxy for arbitrage activity.

D Market Cap is the change in(log)market capitaliza-

tion,de?ned as(log)average daily shares outstanding times closing stock price.The change in market capitalization is calculated as post-period market capitalization minus pre-period capitalization.

D Volatility(used in liquidity regressions only)is the

change in the standard deviation of daily returns.

D Institutional Holdings is the change in institutional

holdings(shares held by13f institutions)divided by total shares outstanding.The change is calculated as the holdings at the issuing calendar year end minus the holdings at the prior calendar year end.

Pre-Issue Price is the average(log)price during the pre-issue period.

NYSE is a dummy variable,equal to one if the?rm is listed on NYSE and zero otherwise.

Public is a dummy variable,equal to one if the convertible bond is a public offering,and zero other-wise.

D PrePost is the number of days between the pre-and

the post-issue period.25

YearMonthDum t are year and month?xed effects, indicating timing of the convertible bond issue.

The estimated coef?cient on D SI is of primary interest. We expect to observe a positive role for D SI in liquidity changes(Prediction P1)and no impact of D SI on changes in price ef?ciency(Prediction P2).Control variables include changes in size,stock return volatility,and institutional holdings(a proxy for the supply of shares to short sellers).We also control for changes in volatility in the liquidity regressions due to relationships found in the literature.For example,Pastor and Stambaugh(2003)?nd correlation of0.57between market illiquidity and volatility.Spiegel and Wang(2005)report high correlation between idiosyncratic volatility and liquidity(i.e.,liquid-ity produces perfect volatility sorts for a cross-section of stocks).We anticipate more room for marginal liquidity improvements in less-liquid stocks,so pre-issue price is included as a proxy for liquidity level(price and liquidity are negatively correlated;higher-priced stocks have lower spreads due to the?xed component).We also allow for variation based on exchange and whether an issue is public or private(e.g.,liquidity of the bond issue might be higher for public issues),and we also include time effects.

The main results are presented in Table4.All standard errors are heteroskedasticity-consistent and include in-dustry clustering based on Fama and French(1997) industry de?nitions.The proxy for convertible bond arbitrage activityeD SITis signi?cantly and positively related to liquidity improvements based on?ve of the seven liquidity measures:number of trades,turnover,

24The inputs to the score measure for a year t issue are calculated as follows:turnover tà1is the average monthly turnover in year tà1; marketcap tà1and book-to-market tà1are year-end values.The mean (median)score of the846control?rms is0.241(0.198).

25In order to separate the potential impact of the announcement on liquidity and ef?ciency variables,we skip the20trading days prior to the announcement of the issue through20trading days following the issue date.

D.Choi et al./Journal of Financial Economics91(2009)227–251239

Amihud,depth,and spread=depth.We do not observe systematic variation of D SI with either order imbalance or spread.The spread result is somewhat puzzling because this measure showed signi?cant changes based on portfolio sorts;however,change in market capitalization already captures a price change,and therefore the coef?cient on percentage spread(change in spread divided by price)in the regression equation may pick up changes in dollar spread,rather than percentage spread. Importantly,the spread=depth measure,a more complete measure of the quality of the quote than spread or depth alone,suggests a signi?cant relationship between con-vertible bond arbitrage activity and liquidity improve-ments.Although it is not the main focus of the analysis,it is also interesting to note that liquidity increases with increases in institutional holdings,market capitalization, and volatility.Neither of the price-ef?ciency measures are related to D SI.We interpret this as evidence that these traders do not enhance ef?ciency and simply provide supply to equity markets,as in the predictioneP2T.26In the next section,we provide another returns-based ef?ciency test.

An assumption underlying much of the analysis in this paper is that the change in short interest near issuance is due to convertible bond arbitrage activity,which we do not directly observe.It is possible that the observed short selling near issuance is being driven by valuation shorting. We attempt to separate other possible explanations of the observed short selling by conducting several tests of whether the data are consistent with convertible bond arbitrage.First,we examine long-run stock returns following issuance.If the increase in short interest is due to valuation shorting,we would expect short sellers to make money from their positions.We then conduct a second test using hand-collected announcement dates for the sample of issuers to isolate the impact of convertible bond announcement-versus issue-period shorting,which we interpret as valuation shorting and convertible bond arbitrage,respectively.The basic intuition is that valua-tion short sellers will be able to trade at the announce-ment of the bond,whereas convertible bond arbitrageurs will not short until the actual issue of the bond.This is done in order to avoid stock exposure that would result if convertible bond arbitrageurs took short equity positions prior to issuance.The results of these tests are consistent with short selling due to convertible bond arbitrage and are presented below.

5.3.Long-run returns

As a?nal ef?ciency check,we test whether short sellers make money from their equity market positions. The primary goal is to shed further light on the possibilities noted in Section3,that issue-period short sellers are either:(1)privately informed about the value of the underlying equity or(2)that they exploit known price inef?ciencies such as return autocorrelation.Evidence of negative long-run returns following issuance would be consistent with these possibilities.A?nding of no abnormal returns following issuance would be consistent with prediction P2,that convertible bond arbitrageurs do not play a role in stock price ef?ciency.

Results are presented in Table5and are consistent with the?ndings for the other ef?ciency measures:there is no evidence that issue-period short sellers make money from their positions;however,we do observe a signi?-cantly negative return ofà1:30%per day between announcement and issue date(when they are at least two trading days apart).Therefore,it may be that valuation shorts make money based on positions taken at the announcement of the issue(Day X in Fig.4),while short sellers engaged in convertible bond arbitrage strategies take positions near issuance(Day0in Fig.4) and do not earn abnormal returns from equity positions. Importantly,this also implies that there is no evidence that valuation shorts will have incentive to maintain their short positions following issuance and are unlikely to impact post-issuance liquidity changes that we observe in the main analysis.This is because abnormal returns from the short positions occur only between announcement and issuance.

Table5also suggests that there may be important differences between short selling observed on announce-ment versus issue dates.These differences might provide powerful identi?cation for the type of short selling(i.e., convertible bond arbitrage versus other types of arbitrage) that we are observing in the data.In the next section,we delve deeper into this question by using the data on announcement dates.This allows us to separate the impact of short selling due to the market’s knowledge that the bond is being issued from actual convertible bond arbitrage(which would be more likely to coincide with the issue itself).

5.4.Robustness analysis:convertible bond arbitrage versus valuation shorts

Because we do not observe convertible bond arbitrage activity directly,we face the challenge that we may be picking up the impact of short selling on liquidity and ef?ciency due to some other factor.A particular concern is valuation short selling due to news that the?rm is raising convertible debt.In order to address this issue,we hand-collect announcement dates of all convertible bond issues

26In addition to the control?rms identi?ed according to the

procedure outlined in Section 5.2.2,we conduct robustness checks

based on two‘‘issue matches.’’We match convertible bond issuers to a

sample of straight-debt issuers(matched by exchange,industry,size,

book-to-market,and issue size).The basic aim is to distinguish the effect

of convertible bond issuance from a general increase in leverage.Results

are similar to those in Table4:we?nd that D SI is positively and

signi?cantly related to increases in turnover and number of trades;and

D SI is negatively and signi?cantly related to both spread and Amihud

(2002)illiquidity measure.In our second‘‘issue match,’’we match

convertible bond issuers to?rms issuing seasoned equity because

purchasers of the equity issue would not need to manage a short

inventory,as is the case for convertible bond arbitrage.Results are

similar to those in the straight-debt analysis.In general,we?nd that the

impact of D SI is somewhat stronger in these robustness checks than in

the main analysis.Detailed results and the matching procedure are

available upon request.We thank William Fung for encouraging the

equity issuer robustness check.

D.Choi et al./Journal of Financial Economics91(2009)227–251241

in the sample.27We identify 132issues for which the announcement date and the issue date are such that the observed change in short interest for announcement and issuance occur during different short-interest reporting months.This allows us to clearly separate valuation shorting from convertible bond arbitrage.Table 6presents the results of analysis for this subsample.The ?ndings are consistent with the main regressions in Table 4.With the exception of depth and spread-to-depth,all liquidity changes that are signi?cantly related to the proxy for convertible bond arbitrage in the main analysis are also signi?cant in this subsample analysis.Most important,changes in short interest during the announcement month eD SI _Announcement Tare not signi?cantly related to any observed liquidity and ef?ciency changes.

5.5.Robustness analysis:potential endogeneity of arbitrage

It is possible that convertible bond arbitrageurs are

attracted to stocks for which they expect increases in liquidity.While our prior is that the direction of the causality runs from the arbitrageurs,we explicitly account for potential simultaneity by estimating a simultaneous

equations model of both changes in market quality and short-interest changes.We estimate the following system:D Liquidity i

?a tb 1D SI IV i tb 2D Market Cap i tb 3D Volatility i

tb 4D Institutional Holdings i tb 5Pre-Issue Price i tb 6NYSE i tb 7Public i tb 8D PrePost i t

X 2006Apr t ?1993Jul

b 9t YearMonthDum i ;t t i

(2)

and

D SI i ?a tb 1D Liquidity IV i tb 2Dollar Volume i tb 3Volatility i

tb 4Institutional Holdings i tb 5Dividends i tb 6Conversion Premium i

tb 7NYSE i tb 8Public i tb 9D PrePost i

X 2006Apr t ?1993Jul

b 10t YearMonthDum i ;t t i .

(3)

As in Table 4,all change variables are calculated as deviations from ?rm i ’s control ?rm in order to control for market-wide trends in the variables of interest.The explanatory variables in the liquidity change regressions are identical to those in Table 4,except D SI IV i

is instrumented.Similarly,liquidity change variables are

Table 5

Long-run returns.

This table summarizes post-issuance and post-announcement returns over 6-,12-,18-,and 24-month horizons.In Panels A and B,Cumulative return is the average holding period return from long stock positions starting after market close on the convertible bond issue date and announcement date,respectively.Panel C shows the average daily return of issuers and control ?rms between market close on announcement date and the trading day prior to issue date,for issues that are announced at least two trading days prior to issuance.Control ?rms are matched based on size,book-to-market,and turnover before issuance,exchange,and industry.Industry-and time-clustered t -statistics of the differences in returns are in parentheses.***denotes 1%signi?cance.The sample period is from July 1993to May 2006.Number of observations ?846.Cumulative return (not annualized)Issue date

t6months

t12months

t18months

t24months

Panel A:Long-run returns after issuance Issuing ?rm 6.57%9.22%12.24%16.53%Control ?rm 5.47%8.85%13.68%17.66%Difference 1.10%0.37%à1.44%à1.13%t -stat

(0.58)(0.13)(à0.41)(à0.31)Cumulative return (not annualized)

Announcement date

t6months

t12months

t18months

t24months

Panel B:Long-run returns after announcement Issuing ?rm 3.94% 6.64%9.73%13.82%Control ?rm 6.26%10.16%14.00%18.31%Difference à2.32%à3.52%à4.27%à4.49%t -stat

(à1.14)(à1.14)(à1.21)(à1.21)

Number of observations ?348.

Panel C:Returns between announcement and issuance

Average daily return between announcement and issue dates Issuing ?rm à1.30%Control ?rm 0.13%Difference à1.43%***t -stat

(à6.80)Average number of trading days

10.21

We use Lexis-Nexis and Factiva news searches to identify the

earliest date on which the bond issue is mentioned in the news.

D.Choi et al./Journal of Financial Economics 91(2009)227–251

242

instrumented in the D SI i regressions.The other explana-tory variables in the D SI i regression are chosen to proxy for characteristics of?rms that tend to be attractive to convertible bond arbitrageurs28:

Dollar Volume is the mean daily dollar volume during the pre-issue period.This variable is included to capture the impact of stock liquidity levels on con-vertible bond arbitrage activity.It is easier to dynami-cally hedge more liquid stocks.

Volatility is the mean standard deviation of daily returns during the pre-issue period.Convertible bond arbitrageurs are expected to prefer higher volatility issuers.This is because there are higher potential trading pro?ts due to the embedded option in the bond.

Institutional Holdings is the level of institutional holdings(shares held by13f institutions)divided by shares outstanding at calendar year end prior to issuance.This variable is a proxy for the availability of shares to borrow.

Dividends are stock dividend yields and are included because convertible bond arbitrageurs are expected to prefer low or no dividend-paying stocks since short sellers have to pay dividends.

Conversion Premium is the amount(in percent)by which the conversion price exceeds the market value of the common stock at issuance.Calamos(2003,p.25) states that arbitrageurs tend to prefer stocks with conversion premia that are less than25%because a low conversion premium implies lower interest rate and credit risk.

NYSE is a dummy variable,equal to one if the?rm is listed on NYSE and zero otherwise.

Public is a dummy variable,equal to one if the convertible bond is a public offering,and zero other-wise.

D PrePost is the number of days between the pre-and

the post-issue period.

YearMonthDum t are year and month?xed effects, indicating timing of the convertible bond issue.

In the?rst-stage regressions for arbitrage activity,we use percentage of shares affected by the issue(conversion ratio?number of bonds=shares outstanding)and analyst opinion prior to issuance(percentage of buy recommen-dations)as instruments,in addition to the explanatory variables speci?ed in the simultaneous equations.These instruments are chosen because convertible bond arbi-trageurs will short more when a high percentage of shares are affected by the issue.Analyst recommendations are included because short sellers can have trading strategies based on these recommendations.In the?rst-stage regressions for D Liquidity i,we include change in analyst coverage and change in absolute price deviation from$30 as instruments(in addition to the other exogenous variables).We expect that there is a high correlation between analyst coverage and liquidity levels,and that a stock price close to$30indicates higher liquidity.29 The results from simultaneous equations for each liquidity measure are presented in Table7.The main ?ndings are qualitatively similar to the main regression (with the exception of depth,for which we do not observe a statistically signi?cant increase after controlling for potential endogeneity).Moreover,the liquidity changes do not impact arbitrage activity,which is proxied by D SI (Panel B of the table).

5.6.Robustness analysis:other potential sources of volume

It is possible that following the issue of a convertible bond,there is a mechanical increase in trading volume due to a potential future increase in shares outstanding (i.e.,investors eventually exercising the conversion op-tion).30In this case,we would expect to observe increases in volume and turnover that are proportional to the fraction of new shares.We may also observe correspond-ing increases in other liquidity measures.We would like to distinguish increases in volume from hedging trades due to convertible bond arbitrage(i.e.,the post-issuance trading activity depicted in Fig.1)and increases in volume due to other sources.31To address the important concern that the results may be driven by other sources of volume, we conduct two sets of robustness tests.

First,we replicate the main analysis(i.e.,Table4 regressions),but add an explicit control for expected increases in volume(unrelated to convertible bond arbitrage activity),which is proportional to the fraction of new shares:

EeD VolumeT?

shares underlying the issue

?pre-issueelogTvolume

:32

The results are presented in Table8and show that expected changes in volume are positively and signi?-cantly related to realized changes for trading activity measures that are linked to volume(turnover,number of trades,and the Amihud,2002,illiquidity measure),as one

28See Calamos(2003,p.25).

29The percentage of shares affected is highly signi?cant(t-statistic

of6.21)in the?rst-stage regression of arbitrage activity.We thank an

anonymous referee for suggesting the importance of the conversion

ratio.Analyst opinion is also signi?cant(t-statistic of1.92)in the?rst-

stage.For?rst-stage liquidity regressions,the analyst coverage variable

is signi?cant for four of seven measures:turnover,number of trades,

order imbalance,and depth.Price deviation from$30is signi?cant in

spread and depth.We use all exogenous variables and instruments in the

?rst-stage regressions.We also con?rm that the instruments for the

liquidity changes are not signi?cant in the D SI regressions and vice versa.

First-stage results are not reported(for brevity)and are available upon

request.

30For example,Stein(1992)shows that convertible bonds can

essentially be a‘‘backdoor’’to equity?nancing.It is also possible that the

introduction of the new security causes overall volume to increase;

however,this would be picked up by the estimated intercepts(as in

Kumar,Sarin,and Shastri,1998),not the coef?cient on D SI,the proxy for

arbitrage activity.

31We thank an anonymous referee for suggesting this distinction.

32Shares underlying the issue is de?ned as the conversion shares

ratio(reported in SDC Platinum)times the number of bonds.

D.Choi et al./Journal of Financial Economics91(2009)227–251

244

might expect.However,these expected mechanical volume changes do not explain non-volume-based liquidity improvements (i.e.,insigni?cant relationships with depth,order imbalance,and spread-to-depth,with the exception of a signi?cant and positive relationship with percentage spread).More importantly for this analysis,the signi?cant relationship between the arbit-rage activity proxy eD SI Tand all liquidity changes reported in the main analysis are largely unaffected by the inclusion of expected changes in volume.33

A bene?t of the measures above is that both the proxy for convertible arbitrage activity and expected changes in volume are calculated at time 0relative to the issue date.This is a clean,well-de?ned window for measuring the presence of convertible bond arbitrageurs.Ideally,we would want to measure the impact of actual convertible bond arbitrage activity,controlling for actual changes in volume.A challenge in this paper’s framework is that changes in actual volume include two components:changes in volume due to convertible bond arbitrage and non-arbitrage related changes (the mechanical changes described above or other sources).One possibi-lity would be to put actual volume changes,measured over months t1through t6,into the regression in which the convertible bond arbitrage activity proxy,D SI ,is calculated at issue month 0.This approach is not appealing since one would expect actual volume changes to have the most power in explaining liquidity changes (simply because the volume change measure is calculated over the same t1through t6interval as the liquidity changes).In this case,it would be very dif?cult to distinguish whether the convertible bond arbitrage or non-arbitrage component of volume drives the change.

To circumvent this potential issue,we return to the intuition that convertible bond arbitrageurs will dyna-mically hedge following issuance:they will short more when stock prices rise and cover their short positions as stock prices fall.This will increase the volatility of short interest relative to the pre-issue period.In the second robustness test,we introduce an alternative proxy for dynamic hedging activity,Dynamic _Hedge ,which is de?ned as the average (log)absolute value of short-interest changes during post-issue period minus the average absolute value of short-interest changes during the pre-issue period.34In Fig.4,these are months t1through t6and X à6and X à1,respectively.The intuition for Dynamic _Hedge is that monthly decreases

A l l c o e f f i c i e n t s a r e ?1000P a n e l

B :D S I

W h e n D L i q u i d i t y

I V

T u r n o v e r t -s t a t T r a d e s t -s t a t A m i h u d t -s t a t O I B N U M t -s t a t

S p r e a d t -s t a t D e p t h t -s t a t S p r /d e p

t -s t a t I n t e r c e p t

11.448*(1.78)12.987*(1.85)11.477*(1.83)13.528*(1.90)13.423*(1.67)15.181*(1.69)7.631(1.02)D L i q u i d i t y I V

9.686

(0.89)5.302

(0.71)à5.270

(à1.47)à17.790

(à0.77)à9.180

(à1.55)à3.730

(à0.99)

à11.740

(à0.64)

P r e -i s s u e d o l l a r v o l u m e à0.710(à0.60)à1.120(à1.01)à1.250(à1.07)à1.210(à1.08)à1.520(à1.15)à1.410(à1.07)à1.360(à1.14)P r e -i s s u e v o l a t i l i t y 199.239*(1.95)175.534**(1.96)142.304***(2.70)188.692*(1.73)146.362**(2.50)162.161**(2.37)134.291***(2.73)P r e -i s s u e i n s t i t u t i o n a l h o l d i n g s 6.785**(2.15)5.471*(1.71)5.937*(1.92)5.227(1.52)5.440*(1.72)5.493(1.60)5.434*(1.70)P r e -i s s u e d i v i d e n d à7.350(à1.34)à7.040(à1.20)à7.640(à1.35)à7.760(à1.11)à7.010(à1.22)à5.870(à1.09)à11.330(à0.99)C o n v e r s i o n p r e m i u m (%)à0.050**(à2.42)à0.050***(à2.57)à0.040*(à1.88)à0.060***(à2.91)à0.050**(à2.29)à0.060***(à3.24)à0.040(à1.15)N Y S E à7.120*(à1.82)à7.400**(à2.04)à7.860**(à2.48)à7.300**(à1.96)à8.180**(à2.56)à8.040***(à2.69)à8.200**(à2.56)P u b l i c à6.510**(à1.96)à7.460**(à2.36)à6.580**(à2.07)à7.950**(à2.21)à6.790**(à2.20)à7.690**(à2.38)à6.430*(à1.85)D P r e p o s t

0.158***(2.95)0.176***(2.97)0.176***(2.98)0.169***(3.23)0.175***(2.92)0.179***(3.06)

0.210**(2.19)

N u m b e r o f o b s e r v a t i o n s

846846846846846846846A d j u s t e d R 2

(%)

5.134.985.514.894.724.063.97

T a b l e 7(c o n t i n u e d )

In addition to expected increase in volume,we replicate the

analysis using expected increase in turnover and dollar volume (since volume can be affected by changes in the number of shares outstanding).We also eliminate observations in which there is a change in the number of shares outstanding during the horizon of interest.All results are qualitatively similar to those shown in Table 8.

In unreported analysis,we also conduct a third test,which

controls for mechanical increases in volume due to the potential increase in shares outstanding.We match convertible bond issuers to a sample of straight equity issuers (matched by exchange,industry,size,book-to-market,and issue size),in which there is a clear increase in the number of shares outstanding.We re-run the analysis,where all variables are measured as deviations from this ‘‘issue-control’’sample.As noted earlier,results are similar to those in the main analysis.

D.Choi et al./Journal of Financial Economics 91(2009)227–251

246