Convertibles and hedge funds as distributors of equity
exposure
Stephen J. Brown, Bruce D. Grundy, Craig M. Lewis and Patrick Verwijmeren*
First draft: 11 November 2009
This draft: 8 October 2010
Abstract
By buying convertibles and shorting stock hedge funds distribute equity exposure to welldiversified shareholders. We find that a higher fraction of a convertible is privatelyplaced with hedge funds when seasoned equity offerings would be expensive. Hedge
fund involvement also increases when institutional ownership, stock liquidity, issue size,
limitations on callability and concurrent stock repurchases suggest that shorting costs will
be lower. Discounts are not higher on convertibles issued to hedge funds, which is in line
with hedge funds serving as relatively low-cost distributors of equity exposure rather than
investors of last resort.
JEL classification: G2, G32
Keywords: Convertible securities, convertible arbitrage, hedge funds
*Stephen Brown (sbrown@stern.nyu.edu) is from New York University Stern School of Business
and a professorial fellow at the University of Melbourne, Bruce Grundy
(bruceg@unimelb.edu.au) is from the University of Melbourne, Craig Lewis
(craig.lewis@owen.vanderbilt.edu) is from Vanderbilt University’s Owen Graduate School of
Management and an academic fellow at the Securities and Exchange Commission, and Patrick
Verwijmeren (pverwijmeren@feweb.vu.nl) is from VU University Amsterdam. This paper has
benefited from comments by Renee Adams, Yakov Amihud, Nick Bollen, Sudipto Dasgupta, Abe
de Jong, Robert Faff, Joseph Fan, Doug Foster, Andrew Hertzberg, Sagitas Karpavicius, Timo
Korkeamaki, Mike Lemmon, Josh Lerner, Bryan Lim, Albert Menkveld, Mark Mitchell, Phong
Ngo, Vanitha Ragunathan, Abraham Ravid, Garry Twite, Chris Veld, Kathleen Weiss Hanley,
and seminar participants at the 2009 ANU Summer Camp, VU University Amsterdam, RSM
Erasmus University, the Federal Reserve Bank of Washington D.C., the University of
Queensland, the University of Maryland, the University of Stirling, the Securities and Exchange
Commission, the 2010 LaTrobe Finance and Corporate Governance Conference, and the 2010
European Finance Association Meetings. We gratefully acknowledge funding from a Faculty
Research Grant at the University of Melbourne. We thank Eric Duca for his assistance in
calculating convertible under-pricing and thank Melissa Roodzant and Daniel Selioutine for
assistance in data collection.
Convertibles and hedge funds as distributors of equity exposure
Convertible arbitrage hedge funds combine long positions in convertible securities with
short positions in the convertible issuer’s stock. In this paper we examine the role that the
short-selling strategy of hedge funds can play for firms that wish to issue equity-like
securities.
We construct a database of the initial buyers of 803 privately placed convertibles
issued under Rule 144A. Rule 144A was introduced by the SEC in 1990 and allows
companies to sell securities without registration under the U.S. Securities Act of 1933
and, for non-U.S. issuers, without complying with U.S. GAAP, provided that the
securities are issued only to qualified institutional buyers (QIBs). QIBs are typically large
institutional buyers with more than $100 million of investable assets. Rule 144A also
permits QIBs to trade these securities among themselves and has thereby increased the
liquidity of the securities affected. The names of the QIBs of an issue are contained in the
registration statement. These lists of names allow us to directly examine the participation
of hedge funds in convertible issues. We establish that hedge funds are heavily involved
in the convertible security market: during the 2000 – 2008 period 73.4% of the financing
of newly-issued convertibles in our data set is provided by hedge funds.1
Virtually all the convertibles in our sample are ‘equity-like’ in that the average
convertible delta at the time of issue is 0.867. Only three of 803 issues have deltas below
1
This confirms anecdotal evidence that about 70%-80% of convertibles are bought by hedge funds. A
Financial Times article (Skorecki, 2004) states that in 2003 “some [convertible] bonds have been issued
exclusively to hedge funds and on average they have been responsible for buying about 70 percent of new
issues.” A 2004 Wall Street Journal article (Pulliam, 2004) reports that “hedge funds play a big role in the
roughly $600 billion convertible-bond market, which saw $97 billion in new issues last year. As much as
80% of those issues were bought by hedge funds, according to brokers who work on convertible-bond
trading desks.” Mitchell, Pedersen and Pulvino (2007) state that “convertible arbitrage funds account for up
to 75% of the convertible market.”
2
one half, and only ten percent (twenty-five percent) of issues have deltas below 0.725
(0.816). A similar observation is made by Lewis and Verwijmeren (2009) and is
consistent with firms issuing convertibles as a substitute for equity and suggests the
following possibility. Instead of bearing the relatively high costs of issuing equity, firms
may find it optimal to privately place convertibles with hedge funds. By shorting stock to
hedge against changes in the stock price, these funds then effectively distribute the equity
exposure on to diversified investors in the open market.
By placing a convertible with hedge funds, a firm can receive financing today while
avoiding the discounts and underwriter fees associated with a secondary equity offering.
Where those costs are higher than the costs associated with the private placement and the
security is eventually converted, the firm will have issued equity at a lower cost.
Altinkilic and Hansen (2003), Corwin (2003), and Eckbo, Masulis, and Norli (2007)
argue that a high probability of financial distress, high stock return volatility, and a
NASDAQ-listing are indicative of relatively high costs of issuing seasoned equity. These
characteristics do not necessarily increase the costs of issuing convertibles to hedge
funds. For example, convertible arbitrage hedge funds typically prefer return volatility
because their hedging strategy leads them to buy stock after a stock price decline and sell
after a stock price increase. This strategy is inherently profitable when part of the stock
price movements are liquidity-induced and subsequently reverse, and high return
volatility means more opportunities to trade. For firms with high return volatility, issuing
convertibles to hedge funds might therefore be their least-cost financing option. In line
with our predictions, we find that hedge fund involvement in convertible issues is greater
3
when the issuer is more financially distressed, when the issuer’s return volatility is
higher, and when the firm is listed on NASDAQ.
The attractiveness of convertibles to hedge funds also depends on the cost of
shorting the issuer’s stock and on the design of the security. We find that hedge funds
purchase a smaller fraction of a particular issue if the issue is callable. Call features
complicate hedging since the decision to call is in the hands of the firm. A call will
redistribute wealth between convertible-holders and stock-holders. This redistribution is
not a hedgeable co-movement of the bond and the stock and makes it difficult to
determine the optimal number of shares to short.
Hedge funds are also more involved in issues that are small relative to the market
value of the firm’s equity; i.e., when hedging the issues requires borrowing only a small
fraction of the shares outstanding. This finding is also consistent with the ability to hedge
being a determinant of involvement by hedge funds. We further find evidence that hedge
fund involvement is positively related to concurrent stock repurchases. De Jong,
Dutordoir, and Verwijmeren (2009) argue that these concurrent stock repurchases
facilitate hedge funds in obtaining their short positions.
To further investigate the role of hedge funds as distributors of equity exposure, we
compare firms that issue convertibles to hedge funds to firms that issue seasoned equity.
We find that firms selling convertibles are more financially distressed and have more
volatile returns relative to seasoned equity issuers. The issuers of convertibles would
therefore have faced high costs of issuing seasoned equity compared to firms that did
choose to issue equity. In addition, convertible issuers have a higher average level of
institutional ownership and have more liquid stock than firms that make seasoned equity
4
offers. Institutional ownership facilitates the borrowing of stock to set up a short position
(D’Avolio, 2002), while stock liquidity also reduces the costs of establishing and
maintaining a short position.
Using a two-stage model that accounts for self-selection, we estimate the issue
costs that firms that issue convertibles to hedge funds would have had if they had chosen
a seasoned equity offering instead. We define issue costs as the sum of the offering
discount and gross spread, and find that the forecasted issue cost for a seasoned equity
offering is 11.10% for our sample of convertible issuers. The actual cost of selling
convertibles to hedge funds is 9.23%, in line with convertibles being the least-cost
financing option for these firms.
The paper makes two main contributions to the literature. Primarily, we document
the role that hedge funds play as distributors of equity exposure. We argue that hedge
funds are able to use their knowledge of the borrowing and short-sale market to distribute
risk to a large number of well-diversified investors, which provides financing
opportunities for firms with characteristics that would make seasoned equity offerings
expensive. Brophy, Ouimet, and Sialm (2009) study PIPE (Private Investments in Public
Equity) issues and conclude that hedge funds involved in these issues serve as investors
of last resort for the issuing firms in that hedge funds “provide capital for companies that
are otherwise constrained from raising equity capital” (Brophy, Ouimet, and Sialm, 2009,
p. 541).2 PIPE issuers are in general very small and distressed and provide large discounts
to investors. The firms in our sample are substantially larger and are not as distressed,
2
PIPEs are private placements in which a public company issues equity securities to a group of private
investors without registering the shares. PIPEs differ from traditional private placements because a
registration statement is filed soon after signing of the purchase agreement, which allows for the resale of
shares initially sold to PIPE investors (Chaplinsky and Haushalter, 2009).
5
and issuing convertibles to hedge funds is unlikely to be their only financing option. We
find that in our sample discounts are not higher on convertibles issued to hedge funds,
which is in line with hedge funds serving as relatively low-cost distributors of equity
exposure rather than investors of last resort.
Second, our paper investigates the matching of particular securities and a targeted
group of buyers. The literature on this topic is scarce as the buyers of new security
offerings cannot typically be observed. One of the first studies in this field is Wruck
(1989) which focuses on private equity sales. Our hand-collected database allows us to
study the buyers of 144A privately placed convertible securities. We are able to quantify
the importance of hedge funds in the convertible debt market, and show that both investor
and investee identity matters in the convertible debt market in the sense that hedge fund
involvement depends on characteristics of both the issuing firm and the security design.
We also add to prior studies that have examined security design choice from the
perspective of the suppliers of convertible securities. For example, Lewis and
Verwijmeren (2009) argue that important motivations for design choices are earnings
management, credit rating concerns, and reductions of taxes, refinancing costs, and
managerial discretion costs. We view security design choice from the perspective of the
suppliers of capital. We document a relation between the involvement of hedge funds and
the incorporation of call features, cash settlements, call spread overlays, and put features
into the convertibles’ design.
The remainder of this paper is organized as follows. Section I discusses prior
studies on convertible arbitrage and constructs testable predictions on the role that hedge
funds play. Section II describes our data set and provides information on the proportion
6
of convertible securities that are bought by hedge funds. Section III presents our
empirical tests on the relation between hedge fund involvement and characteristics of the
issuing firm and the issue itself. Section IV investigates differences between firms with
secondary equity offerings and firms issuing convertibles to hedge funds. Section V
examines convertible under-pricing and provides cost estimates for our convertible
sample if they would have chosen a seasoned equity offering instead. We report
additional analyses of the effective life of convertible bond issues in Section VI and of
hedge fund shorting in Section VII. Section VIII contains our conclusions.
I. Hedge funds and convertible arbitrage
A. Prior evidence
Hedge funds have characteristics that avoid restrictions in short-selling. Section
12(a)(3) of the Investment Companies Act of 1940 makes it unlawful for any registered
investment company “to effect a short sale of any security, except in connection with an
underwriting in which such registered company is a participant.” Sections 3(c)(1) and
3(c)(7) set out conditions under which an institution is not a registered investment
company within the meaning of the Act: institutions owned by not more than 100 persons
(Section 3(c)(1)) and institutions owned exclusively by qualified purchasers (Section
3(c)(7)). Qualified purchasers include individuals with not less than $5 million in
investments.3 The business model of a hedge fund includes a restriction on either the
3
Qualified purchasers are defined in Section 2(51)(a) of the Act.
7
number or the wealth of investors in the fund so that it is not precluded from shortselling.4
Calamos (2003) discusses hedge funds’ typical buy-and-hedge strategy of buying
convertibles and shorting the stock of the issuing firm with the short position being
determined by the convertible’s delta. Delta is the sensitivity of a derivative’s price for
small changes in the price of the underlying, and is between zero and one. A delta-neutral
position attempts to exploit under-pricing of the convertible security while hedging
against changes in the stock price.
One way in which prior studies examine the prevalence of hedge fund purchases of
newly issued convertibles is by focusing on short interest in the stock of the issuer. Brent,
Morse, and Stice (1990) document that U.S. firms with convertible debt outstanding
report higher monthly short interest than other companies.5 Choi, Getmansky, and Tookes
(2009) document the effects of convertible arbitrage activity on market liquidity by using
the change in monthly short interest around convertible issue dates as a proxy for
arbitrage activity. They conclude that arbitrage activity increases the liquidity of the stock
because arbitrageurs trade in the opposite direction to the market’s movements:
arbitrageurs add to their short position when the stock price increases (as an increase of
the stock price increases the delta) and close out part of their short position when the
stock price decreases.
4
See Fung and Shieh (1999) for further information on the regulatory environment for U.S. hedge funds
and further explanations for why hedge funds’ trading behavior differs from other investors. Given that
other investors are restricted in using short-selling, Fung and Hsieh (1997) find that mutual fund returns are
highly correlated with standard asset classes, while hedge funds generate returns that have low correlation
with the returns of standard asset classes.
5
Ackert and Athanassakos (2005) and Loncarski, Ter Horst, and Veld (2009) report similar findings for
Canadian firms using bi-monthly short interest data.
8
The main downside of using short interest data to examine convertible arbitrage is
that changes in short interest may be due to changing beliefs about whether the share is
overvalued. Thus it might be that issue announcements are associated with valuation
shorting by those who take a relatively more pessimistic view of an announcement’s
implications for firm value. Moreover, monthly short interest data are noisy as
confounding events can occur in the same month as the convertible issue. An alternative
is to use daily short sale information. De Jong, Dutordoir, and Verwijmeren (2009)
examine daily short sale data from the NYSE TAQ database REG SHO file (which
covers short-selling transactions from January 2005) and document that daily short sales
peak at convertible issue dates. Unfortunately, the daily TAQ short sale data are only
available for a limited number of NYSE firms and the database has been discontinued in
July 2007. Using daily short sale data also does not solve for the effect of valuation
shorting on announcement dates, as De Jong, Dutordoir, and Verwijmeren document that
92.58% of the convertible debt offerings in their sample are announced on the issue date
or the day prior.
A second way of examining convertible arbitrage is to examine fund flows into
convertible arbitrage hedge funds. Choi, Getmansky, Henderson, and Tookes (2009) and
De Jong, Duca, and Dutordoir (2009) show that aggregate convertible bond issuance is
positively related to the flow of funds into convertible arbitrage hedge funds. Mitchell,
Pedersen, and Pulvino (2007) find that convertible prices drop relative to their
fundamental values in periods when convertible arbitrageurs are more capital
constrained. Agarwal, Fung, Loon, and Naik (2009) show that the returns of convertible
arbitrage funds are positively related to the supply of convertible bonds. Agarwal, Fung,
9
Loon, and Naik argue that an increase in the supply of bonds means an increase in the
availability of mispricing opportunities to be exploited. They also show that the returns of
convertible arbitrage hedge funds can be largely explained as the returns to a buy-andhedge strategy.
Our data allow us to directly examine the involvement of specific hedge funds in
specific convertible issues. For each convertible in our sample we are able to observe
how much of the issue is purchased by hedge funds. In this particular sense, our paper is
most closely related to Brophy, Ouimet, and Sialm (2009). Brophy, Ouimet, and Sialm
study traditional and structured PIPEs between 1995 and 2002 using data from the
Sagient database, which reports the involvement of hedge funds in PIPE issues.6 They
find that hedge funds account for 15.6% of investments in traditional PIPEs and 71.9% of
investments in structured PIPEs. They further show that the larger the involvement of
hedge funds in an issue, the worse the post-issue performance of the issuing firm. This
negative relation leads them to conclude that hedge funds are investors of last resort.7
Our paper differs from Brophy, Ouimet, and Sialm (2009) in several ways. First,
Brophy, Ouimet, and Sialm do not distinguish within the set of traditional PIPEs between
convertible PIPEs and common stock PIPEs.8 Second, firms that issue PIPEs are in
general very small: Chaplinsky and Haushalter (2009) report that over the 1995 to 2000
6
Traditional PIPEs are common stock PIPEs, with or without warrants, and convertible security PIPEs,
with or without warrants. Structured PIPEs are common stock reset PIPEs, structured equity lines, floating
convertibles, and reset convertibles.
7
Dai (2007) also uses the Sagient database to focus on PIPEs and compares PIPE investments by venture
capitalists with PIPE investments by hedge funds. Dai finds that venture capital-led PIPEs (issues in which
the lead investor is a venture capital fund) outperform hedge fund-led PIPEs. Dai concludes that venture
capitalists serve a certification role (as distinct from a monitoring role).
8
Ellis and Twite (2008) estimate that during the 2002 to 2005 period, traditional PIPEs accounted for 78%
of PIPE issues and 95.1% of PIPE capital raised. Of the 1,169 traditional PIPEs in their sample only 282
are convertible PIPEs. Ellis and Twite argue that PIPEs are not simply securities issued to hedge funds as
financiers of last resort, but that PIPEs are more likely to be issued when firms have profitable growth
options and face a severe information asymmetry.
10
period the mean (median) asset value of PIPE issuers was $54 million ($18 million), and
Brophy, Ouimet, and Sialm report that over the 1995 to 2002 period the mean asset value
of PIPE issuers was $178 million. In contrast, our sample consists of substantially larger
firms: the average value of the assets of the firms issuing the convertibles in our sample is
over $3 billion.9 Our data allow us to examine the role that hedge funds play when issuers
are likely to have a choice of financing methods open to them. Third, we have detailed
information on the contractual features of the convertibles in our sample. This allows us
to examine the relation between hedge fund involvement and convertible security design
as well as the relation between the decision to issue a convertible and characteristics of
the issuing firm.
B. Empirical predictions
Consider a firm that seeks to sell shares when an underwriter would be unwilling to
bear a large exposure to the firm’s equity unless the firm pays a substantial fee and/or
offers a large discount on its shares. Such a firm may be able to use the comparative
advantage of hedge funds to distribute equity exposure via short-sales. Hedge funds
engaged in convertible arbitrage are able to use their knowledge of the borrowing and
short-sale market to hedge themselves while distributing risk to a large number of welldiversified investors. Issuing convertibles may allow ‘would-be’ equity issuers to raise
capital at lower costs. Although an underwriter could also hedge by shorting stock, they
may not have the same ability to do so and their marketing claims may not be seen as
credible while they maintain a large short position in the shares they are seeking to place.
9
Brophy, Ouimet, and Sialm exclude 144A offerings as 144A private placements are “issued by larger and
more mature companies and are not considered PIPEs due to different regulatory treatments” (Brophy,
Ouimet, and Sialm (2009, p.547)).
11
B.1. Empirical predictions about the decision to issue a convertible
We predict that firms will issue convertibles to hedge funds when the costs of
issuing seasoned equity are high relative to the costs of establishing and maintaining a
short position. We use three main proxies for the costs of issuing seasoned equity. The
first proxy is the firm’s probability of financial distress, as the firm’s financial condition
is a strong predictor of the costs of issuing securities (Eckbo, Masulis, and Norli, 2007).
Kim, Palia, and Saunders (2005) show that underwriter spreads are higher for firms with
higher leverage and lower profitability. Provided that an increase in the likelihood of
financial distress leads to a rise in the costs of a seasoned equity offering that is larger
than the rise in the cost of establishing and maintaining a short position, firms with a
higher probability of financial distress are more likely to choose to issue convertibles to
hedge funds. Our second proxy is the return volatility of the firm’s stock. Altinkilic and
Hansen (2003) and Corwin (2003) report that the costs of seasoned equity offers are
significantly higher for issuers with more volatile stock returns. Provided that the costs of
establishing and maintaining a short position are not comparably higher for more volatile
firms, volatile firms are predicted to be more likely to issue convertibles to hedge funds.
Altinkilic and Hansen (2003) and Corwin (2003) also find that NASDAQ firms have
substantially higher costs of issuing seasoned equity, even after controlling for variables
like return volatility. We use a NASDAQ-listing dummy as a third proxy for the costs of
issuing seasoned equity.
A potential fourth proxy for the costs of issuing equity is firm size as measured by
the market value of equity. However, evidence on the effect of firm size on the costs of
issuing securities is mixed. Hansen and Torregrosa (1992) and Corwin (2003) provide
12
some evidence that larger firms have lower costs of issuing equity, while Gompers and
Lerner (1999) find that issuing costs are positively related to firm size for venture capitalbacked IPOs. Many other studies find no strong effect of firm size on underwriter spreads
and security under-pricing; see Eckbo, Masulis, and Norli (2007) for an overview of
studies on the relation between firm characteristics and the costs of issuing seasoned
equity.
Just as certain firm characteristics may make a secondary equity offering more
expensive, other characteristics of the issuing firm affect the cost of establishing and
maintaining a short position. The difficulty of shorting shares depends on the ease with
which shares can be borrowed. D’Avolio (2002) finds that institutional ownership
explains about 55% of the variability in loan supply across stocks. Since issuers with
higher institutional ownership will have a higher availability of shares to be borrowed
(see also Asquith, Pathak, and Ritter, 2005), such issuers are more likely to find that
issuing convertibles is cheaper than issuing seasoned equity.
All else equal, a would-be arbitrageur is more likely to be able to short the desired
number of shares when that number of shares is small relative to the number of shares
outstanding. When investigating the choice between issuing seasoned equity and
distributing exposure via hedge funds we take as our measure of relative size the ratio of
the issue proceeds to the market value of the equity outstanding. Similarly, the costs of
establishing and maintaining a short position will be lower when the issuer’s stock has
greater liquidity and again the likelihood of a convertible issue in preference to a
seasoned equity offering should be higher. Finally, since short sellers must pay cash in
13
lieu of dividends to the lenders of stock, the management of a hedge fund’s cash flows
may be more expensive when the convertible is issued by a dividend-paying company.
Conditional on the firm issuing a convertible, the attractiveness of the convertible
to hedge fund investors versus other potential buyers is a second question.
B.2. Empirical predictions about hedge fund purchases of particular convertible issues
When the cost of issuing seasoned equity is relatively high and the firm does decide
to issue a convertible, it does not necessarily follow that the bond is more attractive to
hedge fund buyers than to other investors in convertibles. But if the decision to issue the
convertible was in part driven by an investigation of potential demand from hedge funds,
then the same factors that predict an increased likelihood of a convertible issue relative to
an equity issue will be associated with a higher fraction of the convertible being
purchased by hedge funds. This will imply that the fraction of a convertible issue
purchased by hedge funds should be higher when the probability of financial distress is
higher, when the issuer’s return volatility is higher, and when the issuer’s stock has a
NASDAQ-listing.
There is a separate reason why hedge fund involvement may be higher when the
issuer’s return volatility is higher. Part of a hedge fund’s profits can come from playing
the role of a market-maker willing to buy stock after a stock price decline and sell after a
stock price increase. When stock price movements are liquidity-induced and
subsequently reverse, the fund’s dynamic hedging strategy can be inherently profitable
and hedging a more volatile stock involves more opportunities to trade.
Following the reasoning in subsection I.B.1, certain issuer characteristics are
predicted to make a convertible bond more or less attractive to hedge funds. Higher
14
institutional ownership and greater liquidity of the issuer’s stock and a smaller relative
size for the issue are all predicted to make a convertible more attractive to hedge fund
investors. When investigating the attractiveness of different convertible issues to hedge
fund buyers we take as our measure of relative size the ratio of the delta-neutral short
stock position to the number of shares outstanding. Issues by dividend-paying companies
are predicted to be less attractive.
Not only do particular characteristics of the issuer affect the relative costs of
secondary offerings versus the distribution of equity exposure via hedge funds, firms that
do decide to issue convertibles should structure the issue so as to reduce the cost of
establishing and maintaining a short position. There are two ways to do this: first, by
restricting or eliminating the bond’s call features, and second, by undertaking a
concurrent share repurchase. Limits on callability increase the attractiveness of
convertibles to hedge funds because hedge funds need to constantly balance their long
bond position with a short stock position. Call features complicate this balancing since
the decision to call remains in the hands of the issuing firm. Whenever the occurrence of
a call is not a deterministic function of the stock price and time, hedging will not be
perfect.
A concurrent stock repurchase by the issuing firm will cater to the needs of hedge
funds by allowing funds to short-sell borrowed stock at a predetermined price, namely the
repurchase price. De Jong, Dutordoir, and Verwijmeren (2009) examine instances where
firms combine convertible issues with stock repurchases (the combination is known as a
Happy Meal), and conclude that convertible arbitrage explains both the size and speed of
execution of these stock repurchases.
15
We predict that hedge funds will purchase a larger fraction of convertible bond
issues with limited callability and a larger fraction of convertible issues accompanied by
a stock repurchase.
II. Data and summary statistics
We collect a sample of 1,142 privately-placed convertible issues in the period
January 2000 to March 2008 from SDC. Most recent convertible issues in the U.S. have
been privately placed under Rule 144A: Marquardt and Wiedman (2005) report that 84%
of convertibles issued during 2000 – 2002 are privately placed, and De Jong, Dutordoir,
and Verwijmeren (2009) report that for the period 2003 – 2007 the percentage of
privately-placed convertible issues is about 95%. For our sample period, the percentage
of privately-placed convertibles is 85%, and 84% of the total proceeds raised by all the
convertible bond issues in the SDC database come from privately-placed issues.10
We require that firms have an offering prospectus available on the SEC’s Edgar
database. This eliminates 201 of the 1,142 issues. We also require a registration
statement, which eliminates an additional 138 issues. The registration statement lists the
buyers of the convertible issue.11 This leaves 803 offerings with detailed information on
the design of the convertible and the identity of the buyers.
Many buyers are easily classified as hedge funds since they have the words
“convertible arbitrage” in their name. We use the full lists of hedge fund managers in
Bloomberg and TASS and undertake an extensive internet search on each buyer (various
websites
allow
for
a
search
of
self-registered
hedge
funds,
for
example
10
Convertible issues have been relatively popular since 2000. Aggregate convertible proceeds are on
average $68 billion per year for the period 2000 to 2008. In the 1990s this average was $26 billion.
11
The registration filings are typically S-3/A filings, although in some cases the selling security-holders can
be found in S-3, S-3ASR, or 424B filings.
16
http://www.hedgeco.net) in an effort to determine which buyers are hedge funds. We can
classify 39.4% of the 4,335 buyers as hedge funds.12
Panel A of Table I reports the average number of buyers per privately placed
convertible issue.
[ please insert Table I here ]
On average, a convertible issue is bought by 64 different identified buyers. Note that 64 ×
803 is much larger than 4,335, i.e., many buyers are involved in multiple convertible
offerings. The number of buyers varies considerably over the convertible issues: some
convertibles are bought by a single buyer, and the maximum number of different
identified buyers of a single issue is 320.
That less than half of all buyers are hedge funds is not inconsistent with financial
press reports that hedge funds buy 70% to 80% of all convertible issues. A typical hedge
fund is involved in a larger number of different convertible issues than a typical nonhedge fund buyer of convertibles. Panel A of Table I indicates that on average more than
half the buyers of individual convertible bond issues (56.4%) can be classified as hedge
funds. Further, hedge funds often buy a larger percentage of a particular offering than
12
There are three hedge funds in our sample that TASS classifies as “Global Macro” hedge funds, and an
additional two hedge funds in our sample have the words “Global Macro” in their name. As global macro
funds do not necessarily combine a long position in a convertible with a short position in stock, we have reestimated all the results in this paper with global macro hedge funds classified as non-hedge funds. We
have also checked the impact of the classification of brokerage firms on our results, as one practitioner has
suggested that brokerage firms possibly trade on behalf of small hedge fund clients. We find that our
conclusions in the paper are robust to changing the classifications of global macro hedge funds and
brokerage firms.
17
other buyers.13 Panel A reports that on average hedge funds account for 73.4% of the
investments in individual convertible issues.
The amount purchased by investors that are identified in the registration statements
can be lower than the total offering proceeds reported in SDC. This indicates that there
can be unidentified investors involved in the security offering. The sum of investments by
identified investors is on average 91.7% of the reported proceeds of the convertibles in
our sample (the median is 94.0%). We do not expect that the group of unidentified buyers
will strongly bias the results in this paper. For example, we find that the fraction
purchased by hedge funds is very similar for issues in which identified investors buy
more than 94.0% of the reported proceeds and issues in which identified investors buy
less than 94.0% of the reported proceeds: in both subsamples hedge funds account for
between 73% and 74% of the investments by identified investors. Throughout the paper
we calculate the involvement of hedge funds in an issue as the number of hedge fund
investors divided by the number of identified investors and/or as the total investment by
hedge fund investors divided by the total investment by identified investors.
Panel A further shows that there is dispersion in the percentage of each issue
purchased by hedge funds: some issues are entirely purchased by hedge funds, while
other issues have no hedge funds involvement at all. In a first attempt to shed light on this
heterogeneity, we report the fraction of the issue purchased by hedge funds per industry
in Panel B of Table I. Hedge funds account for the majority of the convertible proceeds in
every one of the 12 Fama-French industry classifications. No simple industry affect is
apparent.
13
The average investment by an individual hedge fund expressed as a fraction of the offering proceeds is
2.31% in the sample. The average individual non-hedge fund investor buys 0.82% of an issue.
18
[ please insert Figure 1 here ]
Hedge fund involvement has grown through time. Figure 1 reports the average
percentage of convertible issues purchased by hedge funds per year. Hedge funds account
for about 60% of the investments in privately-placed convertibles in 2000. By the first
quarter of 2008, this percentage has grown to 80%.
We construct a final sample that we use to examine the relation between hedge
fund involvement, security design, and firm characteristics. Following common practice
we delete financial firms and utilities (112 issues). We also require that the issuing firms
have data available on Compustat, CRSP and the Thomson-Reuters Institutional
Holdings database and this requirement deletes an additional 62 observations.
III. Determinants of the fraction of a convertible issue acquired by hedge funds
In this section we examine the relation between the fraction of a convertible issue
privately-placed with hedge funds and proxies for the costs of directly issuing seasoned
equity and the costs of indirectly distributing equity exposure via hedge funds. The set of
issuer characteristics examined include the likelihood of financial distress as measured
by a firm’s Altman Z-score (Z-scores are higher for firms with a lower chance of
bankruptcy); the return volatility of the issuer’s stock; a dummy for whether the issuer’s
stock have a NASDAQ-listing; firm size as measured by the market value of equity (in the
regression analyses we employ the natural logarithm of this variable); the percentage
institutional ownership of the issuer’s stock; the relative size14 of the issue measured as
the fraction of the outstanding stock that would have to be sold short in order to hedge
14
For a given issue size, relative size is an issuer characteristic. For a given issuer size, relative size is a
characteristic of the issue.
19
ownership of the entire bond issue; the Amihud liquidity measure (a high Amihud-score
denotes illiquidity); and a dummy for whether the bond is issued by a company with
dividend-paying stock.
The set of issue characteristics examined are those predicted in subsection I.B.2 to
be related to hedge fund involvement (i.e., callability and concurrent stock repurchases)
plus other issue characteristics studied in Lewis and Verwijmeren (2009). Issue
characteristics involve both dummy and continuous variables. The set of dummies denote
whether an issue is callable; whether an issue is accompanied by a stock repurchase;
whether an issue occurs in conjunction with a call spread overlay; whether an issue has a
cash settlement feature; and whether an issue is accompanied by put rights. The
continuous variables measure the size of the convertible’s delta and the size of the issue
proceeds. We make no prediction about how the issue characteristics other than
callability and concurrent stock repurchases will be related to hedge fund involvement,
but include these variables simply as controls. Exact definitions of the issue and issuer
characteristics are reported in Appendix A.
[ please insert Table II here ]
Table II provides a univariate analysis of the relation between various issuer and
issue characteristics and the fraction of a convertible issue sold to hedge funds. For our
overall sample, the average equity value of the issuing firms is in excess of $4 billion
dollars, and the average issue proceeds are $313 million dollars. A substantial fraction
(53.6%) of the issuing firms are listed on NASDAQ. Of the 629 convertible issues in the
sample, 8.1% involve a call spread overlay, 40.4% have a cash settlement feature, and
20
42.4% have attached put rights. Interestingly, only 72.3% of the convertible issues are
callable some time prior to their maturity; Korkeamaki and Moore (2004) report that this
percentage is 98.2% for convertibles issued during the period 1980 – 1996.
Table II also reports average values of issuer and issue characteristics for
subsamples. The first two subsamples contain equal numbers of issues and consists of
convertible securities with above-median purchases by hedge funds (meaning that hedge
funds buy more than 75.3% of the issue), and issues with below-median hedge fund
participation. We also construct two subsamples based on whether hedge funds buy the
majority of the convertible offering (584 of the 629 issues) or only a minority of the issue
(45 issues).
We find that differences in issuer characteristics are significant at the 1% level in
three instances. Convertibles with above-median hedge fund involvement are
significantly more likely to have been issued by firms whose stock are more likely to be
listed on NASDAQ and by firms with higher return volatility.15 Both these characteristics
are identified by Altinkilic and Hansen (2003) and Corwin (2003) as likely to increase the
cost of a seasoned equity offering. The third significant univariate relation between issuer
characteristic and hedge fund involvement is that hedge funds are more likely to buy only
a minority of a convertible issue when the issuing firm is smaller.
When focusing on issue characteristics, we find that hedge funds have a
significantly lower involvement in convertibles with a call feature and a significantly
higher involvement in convertible issues accompanied by a stock repurchase. Both of
15
We measure return volatility as the annualized stock return volatility, estimated with (up to) ten years of
monthly stock return data. In robustness tests we have measured volatility as the annualized daily stock
return volatility over trading days [−240, −40] relative to the issue date, as in Lewis, Rogalski, and Seward
(1999). The results throughout our paper are qualitatively unchanged.
21
these findings are in line with our predictions.16 We further find that hedge fund
involvement is significantly higher in issues with call spread overlays and issues with
cash settlement features.
We draw our main conclusions from the multivariate analysis reported in Table III.
For ease of interpretation, Table III also sets out the predictions for the signs of the
coefficients developed in subsection I.B.2. Some firms in our sample are responsible for
multiple convertible offerings.17 In line with recommendations of Petersen (2009), we
therefore cluster standard errors at the firm level.
[ please insert Table III here ]
In Model 1, the dependent variable is the percentage of proceeds purchased by
hedge funds.18 Firms that issue convertibles because they face high costs of directly
issuing equity are likely to have first confirmed that demand from hedge funds is likely to
be high. Thus a higher fraction of convertibles issued by relatively distressed, more
volatile and/or NASDAQ-listed firms is predicted to be purchased by hedge funds. We
find that hedge fund involvement is positively related to the likelihood of financial
distress (low values for the Altman Z-score)19, and is also significantly higher for firms
with high return volatility and a NASDAQ-listing. The attraction to convertibles issued by
16
We have collected more detailed call information for the callable convertible issues with an abovemedian hedge fund involvement. We find that only 4.9% of these issues have a time to first call of zero.
The average (median) time to first call for these issues is 4.69 (5.00) years. To the extent that hedge funds
can be expected to hold their positions for less than 5 years, many callable convertibles can still be treated
as non-callable by hedge funds.
17
The 629 convertibles in the sample are issued by 474 different firms: 364 firms issue a single
convertible, 76 firms issue two convertibles, 26 firms issue three convertibles, 5 firms issue four
convertibles, and 3 firms are responsible for five different convertible issues.
18
One observation in our sample has an involvement of hedge funds close to 0%, and 14 observations have
100% hedge fund involvement. Estimating a tobit regression in which one or both of these boundaries are
censored provides results that are very similar to the results from our OLS estimation.
19
For expositional purposes, the coefficients for the Altman Z-score in our regression estimates are
multiplied by 100.
22
companies with highly volatile stock may also reflect an attraction to the trading profits
from market-making while dynamically hedging. Note that a significantly smaller
percentage of a convertible issue is purchased by hedge funds when the convertible is
issued by a larger firm.
Hedge fund involvement is predicted to be higher when the costs of establishing
and maintaining a short position are lower. The significant relation between relative size
and hedge fund involvement is in the predicted direction and, also as predicted,
convertibles with call features are of less interest to hedge fund investors. We find some
evidence (at the 10% level) that hedge fund involvement in an issue is positively related
to the concurrent repurchase of stock. We find no evidence that hedge fund involvement
is significantly higher when more of the issuer’s stock is held by institutions, when the
stock is more liquid, or when the firm pays no dividends.
Regarding the control variables, we find that cash settlements, call spread overlays,
and put features are all positively related to the fraction of a convertible issue that is
purchased by hedge funds. Lewis and Verwijmeren (2009) argue that cash settlement
features and call spread overlays facilitate earnings management.20 A potential
explanation for the relation between these design characteristics and hedge fund
involvement is that firms with relatively high costs of issuing seasoned equity are more
likely to try to make their financial reporting look as favorable as possible. Put features
20
Cash settlement allows firms to decide whether payment will be in common stock or in cash (for the
value of common stock). At the time of our study, accounting rules were such that the potential dilution
associated with the offer is not reflected in fully diluted earnings for most cash settlements (see Lewis and
Verwijmeren, 2009). When a convertible issue is accompanied by a call spread overlay, a firm uses part of
the issue proceeds to purchase call options on its own shares, struck at the conversion price, and writes call
options on its own shares at a higher strike price. The net effect is an increase of the strike price in the
conversion option. Had the issuer simply offered the convertible bond with a higher conversion price, the
interest offered on the convertible would have been higher and the firm would report a higher interest
expense.
23
provide investors with more downside protection than is typically associated with a
convertible security. The positive relation with hedge fund involvement can possibly be
explained by put features being issued by risky firms with high informational asymmetry,
as these are firm characteristics that are likely to make a seasoned equity offering
relatively expensive.
In Model 2 we use the percentage of buyers classified as hedge funds as the
dependent variable. This variable focuses on the number of hedge funds serving as
distributors, instead of the size of their involvement. The variables financial distress,
NASDAQ-listing, and cash settlement lose their significance at the 5% level (but are still
significant at the 10% level). Overall, the results are qualitatively similar to those
obtained from Model 1.
IV. Determinants of the decision to distribute equity exposure via hedge funds
In this section we compare seasoned equity issuers to firms that issue convertibles
to hedge funds. This analysis can shed light on whether selling equity-like convertibles to
hedge funds is indeed a substitute for ‘would-be’ equity issuers with relatively high costs
of directly issuing seasoned equity.21 We obtain seasoned equity offerings from the SDC
database from January 2000 to March 2008. We impose the same restrictions as on our
sample of convertibles; i.e., we delete financial institutions, utilities, and firms with
21
We are not the first to compare firms issuing seasoned equity to firms that issue convertible securities.
For example, Lewis, Rogalski, and Seward (1999) study Stein’s (1992) prediction that convertible debt
issuers have significantly higher adverse selection and financial distress costs than issuers of seasoned
equity. They find evidence in line with Stein’s prediction and conclude that the likelihood of an equity-like
convertible debt issue increases when the costs of a common stock issue are high.
24
missing data in Compustat, CRSP, or the Thomson-Reuters Institutional Holdings
database. Our seasoned equity sample consists of 2,198 offerings.22
We use a binary logit model to compare the firm characteristics of seasoned equity
issuers to the characteristics of the 584 convertible issues in which hedge funds purchase
the majority of the issue. Table IV reports the results.
[ please insert Table IV here ]
The dependent variable equals one for convertible issues in which the majority of the
issue is purchased by hedge funds, and zero for seasoned equity offerings. We find that
firms issuing convertibles to hedge funds are more financially distressed than equity
issuers, as the coefficient on the Altman Z-score is negative and statistically significant at
the 1% level. We find an insignificant increase in the likelihood of issuing a convertible if
the issuing firm is listed on NASDAQ.
Altinkilic and Hansen (2003), Corwin (2003), and Eckbo, Masulis, and Norli
(2007) show that stock return volatility increases the issue cost of seasoned equity
offerings. In contrast, convertible arbitrageurs might be attracted to stock price volatility,
since their trading profits from market-making are higher for more volatile stock. In line
with this story, we find that high stock return volatility increases the probability that
firms issue convertibles to hedge funds instead of issuing seasoned equity.
The results in Table IV also show that firms issuing to hedge funds are significantly
larger companies with significantly more liquid stock and significantly higher
22
A difference with our convertible sample is that not all our seasoned equity offerings are privately
placed. In our sample of 2,198 seasoned equity offerings, only 2 offerings are identified by SDC as 144A
private placements. The private placement information is missing for 1,412 of the seasoned equity
offerings.
25
institutional ownership than are firms that issue seasoned equity. Greater liquidity and
higher institutional ownership make it easier for hedge funds to establish their desired
short positions.
In Model 2 we include a number of macroeconomic variables as additional control
variables. Macroeconomic conditions could potentially have an impact on the choice
between a seasoned equity offering and a convertible debt offering: Choe, Masulis and
Nanda (1993) and Korajczyk and Levy (2003) show that macroeconomic conditions
affect capital structure choice, and Mann, Moore and Ramanlal (1999) show that
macroeconomic variables are related to the timing of convertible issues. The macrovariables we examine are the one-year stock return on the S&P 500, the yield on a 10year Treasury bond, the credit spread between the Moody’s Baa corporate bond yield and
the yield on a 10-year Treasury bond, and a composite index of leading indicators.23
Macro-data for the month before the issue are obtained from Datastream. It can be seen
from Model 2 that the significant effects of the financial distress, return volatility, firm
size, institutional ownership, and liquidity variables are robust to controlling for
macroeconomic conditions. The interest rate, credit spread, and leading indicator
variables are all positively related to the likelihood of a secondary equity offering rather
than a convertible offering.
The results of Table IV suggest that firms choosing to issue convertibles to hedge
funds rather than to issue seasoned equity are firms that face relatively high costs of
23
The composite index contains the following ten leading indicators: the average weekly hours worked by
manufacturing workers, the average number of initial applications for unemployment insurance, the amount
of manufacturers’ new orders for consumer goods and materials, the speed of delivery of new merchandise
to vendors from suppliers, the amount of new orders for capital goods unrelated to defense, the amount of
new building permits for residential buildings, the S&P 500 stock index, the inflation-adjusted monetary
supply, consumer sentiment, and the spread between long and short interest rates.
26
directly issuing equity and have characteristics that facilitate the establishment and
maintenance of the short positions; i.e., that have relatively low costs of indirectly
distributing equity exposure via hedge funds.
V. Offering discounts
Convertible securities are typically issued at a discount (Ammann, Kim, and Wilde,
2003; Chan and Chen, 2005; Loncarski, ter Horst, and Veld, 2009; De Jong, Dutordoir,
and Verwijmeren, 2009). Potential reasons for convertible debt under-pricing include
illiquidity and complexities associated with the valuation of hybrid securities (Lhabitant,
2002). In this section we study these discounts. In Section V.A. we use the offering
discounts to distinguish the distribution role of hedge funds from their possible role as a
last resort provider of finance. In Section V.B. we use the offering discounts to examine
the total issue costs for convertible issuers and seasoned equity issuers. We forecast what
convertible issuers would have had as issue costs if they had chosen a seasoned equity
offering instead.
A. Convertible offering discounts and the role of hedge funds
As distributors of equity exposure, hedge funds require a discount to cover their
costs of shorting the underlying stock. But we do not expect a discount that is
substantially larger than any discount on convertibles issued to other investors. Under the
last resort hypothesis, we would expect higher discounts for convertibles issued to hedge
funds. Brophy, Ouimet, and Sialm (2009) report that when the majority of a PIPE is sold
to hedge funds the average discount is 14.12%, whereas the average discount is
27
significantly lower (9.02%) when the majority of a PIPE is issued to non-hedge fund
investors.
We follow Ammann, Kim, and Wilde (2003), Chan and Chen (2005), Loncarski,
ter Horst, and Veld (2009), and De Jong, Dutordoir, and Verwijmeren (2009) in using a
variant of the Tsiveriotis-Fernandes (1998) model to calculate the theoretical value of
convertibles. Tsiveriotis and Fernandes (1998) use a binomial-tree approach to model the
stock price process and decompose the total value of a convertible bond into an equity
component and a straight debt component. According to Grimwood and Hodges (2002),
this model is the most popular convertible bond valuation method among practitioners.
MATLAB has a convertible bond pricing algorithm based on the approach of Tsiveriotis
and Fernandes (1998).24 To use this algorithm, we require some additional data: the riskfree rate and credit spread data are taken from Datastream and matched as closely as
possible with the maturity of the convertible bond; the relevant credit rating for the
spread is obtained from Mergent (following Loncarski, ter Horst and Veld (2009) and De
Jong, Dutordoir and Verwijmeren (2009) we assume a BBB rating when the credit rating
of the convertible is unavailable); and call schedules and coupon rates are taken from the
issue prospectuses. We calculate the offering discount by dividing the difference between
the theoretical price and the offer price by the theoretical price. We are able to calculate
the offering discount for 603 convertible issues.25
[ please insert Table V here ]
24
See http://www.mathworks.com/access/helpdesk/help/toolbox/finfixed/cbprice.html for a description of
this algorithm.
25
We are not able to calculate the offering discount with MATLAB’s pricing algorithm for our full sample
of observations, as 26 convertibles in our sample have a floating or varying coupon rate. We have reestimated all the regression models in this paper when we exclude these 26 convertibles, and find that our
results are qualitatively unchanged.
28
Panel A of Table V provides a univariate analysis of the average offering discount.
The average offering discount on the 603 issues is 4.9%. As in Brophy, Ouimet, and
Sialm (2009), we distinguish firms in which hedge funds purchase the majority of the
convertible issue from firms with a minority of hedge fund involvement. Firms with a
majority involvement of hedge funds have an average discount of 4.8% on their
convertible issues, while firms with a minority hedge fund involvement have an average
discount of 6.1%. The difference between the two subsamples is not significantly
different (t-statistic equals −0.510). The finding that the discount is not significantly
higher for issues to hedge funds is evidence against the view that convertibles are sold to
hedge funds as a last resort source of financing.
In unreported analyses we have compared issue discounts in a multivariate setting.
The dependent variable is the offering discount and the primary explanatory variable is a
dummy variable that equals one when hedge funds buy the majority of the security
offering and zero otherwise.26 Control variables are the Altman Z-score, return volatility,
NASDAQ-listing, firm size, institutional ownership, relative offering proceeds, Amihud
liquidity, whether the firm pays a dividend, and whether the convertible is callable,
putable, combined with a stock repurchase, or a cash settlement. We again find no
evidence that hedge funds obtain higher discounts than other investors. In fact, discounts
are insignificantly smaller when the majority of the issue is sold to hedge fund investors
(coefficient equals −0.020, t-statistic equals −0.769).
26
We follow Brophy, Ouimet, and Sialm (2009) in measuring hedge fund involvement with a dummy
variable that equals one when we observe that hedge funds buy the majority of the security offering, and
that equals zero otherwise. The results are robust to measuring the hedge fund involvement dummy as
either an above-median percentage of the issue purchased by hedge funds or an above-median percentage
of initial buyers of the issue classified as hedge fund buyers.
29
We conclude that although hedge funds purchase convertibles at a discount, the
discount is not significantly larger than the discount given to other investors in
convertibles. This finding is consistent with convertible bond issues to hedge funds being
a low-cost way of distributing equity exposure, rather than the last resort financing
opportunity open to the issuers.
B. Total issue costs: Convertibles to hedge funds versus seasoned equity issues
We can use our estimates of convertible offering discounts to compare the costs
of issuing convertibles to the costs of a seasoned equity offering. The idea is to estimate
what the costs would have been for our sample of convertible issuers when they had
chosen a seasoned equity issue instead of a convertible offering. We follow the procedure
of Dunbar (1995) and Ng and Smith (1996) to provide cost estimates for when a different
issue method would have been chosen. They examine the use of warrants as underwriter
compensation, and find that warrants are used to compensate underwriters if the cost of
this method is lower than what it would have been when cash compensation alone had
been used. Both papers stress the importance of using a two-stage procedure to control
for self-selection issues.
We calculate the issue costs of a security as the sum of the offering discount and
gross spread. Our convertible sample in this subsection consists of convertible issues in
which hedge funds account for the majority of issue proceeds. Firms in 144A offerings
typically sell their convertibles to qualified institutional buyers through an underwriter,
who demands a spread. We obtain the gross spread (as a percentage of gross issue
30
proceeds) from SDC.28 For SEOs, we calculate the offering discount as the difference
between the offer price and the closing price on the offer date, and scale by the closing
price on the offer date. Both the variables required for the offering discount and the gross
spread for our SEO sample are obtained from SDC. Because issue cost data are not
available for all observations, our analysis in this subsection relates to a subset of our
earlier sample. We have all necessary information for 1,343 SEOs and 151 convertible
issues in which hedge funds account for the majority of proceeds.
The average issue cost of a seasoned equity offering for the 1,343 firms in our
sample is 7.75%, which consists of an average SEO discount of 3.01% and an average
gross spread of 4.74%. These averages are similar to those reported in other recent papers
(see Eckbo, Masulis, and Norli, 2007). The average issue cost for the 151 convertibles in
our sample is 9.23%, which consists of an average issue discount of 6.55% and an
average gross spread of 2.68%.
Self-selection might be an issue in calculating what the cost of an offering would
have been because we can only observe those choices that are regarded by the firm as
most favorable, which can lead to biased estimates of expected issue costs. To control for
self-selection, we use a two-stage model. The first stage consists of the choice between a
seasoned equity offering and issuing convertibles to hedge funds. We have modeled this
choice in Table IV, and will use Model 2 of this table to estimate the inverse Mills ratio.29
We then analyze the determinants of SEO and convertible issue costs by adding the
28
We have checked and extended the gross spread data in SDC (available for 143 observations) with data
from the Mergent Fixed Income Securities Database (5 additional observations) and the issue prospectuses
(3 additional observations).
29
See Dunbar (1995) for a more detailed description of this procedure (which is based on Lee, 1978).
31
estimate of the inverse Mills ratio to regressions of issue costs on a range of issuer
characteristics. These regression estimates are reported in Panel B of Table V.
Model 1 is the most important model of Panel B of Table V. It shows the
estimation of the determinants of issue costs for our sample of SEO issues. It are these
coefficients that we will use to forecast the issue costs of an SEO for our sample of
convertible issuers. It can be seen from Model 1 that the issue costs of an SEO are higher
for firms that have a higher likelihood of financial distress, have volatile returns, and are
listed on NASDAQ. These results corroborate the findings of prior studies on the costs of
seasoned equity offerings. Issue costs are on average lower when firms are large, when
institutional ownership is high, and when firms do not pay dividends.
We use the estimated coefficients in Model 1 of Panel B to obtain forecasts of
expected issue costs of convertible issuers had they used a seasoned equity offering.
Forecasts are calculated as the product of regression coefficient estimates and the
independent variables, excluding the inverse Mills ratio. The coefficient for the inverse
Mills ratio is not used in obtaining cost estimates since the ratio’s unique purpose is to
adjust for potential bias in the regression errors. The results, presented in Panel C, show
that for the 151 convertible issuers in our sample the estimated issue cost of an SEO is
11.10%. This estimated cost is significantly higher than the cost of issuing convertibles to
hedge funds, which is 9.23%. This finding is in line with our story that convertibles sold
to hedge funds are the least-cost financing choice for firms with relatively high costs of
seasoned equity offerings.
Model 2 of Panel B shows the estimation of the determinants of issue costs when
a firm sells the majority of a convertible issue to hedge funds. Due to our limited sample
32
size in Model 2, this analysis has to be interpreted with the appropriate caution. In
contrast to seasoned equity offerings, we find that the Altman Z-score, return volatility,
and firm size do not significantly affect the cost of issuing convertibles. Similar to
seasoned equity offerings, a NASDAQ-listing is positively related to issue costs. The
significant effect of the inverse Mills ratio indicates that self-selection is important. The
positive sign of the inverse Mills ratio is in line with firms choosing securities to
minimize issue costs (see Dunbar, 1995). We use the estimation in Model 2 to predict
what SEO firms would have paid if they had chosen to sell convertibles to hedge funds.
We find that these forecasted costs are 11.03%, indicating that for our sample of SEO
firms it would have been more expensive to go to the convertible market.
VI. The potential maintenance of short positions by hedge funds
If hedge funds are low-cost distributors of equity exposure, the question arises as
to how long hedge funds maintain their ownership of a newly issued bond; i.e., for how
long might hedge funds bear the cost of maintaining a short position? This period could
be very short if hedge funds sell their convertibles on to non-hedge fund qualified
institutional buyers. The period could also be relatively short as Huang and Ramirez
(2010) show for a sample from 1996 to 2004 that 88% of 144A convertible offerings are
subsequently registered for public trading, typically within 90 days after the deal’s
closing date.
If hedge funds were to never sell convertible bonds on to non-hedge fund investors,
they would need to hedge for the realized life of the bond. The realized life will often be
less than the contractual life of the bond. While a convertible can survive until its
33
notional maturity, the issuer may go bankrupt.30 Or, the convertible holder may
voluntarily convert, or a call may force conversion. Finally, the convertible holder may
exercise a put option inherent in some bonds. Therefore, in order to determine an upper
bound on just how long hedge funds may remain short in an issuer’s stock, we investigate
how long convertible issues survive in practice.
Using balance sheet data (Compustat Item DCVT) we determine the fraction of a
convertible still outstanding in the five years after issue. We examine only instances
where the firm did not already have convertibles outstanding (from an earlier offering) at
the time of issue since we are unable to assign aggregate reductions in a firm’s
convertibles outstanding to particular issues. We assign a missing value code to a
particular year for a given bond if a second convertible bond is issued by that firm. We
also assign a missing value code if the firm seizes to exist in Compustat.
[ please insert Table VI here ]
Table VI reports the average (across the non-missing data) of the percentage of the
original issue still outstanding each year after issue. This average is likely to be an
upward biased estimate of the fraction of a convertible issue that actually survives for two
reasons. First, if a firm no longer exists its convertible bonds may have effectively
“matured” as a result of bankruptcy. Or a firm may no longer exist because it has been
taken-over, in which case the bondholders may have voluntarily converted. Second,
instances where a firm makes a second convertible bond issue may be cases where the
30
Interestingly, in court-administered reorganizations convertible bondholders have at times been awarded
only the same amount as that awarded to the holder of the number of shares the bond was convertible into;
i.e., bondholders were effectively forced to convert just when they would have most valued down-side
protection.
34
first bond was called (and the holders were forced to convert). In both of these events, 0%
of the (initial) issue remains outstanding. The number of observations used in calculating
the average each year is reported in parentheses. In forming subsamples, we determine
whether a convertible bond issue fell into the below-median or the above-median hedge
fund involvement subsample. We do not consider the minority and majority hedge fund
involvement distinction in this analysis because of the limited number of observations
with minority hedge fund involvement (only 5 observations with minority hedge fund
involvement have a value for “% outstanding after 5 years”).
On average no more than 13.38% of convertibles are still outstanding five years
after issue. For bonds with above-median issuance to hedge funds, the average
survivorship rate after five years declines to 7.82%. Since the mean (median) time to
maturity at issuance of our sample of 629 privately-placed convertible bond issues is
15.26 years (20 years), we can conclude that the effective life of convertible bonds
privately-placed with hedge funds is much less than their notional maturity.31
VII. The establishment of short positions by hedge funds
A potential second way to examine how long hedge funds maintain their ownership
of a newly issued bond is to consider changes in short interest. We have examined the
changes in short interest in the years after a convertible issue. Although the results seem
to indicate that the initial increase in short interest has evaporated 5 years after the issue,
changes in short interest can be quite volatile. The analysis is also complicated as the
31
The conversion of a high fraction of the convertible bonds issued is consistent with the sample’s mean
(median) conversion premium at the time of issue of 33.81% (30%). The conversion premium is the excess
of the conversion price over the stock price expressed as a percentage of the stock price. Equivalently, the
conversion premium is the face value of the bond relative to its conversion value at the time of issue.
35
expected short positions of arbitrageurs change when the firm’s stock price changes (due
to changes in the delta-neutral position), and changes in short interest can also be caused
by the arrival of new information about the firm. As mentioned in Section I.A, another
downside of focusing on short interest is that the initial increase in short interest around
the issue date could be partly due to valuation shorting by those who believe their
information is not appropriately reflected in prices.
As a final test we follow Choi, Getmansky, and Tookes (2009) in examining
changes in monthly short interest data around convertible issue dates. Our data allow us
to directly tie the peak in short interest to the arbitrage activities of hedge fund investors.
We relate the increase in monthly short interest around convertible issue dates to the
increase expected as hedge funds establish delta-neutral hedge positions. The expected
volume of shorting by hedge funds is the product of the percentage of an issue purchased
by hedge funds with the delta-neutral short position for the entire issue:
Expected short sales =
face value of entire issue
× delta × % purchased by hedge funds.
conversion price
We use the Compustat mid-month short interest files (available from 2003) to
compute the actual monthly change in short interest.32 We are able to observe the actual
change in monthly short interest at the time of issue for 308 of the convertible bonds in
our sample. We find that the correlation between expected changes and actual changes is
66.4% (significant at the 1% level). This high correlation coefficient implies that the
contemporaneous jump in short interest is in fact the result of hedging by hedge funds.
32
As the cutoff date of the monthly short interest numbers is three trading days prior to the 15th of each
month, we carefully assign the convertible issues to the relevant short interest month (as in Bechmann,
2004).
36
VIII. Conclusion
Although the majority of buyers in the convertible market are not hedge funds, we
find that on average hedge funds account for 73.4% of the proceeds of privately-placed
convertible issues. Further, the bulk of capital raised via convertibles is via a privateplacement. The typical hedge fund buyer is involved in a larger number of new issues of
convertibles than is the typical non-hedge fund buyer. And, the typical hedge fund buyer
invests more in any particular new convertible than the typical non-hedge fund buyer
invests.
We exploit the variation in hedge fund involvement across issues to show that
investor identity matters in the convertible debt market. We argue that firms with high
costs of seasoned equity offerings privately place convertibles with hedge funds. These
hedge funds simultaneously short stock so as to hedge themselves against changes in the
stock price. In effect, hedge funds are distributing equity exposure into the open market
via their short positions. Firms that have trouble finding investors willing to bear
exposure to large equity positions can instead use hedge funds to distribute this equity
exposure to a larger number of well-diversified investors in the open market.
Although we find that firms attracting hedge fund investors have a higher chance of
bankruptcy and more volatile stock returns, we do not find that these firms offer higher
discounts on their convertibles. This is in line with hedge funds serving as relatively
cheap distributors and not as hedge funds being investors of last resort. The difference
with the findings of Brophy, Ouimet, and Sialm (2009), who study PIPE issuers and do
find evidence for the last resort hypothesis, can be explained by differences in the issuers
of PIPEs and convertibles. PIPE issuers are generally very small and distressed firms,
37
while the convertible issuers in our sample are much larger. The firms in our sample
choose to issue convertibles to hedge funds because this is their least-cost financing
choice, not because it is their only choice.
38
Appendix A: Description of variables
Amihud Liquidity. The Amihud (2002) measure for liquidity is the daily average of a
firm’s absolute return over trading dollar volume in the year before the offering (× 106).
We use CRSP data to calculate this variable. A high Amihud score denotes illiquidity.
Call spread overlay. A dummy variable equaling one if the convertible is issued with a
call spread overlay, and zero otherwise. In a call spread overlay, the issuer purchases a
call option that mimics the call option embedded in the convertible bond and
simultaneously writes a call option on the same number of underlying shares at a higher
strike price. The net effect is analogous to issuing a convertible bond with a higher
conversion price. We obtain information on call spread overlays from the issue
prospectuses.
Callable. A dummy variable equaling one if the convertible has a call feature, and zero
otherwise. We obtain call information from SDC.
Cash settlement. A dummy variable equaling one if the convertible can potentially be
settled in cash, and zero otherwise. Settlement information is obtained from the issue
prospectuses, as in Lewis and Verwijmeren (2009). Securities that contain cash
settlement features include one of the following conversion choices. Either an issuer 1)
must pay the conversion value (the number of shares a bondholder is entitled to receive
times the stock price at the conversion date) in cash (Instrument A); 2) may choose to
pay either fully in cash or the number of shares a bondholder is entitled to receive
(Instrument B), 3) must pay cash for the accreted value (principal value plus accrued
interest) and may satisfy the conversion spread (the excess of the conversion value over
the accreted value) in either cash or equity (Instrument C or net share settlements), or 4)
may pay any combination of cash and equity (Instrument X), but often there is a stated
policy to settle in cash.
Delta. Delta is the convertible’s sensitivity for small stock price changes and is calculated
as
39
 S
σ2 
ln(
)
+
(
r
−
δ
+
)T 


−δT
−δT
X
2
Delta = e N (d1 ) = e N 
,
σ T




where N(•) is the cumulative probability under a standard normal distribution, S is the
price of the underlying stock measured at day −5 (from CRSP), X is the conversion
price (from SDC), r is the yield on a 10-year U.S. Treasury Bond (from Datastream), δ
is the continuously-compounded dividend yield calculated as Compustat Item DVC
divided by the equity market value (Item PRCC_C x CSHO), σ is the annualized stock
return volatility, estimated with ten years of monthly stock return data (from CRSP),
and T represents the stated maturity of the convertible as of its issuance date (from
SDC).
Delta-neutral short position. The delta-neutral short position is the total number of
common shares that buyers of the convertible issue have to short to obtain a deltaneutral position. This number of shares can be calculated as (Calamos, 2003):
Delta-neutral short position =
face value of entire issue
× delta.
conversion price
We obtain information on the face value and the conversion price from SDC.
Dividend-paying. A dummy variable equaling one if Compustat Item DVC exceeds zero
at the beginning of the fiscal year, and zero otherwise.
Financial Distress (Z-score). The Altman Z-score is an estimate of the probability of a
firm’s bankruptcy, and is calculated as 1.2 (Working capital / Total assets) + 1.4
(Retained earnings / Total assets) + 3.3 (EBIT / Total assets) + 0.6 (Market value of
equity / Book value of liabilities) + (Sales / Total assets), which is implemented using
Compustat Items as 1.2 ((ACT − LCT) / AT) + 1.4 (RE / AT) + 3.3 (OIADP / AT) +
0.6 ((PRCC_C × CSHO) / (DLTT + DLC)) + SALE / AT. All variables are measured at
the beginning of the fiscal year. Z-scores above 100 and below −100 are winsorized. In
our regression estimations, we multiply the coefficient for the Altman Z-score by 100.
40
Firm size. Firm size is the market value of equity (measured at the beginning of the fiscal
year) calculated with Compustat Items PRCC_C × CSHO. In regression analyses we
employ the natural logarithm of the market value of equity as a measure for firm size.
Institutional ownership. The level of institutional ownership reported in the ThomsonReuters Institutional Holdings database scaled by total shares outstanding (both
measured at the fiscal-year end preceding the issue date).
Issue proceeds. Issue proceeds are the gross proceeds of the issue in millions of dollars,
as reported in SDC.
NASDAQ-listing. A dummy variable equal to one if the firm is listed on NASDAQ
(Compustat Stock Exchange Code 14), and zero otherwise.
Put rights. A dummy variable equaling one if the convertible has a put feature, and zero
otherwise. We obtain put information from SDC.
Relative size. A measure of the additional equity exposure being distributed compared to
the initial equity exposure. When comparing convertible bonds with each other we
measure relative size as the ratio of the delta-neutral short position to the shares
outstanding. When comparing convertible issues to hedge funds with seasoned equity
offerings we measure relative size as the ratio of the issue proceeds to the market value
of equity.
Return volatility. Volatility is calculated as the annualized standard deviation of monthly
stock return data (from CRSP) for ten years of data (or for a shorter period if ten years
of data are not available; we set the minimum requirement to twelve months of data).
Stock repurchase. A dummy variable equaling one if the convertible issue is combined
with a stock repurchase. This is the case if either the firm announces that it uses part of
the proceeds of the convertible issue to repurchase stock (in SDC or Factiva), or if both
transactions are announced separately on the same date (in Factiva).
41
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Figure 1
10 0 .0 %
9 0 .0 %
8 0 .0 %
70 .0 %
6 0 .0 %
50 .0 %
4 0 .0 %
3 0 .0 %
2 0 .0 %
10 .0 %
0 .0 %
2000
2001
2002
2003
2004
2005
2006
2007
2008
Figure 1. Percentage of convertible proceeds purchased by hedge funds
This figure shows the average involvement of hedge funds in convertible securities that
are privately placed under Rule 144A in a given year. The year 2008 percentage applies
to convertible issues during the first quarter of the year.
46
Table I. Hedge fund involvement and industry classifications
The sample period is January 2000 – March 2008. Panel A of this table reports the
number of buyers per privately placed convertible issue in our sample. Panel A also
reports the percentage of buyers in a convertible security that can be classified as a hedge
fund as well as the fraction of the issue purchased by hedge funds. Panel B shows the
fraction of the issue purchased by hedge funds for issues of firms in each of the 12 FamaFrench industry classifications.
Panel A.
Number of buyers
% of buyers classified
as hedge funds
% of issue purchased
by hedge funds
N
803
Mean
64.1
Median
54.0
St.dev.
44.6
Min.
1
Max.
320
803
56.4%
55.6%
18.6%
0.0%
100.0%
803
73.4%
75.3%
15.9%
0.0%
100.0%
N
15
9
50
41
9
224
33
22
53
160
90
97
Mean
66.4%
65.0%
70.0%
72.9%
78.8%
72.8%
72.8%
72.4%
72.6%
75.5%
74.3%
75.2%
Median
73.3%
65.8%
73.7%
74.1%
83.6%
75.4%
71.6%
75.4%
71.6%
75.9%
77.8%
75.7%
St.dev.
22.9%
14.7%
19.0%
19.3%
18.0%
16.1%
11.1%
19.3%
14.4%
14.4%
17.0%
13.5%
Min.
3.0%
47.7%
1.5%
0.0%
38.5%
10.8%
47.4%
7.2%
40.3%
34.6%
0.0%
39.2%
Max.
90.4%
82.8%
100.0%
99.3%
100.0%
100.0%
100.0%
94.5%
97.9%
100.0%
100.0%
100.0%
Panel B.
Consumer nondurables
Consumer durables
Manufacturing
Energy
Chemicals
Business equipment
Telecommunications
Utilities
Wholesale & retail
Healthcare
Financial
Other
47
Table II. Issuer and issue characteristics and hedge fund involvement
The sample period is January 2000 – March 2008. Issues by utilities and financial
institutions are excluded. This table presents a univariate analysis of the differences in
issuer and issue characteristics for privately placed convertible issues with an abovemedian participation by hedge funds (hedge funds purchase more than 75.3% of the
convertible) and a below-median participation of hedge funds (less than 75.3%). The
table also reports the differences for issues in which the majority is purchased by hedge
funds versus issues with only a minority purchased by hedge funds. The difference in
means t-statistics do not assume equal variances for the two samples being compared. See
Appendix A for a description of issuer and issue characteristics. * and ** indicate
significance at the 5% and 1% levels.
All
Issues
Subsamples with differing levels of
hedge fund involvement
Abovemedian
Belowmedian
Diff. of
means tstatistic
Majority
16.070
13.813
18.349
−1.907
15.946
17.674
−0.367
Return volatility
0.326
0.339
0.312
2.898**
0.327
0.303
1.393
NASDAQ-listing
0.536
0.595
0.476
3.006**
0.543
0.444
1.266
Firm size ($ mill)
4143
3860
4429
−0.609
4299
2126
3.555**
Institutional ownership
0.680
0.684
0.676
0.481
0.677
0.721
−1.306
Relative size: Delta-neutral
short position ÷ shares
outstanding
0.134
0.138
0.130
0.715
0.130
0.180
−1.323
Amihud Liquidity
0.030
0.024
0.037
−0.581
0.031
0.018
0.926
Dividend-paying
0.197
0.168
0.227
−1.865
0.200
0.156
0.784
Minority
Diff. of
means tstatistic
Issuer characteristics
Financial Distress (Z-score)
Issue characteristics
Callable
0.723
0.646
0.802
−4.448**
0.714
0.844
Stock repurchase
0.116
0.152
0.080
2.837**
0.123
0.022
3.878**
Call spread overlay
0.081
0.127
0.035
4.265**
0.086
0.022
2.530*
Cash settlement
0.404
0.494
0.313
4.689**
0.411
0.311
1.373
Put rights
0.424
0.421
0.428
−0.183
0.425
0.422
0.032
Delta
0.867
0.860
0.873
−1.681
0.865
0.888
−1.834
313
304
322
−0.478
319
241
Issue proceeds ($ mill)
−2.258*
2.537*
48
Table III. Hedge fund involvement, issuer characteristics, and issue characteristics
The sample period is January 2000 – March 2008. Issues by utilities and financial
institutions are excluded. This table presents the results of an OLS regression model
estimating the relation between various issuer and issue characteristics and the
involvement of hedge funds. The dependent variable in Model 1 is the percentage of the
issue purchased by hedge funds. The dependent variable in Model 2 is the percentage of
the issue’s buyers classified as hedge funds. See Appendix A for a description of the
issue and issuer characteristics. We report standard errors clustered at the firm level in
parentheses. * and ** indicate significance at the 5% and 1% levels.
Prediction
Constant
Financial distress (Z-score)
−
Return volatility
+
NA SDA Q-listing
+
Firm size
Institutional ownership
+
Relative size: Delta-neutral short
position ÷ shares outstanding
Amihud Liquidity
−
Dividend-paying
−
Callable
−
Stock repurchase
+
Call spread overlay
Cash settlement
Put rights
N
R2
−
% of issue
purchased by
hedge funds
(1)
0.874**
(0.061)
−0.044*
(0.021)
0.214**
(0.071)
0.025*
(0.012)
−0.022**
(0.005)
−0.045
(0.030)
−0.200**
(0.053)
0.004
(0.008)
0.025
(0.016)
−0.055**
(0.016)
0.030
(0.017)
0.054*
(0.022)
0.034*
(0.013)
0.036**
(0.014)
629
0.132
% of purchasers
classified as hedge funds
(2)
0.769**
(0.079)
−0.036
(0.024)
0.317**
(0.083)
0.024
(0.014)
−0.037**
(0.007)
−0.069
(0.041)
−0.204**
(0.076)
−0.005
(0.011)
0.030
(0.020)
−0.040*
(0.020)
0.019
(0.024)
0.050*
(0.031)
0.030
(0.017)
0.065**
(0.017)
629
0.137
49
Table IV. Determinants of the decision to distribute equity exposure via hedge funds
This table compares convertible issues in which the majority of the issue is purchased by
hedge funds with seasoned equity offerings. The sample period is January 2000 – March
2008. Issues by utilities and financial institutions are excluded. The dependent variable of
the binary logit model is a dummy variable equal to one for convertible issues in which
the majority of the issue is purchased by hedge funds and to zero for seasoned equity
offerings. The elasticities are in the form d(lny)/d(lnx). See Appendix A for a description
of the issue and issuer characteristics. We report standard errors clustered at the firm
level in parentheses. * and ** indicate significance at the 5% and 1% levels.
Constant
Financial distress (Z-score)
Return volatility
NA SDA Q-listing
Firm size
Institutional ownership
Relative size: proceeds ÷
market value of equity
Amihud Liquidity
Dividend-paying
Convertible issues to hedge funds versus seasoned
equity issues
(1)
(2)
Coefficients
Elasticities
Coefficients Elasticities
11.800**
−3.989**
(3.246)
(0.475)
−0.775**
−0.151
−0.563**
−0.110
(0.182)
(0.185)
0.703**
0.420
0.637**
0.385
(0.207)
(0.234)
0.122
0.064
0.209
0.111
(0.138)
(0.146)
0.252**
1.354
0.335**
1.822
(0.059)
(0.063)
1.785**
0.775
1.694**
0.742
(0.257)
(0.264)
0.045
0.010
0.051*
0.011
(0.024)
(0.024)
−11.341**
(1.941)
−0.239
(0.179)
Equity market return
Interest rate
Credit spread
Leading indicators
N
Pseudo R 2
2,782
0.172
−0.600
−0.032
−11.069**
(1.933)
−0.247
(0.188)
0.279
(0.488)
−1.146**
(0.149)
−0.868**
(0.285)
−0.095**
(0.021)
−0.591
−0.033
0.010
−4.711
−1.757
−7.871
2,782
0.206
50
Table V. Hedge fund involvement and offering discounts
The sample period is January 2000 – March 2008. Issues by utilities and financial
institutions are excluded. Panel A reports the offering discount for our overall sample,
issues in which the majority of the convertible is bought by hedge funds, and issues in
which the minority of the convertible is bought by hedge funds. The offering discount is
the difference between the theoretical price and the offer price relative to the theoretical
price. Theoretical prices are calculated using MATLAB’s pricing algorithm:
http://www.mathworks.com/access/helpdesk/help/toolbox/finfixed/cbprice.html. Panel B
presents the estimated relation between issue costs and issuer characteristics. Issue costs
are the sum of the offering discount and gross spread. We estimate the cost of a seasoned
equity issue in Model 1, and we estimate the cost of a convertible offering in which the
majority is purchased by hedge funds in Model 2. See Appendix A for a description of
the issuer characteristics. We report standard errors clustered at the firm level in
parentheses. In Panel C we use the estimated coefficients in Panel B (excluding the
inverse Mills ratio) to forecast the issue costs for firms had they chosen the alternative
security issue. The difference in means t-statistics do not assume equal variances for the
two samples being compared. * and ** indicate significance at the 5% and 1% levels.
Panel A.
All Issues
Offering discount
0.049
Issues with a
majority of the
issue purchased
by hedge funds
0.048
Issues with a
minority of the
issue purchased
by hedge funds
0.061
Difference of
means tstatistic
−0.510
51
Panel B.
Constant
Financial Distress (Z-score)
Return volatility
NASDAQ-listing
Firm size
Institutional ownership
Relative size: proceeds ÷
market value of equity
Amihud Liquidity
Dividend-paying
Inverse Mills ratio
N
R2
Issue costs
(1)
(2)
Seasoned equity
Convertible issue to
issue
hedge funds
0.157**
−0.101
(0.013)
(0.102)
−0.011**
−0.003
(0.004)
(0.003)
0.016**
0.008
(0.004)
(0.043)
0.005*
0.050*
(0.002)
(0.023)
0.013
−0.008**
(0.011)
(0.001)
0.090
−0.011*
(0.052)
(0.005)
0.044
0.138
(0.064)
(0.105)
0.019
0.003
(0.032)
(0.325)
0.006*
0.018
(0.003)
(0.028)
0.086**
−0.004
(0.023)
(0.003)
1,343
0.265
151
0.194
Panel C.
Mean actual cost of issuing
Mean forecasted cost of issuing if other
security was issued
Mean change in cost of issuing if other
security was issued
Difference of means t-statistic
Convertible
sample
9.23%
11.10%
Issue costs
Seasoned equity
sample
7.75%
11.03%
1.87%
3.28%
2.002*
4.636**
52
Table VI. Estimated percentage of convertible bond issue outstanding in years after
issue
The sample period is January 2000 – March 2008. Issues by utilities and financial
institutions are excluded. In this table we determine the fraction of a convertible still
outstanding in the five years after issue. We assign a missing value code to a particular
year for a given bond if a second convertible bond is issued by that firm. We also assign a
missing value code if the firm no longer exists. The number of issues used in calculating
the average is shown in parentheses. An above-median participation by hedge funds
indicates that hedge funds purchase more than 75.3% of the convertible. The difference
in means t-statistics do not assume equal variances for the two samples being compared.
% outstanding after n years
1 year
2 years
3 years
4 years
5 years
Total
AboveBelowmedian hedge median hedge
fund
fund
involvement
involvement
94.22%
93.02%
95.50%
(280)
(144)
(136)
86.69%
83.17%
90.17%
(221)
(110)
(111)
65.40%
64.14%
66.50%
(172)
(80)
(92)
41.42%
33.45%
47.71%
(145)
(64)
(81)
13.38%
7.82%
18.15%
(104)
(48)
(56)
Difference of
means tstatistic
−1.12
−1.73
−0.35
−1.89
−1.73
53