Convertible Bonds

In Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. The valuation model of inflation-indexed (or equivalently foreign-currency) convertible bonds derived in this paper considers two sources of uncertainty allowing both the underlying stock and the consumer-price-index to be stochastic and incorporates credit risk in the analysis. We approximate the pricing equations by using a Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate the sensitivity of the theoretical values with respect to the characteristics of the issuer, the economic environment and the security s characteristics (number of principal payments). Moreover, we demonstrate the usefulness and the limitations of the pricing model by using inflation-indexed and foreign-currency linked convertibles traded on the Tel- Aviv stock exchange.

CASSAZIONE CIVILE, I Sezione, 7 gennaio 2010, n. 11125 -CARNEVALE Presidente -PATRONE Relatore -(diff.) P.M. -C.C. S.P.a (avv. Fusillo, Nardulli e Cossu) c. Russo (avv. Zacchia e Crispo). Cassa e decide nel merito, App. Genova, 28 ottobre 2003, n. 884.

Efek derivatif merupakan efek turunan dari efek utama baik yang bersifat penyertaan maupun utang. Efek turunan dapat berarti turunan langsung dari efek utama maupun turunan selanjutnya. Derivatif merupakan kontrak atau perjanjian yang nilai atau peluang keuntungannya terkait dengan kinerja aset lain. Aset lain ini disebut sebagai underlying assets. Dalam pengertian yang lebih khusus, derivatif merupakan kontrak finansial antara dua atau lebih pihakpihak guna memenuhi janji untuk membeli atau menjual assets atau commodities yang dijadikan sebagai obyek yang diperdagangkan pada waktu dan harga yang merupakan kesepakatan bersama antar pihak penjual dan pihak pembeli. Adapun nilai di masa mendatang dari obyek yang diperdagangkan tersebut sangat dipengaruhi oleh instrumen induknya yang ada di spot market.

This paper analyzes convertible arbitrage, one of the most successful hedge fund strategies. We start by identifying convertible arbitrage activities. We find convertible bonds to be underpriced at the issuance dates. At the same time, short sales of underlying equity significantly increase. Both effects are stronger and more persistent for equity-like than for debt-like convertibles. Although convertible arbitrage positively affects markets by providing liquidity, we argue that short sales pressures negatively affect both shareholders and existing bondholders. An investigation of the determinants of convertible arbitrage returns shows that, over a one-year period following the issue, equity-like convertibles earn a return that is more than 20 percentage points higher than the return of debt-like convertibles. In recent years the returns from convertible arbitrage have strongly decreased, because the universe of issuers shifted from the issuance of equity-like to debt-like convertibles.

This report is the result of a collaboration between CGAP and J.P. Morgan. CGAP is solely responsible for the printing and distribution of this Occasional Paper. CGAP is not affiliated with J.P. Morgan. Our objective is to provide benchmarks for valuation of microfinance equity, both private and publicly listed. Our analysis is based on two datasets: a sample of 144 private equity transactions, which represents the largest such dataset gathered to date, and data on 10 publicly traded micro finance institutions (MFIs) and low-income consumer lenders. 1

In this paper we discuss the significant computational simplification that occurs when option pricing is approached through the change of numeraire technique. The original impetus was a recently published paper (Hoang, Powell, Shi 1999) on endowment options; in the present paper we extend these results to the case of stochastic interest rates. We also discuss four additional option pricing problems within the framework of a change of numeraire:

In this paper we discuss the significant computational simplification that occurs when option pricing is approached through the change of numeraire technique. The original impetus was a recently published paper (Hoang, Powell, Shi 1999) on endowment options; in the present paper we extend these results to the case of stochastic interest rates. We also discuss four additional option pricing problems within the framework of a change of numeraire:

We compare valuation effects associated with debt issuance under SEC Rule 144A versus issuance in the public market. We find that nonconvertible debt Rule 144A issuers experience an incremental positive announcement effect when compared to their counterparts issuing in the public market. We attribute this to the timing of issuance under favorable market conditions and a reduction in informational asymmetry due to lender specialization. When compared to their public counterparts, convertible Rule 144A bond issuers often experience negative announcement effects and inferior post-issuance stock performance. We argue that this negative market reaction arises from a stronger opportunistic market-timing signal.

In this paper we solve a two-factor convertible bonds model that ÿts the observed term structure, calibrates the volatility parameters to market data and allows for correlation between the state variables. We propose the method of characteristics together with ÿnite elements for time and space discretization. An empirical investigation into the pricing of National Grid Group's convertible issue produced prediction errors of less than 5% for 215 successive trading days. ? (J. Hatgioannides). 0165-1889/03/$ -see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 -1 8 8 9 ( 0 2 ) 0 0 0 8 3 -0

The literature on the motives for the issuance of convertible debt is reviewed. This literature shows a large discrepancy between theory and practice. Surveys show that managers base their motives for the use of convertible debt on factors that are irrational according to the theoretical literature. This theoretical literature in turn offers a number of rational motives. These motives are based on the resolution of the problems of informational asymmetry and agency costs, on tax motivations and managerial entrenchment arguments. Most of the rational motives have been investigated in the cross-sectional studies, which offer general support to at least some of them. However, the survey studies find very little to no support for the rational motives. This might be due to either the sensitivity of the surveys to the question contents, to the use of weak proxies in the crosssectional studies, or a combination of these. In our view, future research in this field should aim for an approach that combines the use of survey data and cross-sectional analysis. We believe that such an approach may bridge the gap between theory and practice.

Since the seminal work of Ingersoll (1977b) the optimal time in which a firm should redeem its outstanding convertible bonds has received large attention by the financial literature. Several studies have put forward a number of possible costs and benefits for a firm if it interrupts the life of its convertible bonds prior to their contractual maturity. However, in this paper we argue that the managerial decision to call back a convertible bond is mainly driven by a fundamental variable almost neglected up until now: the time value extraction from bondholders' conversion option. Accordingly, we propose a measure for the effective convenience of calling-which we define as net time value advantage-and we show, using a survival analysis, that it is more effective than previously proposed measures in explaining the firms' observed call policy.

1 The economics literature does show that risk averse agents have an incentive to purchase insurance from risk neutral agents, i.e., insurance companies, in a competitive insurance market but the analysis has not been replicated in a financial market setting. In fact, if it were and the usual definition of complete financial markets was employed then we could obtain another irrelevance result in which risk averse individuals would be indifferent between purchasing insurance and purchasing a portfolio of securities. 2 See . There are also other generalizations that show other financial instruments to be redundant. For example, see . 3 The current paradigm is the complete financial market model; it is not the CAPM. 4 The literature in finance also provides a number of motivations for hedging but does not typically distinguish between hedging instruments or provide guidance on the use of the many hedging instruments available, e.g. see

... The payoff to the underwriter per bond, ignoring transaction costs, is FS whenm * SL CUw,Huw=FS+FT+m'SLCL.V when m*SL CL,IV. ... in the underwrittencall sample; the difference is significant at the 0.01 level according to the t test and at 0.05 according to the Wi(coxon test. ...

This paper analyzes the effect of corporate debt offerings on stock prices. Straight debt offerings have non-positive price effects, while convertible debt offerings have significantly negative effects. Public utility mortgage (non-convertible) bond offerings have marginally negative effects, and the effect is significantly negative when the proceeds are used to finance the utility's investment program. Cross-sectional regressions reveal no relation between offer-induced price effects and offering size, rating, post-offer changes in abnormal earnings or debt-related tax shields. The evidence is inconsistent with theories predicting that the price etTects of capital structure changes go in the direction of the leverage change.

The principle of “numerus clausus” of securities issued by Société Anonyme (shares, bonds, founding titles, warrants) and its disintegration

Οι εξελισσόμενες ανάγκες χρηματοδότησης των επιχειρήσεων, οι αυξανόμενες απαιτήσεις των επενδυτών και η διεθνοποίηση των κεφαλαιαγορών κατέστησαν τις παραδοσιακές μορφές τίτλων ανεπαρκείς, δρομολογώντας αλλεπάλληλη δημιουργία νέων κινητών αξιών. Όμως, τυχόν άρνηση του «κλειστού αριθμού» (numerus clausus) των τελευταίων για την ημεδαπή ανώνυμη εταιρία, δηλαδή αναγνώριση της δυνατότητας των συναλλασσομένων να διαμορφώνουν κατά το δοκούν τους τίτλους της, καταλήγει αντιμέτωπη με την ίδια την πεμπτουσία της. Η μοναδικότητα της άρρηκτης σχέσης που συνδέει κάθε μέτοχο με την εταιρία «του» (affectio societatis), η αρχή της ισότιμης μεταχείρισης των μετόχων, η σταθερότητα του κεφαλαίου, το αδιαίρετο του πλέγματος των δικαιωμάτων που απορρέουν από ορισμένο μετοχικό ή ομολογιακό τίτλο, κλονίζονται σταδιακά, ενώπιον των νέων περίτεχνων τίτλων που δοκιμάζονται επιτυχημένα στις συναλλαγές. Συγκριτικές παρατηρήσεις φανερώνουν την κυρίαρχη τάση απελευθέρωσης και των τελευταίων ρυθμιστικών «στεγανών» στην ηπειρωτική Ευρώπη, ακολουθώντας τις επινοήσεις της χρηματοοικονομικής βιομηχανίας.
Σε συνέχεια προηγούμενων μεταρρυθμίσεων, ο νέος νόμος για την Α.Ε. (Ν. 4548/2018) συστηματοποιεί και εκσυγχρονίζει το δίκαιο των κινητών αξιών της. Θεσπίζει «καταρχήν περιοριστικό» κατάλογο τεσσάρων (4) ειδών τίτλων (μετοχές, ομολογίες, τίτλοι κτήσης μετοχών, ιδρυτικοί τίτλοι), με την επιφύλαξη νομοθετικής καθιέρωσης πρόσθετων τίτλων. Όσον αφορά στις μετοχές, επιβεβαιώνει την καταστατική ελευθερία των μετόχων, ως προς την εξειδίκευση και διαφοροποίηση των προνομίων (περιουσιακής φύσης) των προνομιούχων μετοχών. Διευρύνει τις διαθέσιμες κατηγορίες εξαγοράσιμων μετοχών και διορθώνει παρωχημένες ρυθμίσεις για τους ιδρυτικούς τίτλους. Όσον αφορά στις ομολογίες, αίρει προϋφιστάμενους περιορισμούς της συμβατικής ελευθερίας και προβαίνει σε πανηγυρική καταγραφή επιμέρους σύγχρονων μορφών.
Η εισαγωγή των warrants (επί μετοχών) στο «οπλοστάσιο» των κινητών αξιών της α.ε. αποτελεί ξεχωριστή καινοτομία. Πρόκειται για την αυτόνομη τιτλοποίηση ενός δικαιώματος προαίρεσης με αντικείμενο την απόκτηση μετοχών. Τα σύνθετα χαρακτηριστικά του νέου τίτλου, ιδίως η χρηματοοικονομική μόχλευση, ο «θνησιγενής» χαρακτήρας, η δρομολόγηση ετεροχρονισμένων αυξήσεων κεφαλαίου και οι συνθήκες δευτερογενούς διαπραγμάτευσης στην κεφαλαιαγορά, ανοίγουν σπουδαίες προοπτικές για την αξιοποίησή του, τόσο στην ενίσχυση παραδοσιακών και νεοφυών επιχειρήσεων, ακόμη και υπό συνθήκες αφερεγγυότητας ή ραγδαίας ανάπτυξης, όσο και στην άμυνα έναντι προτάσεων εξαγορών ή στην υλοποίηση εταιρικών μετασχηματισμών.
Τα φαινομενικά στεγανά των (4) ειδών κινητών αξιών και τα όρια του «numerus clausus», έρχονται να αμφισβητήσουν έμπρακτα δύο πρόσθετες ρυθμίσεις.  Χάρη στη δυνατότητα σύζευξης τίτλων (“stapled securities”) και ανάλογα με τα χαρακτηριστικά της (διαρκή, «ασφυκτική», προσωρινή), διανοίγονται περιθώρια de facto δημιουργίας πρωτότυπων συνδυασμών κινητών αξιών και ευθυγράμμισης των οικονομικών συμφερόντων διαφορετικών κατηγοριών εταιρικών stakeholders. Αντίστροφα, η δυνατότητα κατάτμησης των δικαιωμάτων τίτλων (“stripped securities”) συνιστά κάμψη της «αρχής του αδιαιρέτου». Οδηγεί στη δημιουργία νέων αξιών, μέσω κατακερματισμού σύνθετων μορφών, θέτοντας ενδιαφέροντα ερμηνευτικά ζητήματα για τα διαθέσιμα εργαλεία έννομης προστασίας των κατόχων.
Ακόμη και μετά το Ν. 4548/2018 εξακολουθούν να υφίστανται αρκετές «αρρύθμιστες κινητές αξίες», των οποίων δεν επιτρέπεται η έκδοση από την α.ε. Είναι το τίμημα της «λελογισμένης απελευθέρωσης της αγοράς επενδυτικών αξιογράφων», που επέλεξε ο νομοθέτης. Όσο για τις πολυάριθμες πλέον αναγνωριζόμενες κατηγορίες κινητών αξιών, συμπεριλαμβανομένων των συζευγμένων, κατατμημένων και «μεταλλασσόμενων» τίτλων, ενδείκνυται να αξιολογούνται ως ανταγωνιστικά μεταξύ τους, εργαλεία χρηματοδότησης της εκδότριας. Αποδεικνύεται ότι τα ουσιαστικά χαρακτηριστικά των δικαιωμάτων των κομιστών τους είναι προεχόντως ζήτημα της εσωτερικής καταστατικής οργάνωσης και συμβατικής διαμόρφωσης της α.ε., και λιγότερο της αναγκαστικού δικαίου νομοθεσίας. Υπό το ίδιο πρίσμα, αντί της τυπικής ορολογικής ένταξης, ο συνδυασμός επενδυτικού κινδύνου/απόδοσης (risk/return) κάθε συγκεκριμένου τίτλου αποτελεί την πλέον κρίσιμη ιδιότητά του, που μπορεί να συνεισφέρει ιδίως στην ερμηνευτική επίλυση ασαφών και αμφισβητούμενων ιδιωτικών (εταιρικών και συμβατικών) ρυθμίσεων.

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Continuous creation of new securities in international markets practice, based on the needs of corporations, investors and the inventions of financial industry, calls into question the principle of the "numerus clausus" of the securities issued by greek Société Anonyme. Recent L. 4548/2018 systematizes and modernizes the law of companies’ securities, by establishing a "mainly restrictive" catalogue comprising four (4) types of securities. In addition to extending the available features and categories of shares, bonds and founding titles, distinct innovation has been observed in relation to the legislative recognition of warrants, the regulation of autonomous securitization of an option to acquire shares. The apparent frontiers distinguishing among the above types have been further questioned by the legal rules about 'stapled securities' and 'stripped securities'. Ultimately, they lead to the disintegration of the principle of 'numerus clausus', the creation of complex combinations or fragmented forms of securities, which in turn raise interesting interpretative issues in respect of the legal remedies available to their holders.

Convertible exchangeable preferred stock includes an option for the issuer to exchange the preferred for convertible bonds with identical pre-tax cash flows and conversion terms. In other respects this innovative corporate security is identical to traditional convertible preferred stock. The exchange feature provides the issuer with a potentially valuable option to swap a non-tax-deductible expense for a tax-deductible one. The

This thesis examines development of equity-linked securities market in Europe, volumes of which have increased significantly only during the last decade. The area of this study has enjoyed little academic attention that makes this paper more valuable. The following aims had been set for this study:

It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, this holds under mild integrability conditions. However, for practical purposes, existence and uniqueness are not enough. In order to further develop these results in Markovian setups , one also needs a (simply or doubly) reflected BSDE to be well posed, in the sense that the solution satisfies suitable bound and error estimates, and one further needs a suitable comparison theorem. In this paper, we derive such estimates and comparison results. In the last section, applicability of the results is illustrated with a pricing problem in finance.

Arbitrage-free price bounds for convertible bonds are obtained assuming equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior. Uncertainty in volatility is modeled using a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects. Increasingly pessimistic values for the issuer's substitution asset obtain as we introduce more uncertainty during the notice period. Uncertain in volatility, in particular, appears to be an important determinant of the call premium that is so often observed in issuer's call policies.

The paper examines the pricing performance of a convertible bond valuation model developed within the Duffie and Singleton (1999) reduced-form credit risk valuation framework. A sample of monthly US convertible bond prices observed during the period from January 2001 to September 2002 is used. Our results suggest that while it produces prices that are consistently higher than observed market prices when the embedded conversion option is out-of-the-money, the model underestimates prices when the conversion option is in-the-money. While at least part of the in-themoney bias can be attributed to the firm's optimal call policy assumed by the theoretical model, the out-of-the-money bias is more difficult to explain. However, evidence presented in this article suggest that the deep out-of-the-money bias is not related to the theoretical model's performance but rather to the fact that convertible bonds with low conversion value are generally underpriced in the market place to the extent that their prices often imply negative embedded option values.

Convertible bonds (CBs) are an important asset class but their analysis in function of the equity and bond components has received insufficient attention in France. This study investigates the relation between announcement effects and equity components for 141 French CB issues. We use the CB sensitivity to its underlying common stock as a proxy for the equity component. Our results indicate that CB issue announcements imply significantly negative market responses, which are negatively related to the equity component. This result supports the Myers and Majluf (1984) model [Myers, S.C., Majluf, N.S., 1984. Corporate financing and investment decisions when firms have information that investors do not have. J. Financial Econ. 13,. A more detailed analysis reveals that the market reaction is significantly positive for the subset of 'mixed' CBs. Mixed CB issuers are characterized by high informational asymmetries about investment opportunities compared with informational asymmet...

This paper shows that the probability of exercise of convertible bonds issued against a firm’s stock directly affects the liquidity of the stock itself. Using the ratio of absolute stock return to its dollar volume as a proxy for stock liquidity I demonstrate that there is a direct and positive relationship between conversion probability and stock liquidity while controlling for

A convertible bond (CB) is a hybrid security containing elements of both common stock and straight debt. Still, empirical investigations on CB issue announcements have failed to discern any pattern in the stock market reaction that is consistent with announcements of either common equity or straight debt issues. This study shows that (a) motives for issuing the CB and (b) its rating (and to a less extent the riskiness of the issuing firm) help explain the stock market reaction to CB issue announcements. Specifically, announcement of a CB issue with an explicitly stated motive for the use of proceeds, when coupled with a high (low) bond rating, generates a stock market response similar to a straight debt (common stock) issue. On the other hand, the preference of CB holders is dictated by the motive for the use of proceeds and the conversion premium. These findings highlight the critical importance of the motive of issue in determining reactions in both the stock and bond markets.

This report is the result of a collaboration between CGAP and J.P. Morgan. CGAP is solely responsible for the printing and distribution of this Occasional Paper. CGAP is not affiliated with J.P. Morgan. Our objective is to provide benchmarks for valuation of microfinance equity, both private and publicly listed. Our analysis is based on two datasets: a sample of 144 private equity transactions, which represents the largest such dataset gathered to date, and data on 10 publicly traded micro finance institutions (MFIs) and low-income consumer lenders. 1

Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate.The valuation model of inflation-indexed (or equivalently foreign-currency) convertiblebonds derived in this paper considers two sources of uncertainty allowing both theunderlying stock and the consumer-price-index to be stochastic and incorporates

Indian convertible bonds have two peculiar features that make them possibly unique in the world: a) the bonds are compulsorily converted into equity without any option, and b) the conversion terms are not specified at the time of issue but are left to be determined subsequently by the Controller of Capital Issues (CCI) who is the government functionary regulating capital issues in India. A naive model would say that the market simply forms an estimate of the likely conversion terms and then values the bond as if these terms were prespecified. However, the empirical investigation reported in a companion paper, Barua, Madhavan and Varma (1991) convincingly rejects the naive model and makes a more sophisticated model necessary. In this paper, we use the general theory of derivative securities (Cox, Ingersoll and Ross, 1985) to obtain a closed form expression for the value of the Indian convertible bond. The testable implications

We report the average costs of raising external debt and equity capital for U.S. corporations from 1990 to 1994. For initial public offerings (IPOs) of equity, the direct costs average 11.0 percent of the proceeds. For seasoned equity offerings (SEOs), the direct costs average 7.1 percent. For convertible bonds, the direct costs average 3.8 percent. For straight debt issues, the direct costs average 2.2 percent, although they are strongly related to the credit rating of the issue. All classes of securities exhibit economies of scale, although they are less pronounced for straight debt issues. IPOs also incur a substantial indirect cost due to short-run underpricing. Most large equity offers include an international tranche, although debt issues do not. I. introduction In this article we present the average costs of raising external capital for US. corporations from 1990 to 1994. Specifically, we report the average spreads on public equity offerings and debt offerings, along with the...

In this paper, we identify and document the empirical characteristics of the key drivers of convertible arbitrage as a strategy and how they impact the performance of convertible arbitrage hedge funds. We show that the returns of a buy-and-hedge strategy involving taking a long position in convertible bonds ("CBs") while hedging the equity risk alone explains a substantial amount of these funds' return dynamics. In addition, we highlight the importance of non-price variables such as extreme market-wide events and the supply of CBs on performance. Out-ofsample tests provide corroborative evidence on our model's predictions. At a more micro level, larger funds appear to be less dependent on directional exposure to CBs and more active in shorting stocks to hedge their exposure than smaller funds. They are also more vulnerable to supply shocks in the CB market. These findings are consistent with economies of scale that large funds enjoy in accessing the stock loan market. However, the friction involved in adjusting the stock of risk capital managed by a large fund can negatively impact performance when the supply of CBs declines. Taken together, our findings are consistent with convertible arbitrageurs collectively being rewarded for playing an intermediation role of funding CB issuers whilst distributing part of the equity risk of CBs to the equity market.

While convertible bond models recently have come to rest on solid theoretical foundation, issues in model calibration and numerical implementation still remain. This paper highlights and quantifies a number of such issues, demonstrating, among other things, that naïve calibration approaches can lead to highly significant pricing biases. We suggest a number of techniques to resolve such biases. In particular, we demonstrate how applications of the Fokker-Planck PDE allows for efficient joint calibration to debt and option markets, and also discuss volatility smile effects and the derivation of forward PDEs to embed such information into model calibration. Throughout, we rely on modern finite difference techniques, rather than the binomial or trinomial trees that so far have dominated much of the literature.

Clawback provisions allow the issuer to partially redeem a bond issue often within three years of issuance using proceeds only from new equity issues. Empirical evidence indicates the clawback provision is rarely exercised. This poses an interesting dilemma as clawback provisions are an expensive source of funding, often commanding yields that are significantly higher than traditional corporate bonds. We develop a simple model that provides a rationale for the scarcity of call redemptions and the higher yields of clawback bonds. The model predicts a relation between issuance of clawback bonds, cash flow volatility and the probability of renegotiation of clawback debt contracts.

This article discusses the underlying theory of the numeraire technique, and illustrates it with five pricing problems: pricing savings plans that offer a choice of interest rates; pricing convertible bonds; pricing employee stock ownership plans; pricing options whose strike price is in a currency different from the stock price; and pricing options whose strike price is correlated with the short-term interest rate

We report the average costs of raising external debt and equity capital for U.S. corporations from 1990 to 1994. For initial public offerings (IPOs) of equity, the direct costs average 11.0 percent of the proceeds. For seasoned equity offerings (SEOs), the direct costs average 7.1 percent. For convertible bonds, the direct costs average 3.8 percent. For straight debt issues, the direct costs average 2.2 percent, although they are strongly related to the credit rating of the issue. All classes of securities exhibit economies of scale, although they are less pronounced for straight debt issues. IPOs also incur a substantial indirect cost due to short-run underpricing. Most large equity offers include an international tranche, although debt issues do not. I. introduction In this article we present the average costs of raising external capital for US. corporations from 1990 to 1994. Specifically, we report the average spreads on public equity offerings and debt offerings, along with the other direct costs of raising capital, as a percentage of the proceeds. We find substantial economies of scale for initial public offerings (IPOs) of equity and seasoned equity offerings (SEOs). We also find substantial economies of scale for both straight bond offerings and convertible bond offerings. Spreads on bond offerings are highly sensitive to the credit rating of the offering. This article is descriptive in nature; no theories are tested. Its purpose is to provide benchmark numbers for use by issuers of securities. We do not address why firms issue the securities they do. This much broader corporate finance question would have to address taxes, corporate control, debt capacity, long-run performance patterns, investmentfinancing interactions, etc. We would like to thank Charles Calomiris and Tim Loughran for useful comments on an earlier draft