Convertible Bonds

Questo il paper presentato alla Commissione Europea e all'Università Bocconi nell'ambito del contest GENERAZIONE EUROPA.

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Convertible bonds and American warrants commonly contain the provision of the callable feature which allows the issuer to buy back the derivative at a predetermined recall price. Upon recall, by virtue of the early exercise privilege embedded in an American style derivative, the holder may choose either to exercise his derivative or to sell it back to the issuer. Normally, there is a notice period requirement on the recall, that is, the decision of the holder to exercise or to receive the cash is made at the end of the notice period. Also, the period of recall provision may cover only part of option's life. In this article, we examine the effect of the callable feature (with the notice period requirement) on the early exercise policy of a callable American call option. The optimal calling policy for the issuer is explored where the value of the American option is minimized among all possible recall policies. Without the notice period requirement, the critical asset price bounda...

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. In this paper we extend the convertible pricing models of and to the case of indexation of the promised payments of the convertible to a general price index or to the price of foreign exchange. The theoretical framework derived in this paper considers two sources of uncertainty: both the underlying stock price and the consumer-price-index (or equivalently foreign-currency) are stochastic, and incorporate credit risk in the analysis.

Resumen Se diseña un bono indexado al PIB tomando en cuenta factores como la continuidad de los pagos del cupón y la volatilidad del mismo considerando que este tipo de bonos sirve como un seguro para el gobierno contra contingencias adversas. Luego utilizando la metodología de Black y Scholes en la medida real y métodos estadísticos se procede a la valuación matemática del cupón. Por último se realizan análisis de sensibilidad con respecto a las variables macro que más influencian el precio del cupón. Se obtiene como resultado que las condiciones que se imponen al bono indexado al PIB, por el cual se pagan intereses no solo por la diferencia del PIB real con respecto a un PIB base sino que también por la diferencia de la tasa de crecimiento con respecto a la tasa base, reduce la volatilidad del precio del cupón haciéndola más atractiva tanto para los inversores como también para un país que busca estabilizar sus pagos.

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

This paper analyzes the risk dynamics surrounding convertible bond offerings (CBOs) and Seasoned Equity Offerings (SEOs). As convertible bonds are commonly believed to be very effective at mitigating adverse selection or overinvestment problems we would expect differing risk and return patterns for convertible bond and seasoned equity issuers. By analyzing 1148 convertible bond offerings and comparing them to 2905 seasoned equity offerings, we show however that for both issuer types the systematic risk increases prior to issuance and drops sharply thereafter. This result is consistent with the notion of exercising real options, as growth options are always riskier than the underlying assets and exercising them at issuance causes an immediate drop in risk. The real option framework and the proposed dynamics of systematic risk also provide a rational explanation for the negative announcement effect, as well as any long-term underperformance subsequent to the CBO and the SEOs.► We analyze the risk dynamics of convertible bond and Seasoned Equity Offerings. ► Both issuers show an increase in risk prior to and a drop after the issuance. ► This result is consistent with the notion of exercising real options. ► The risk changes are responsible for the underperformance of CBO and SEO issuers.

The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and min-max optimization. Stock prices (underlying asset) were modeled under the assumption of the geometric Brownian motion of their values. The Monte Carlo method was used for calculating the real payoff which is the objective function. The min-max optimization problem was solved using the derivative-free Downhill Simplex method. The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in the Downhill Simplex Method, the number of generated trajectories of underlying asset, the size of the problem and initial trajectories of the behavior of investors and issuers.

This paper presents the first empirical analysis of firms' rationale for issuing putable convertible bonds in the literature. We distinguish between three possible rationales for the issuance of putable convertibles: 1) the risk-shifting hypothesis, 2) the asymmetric information hypothesis, and 3) the tax savings hypothesis. The results of our empirical analysis can be summarized as follows. First, putable convertible issuers are larger, less risky firms, having larger cash flows, smaller growth opportunities, and lower bankruptcy probabilities as compared to ordinary convertible issuers. Second, putable convertible issuers have lower preissue market valuations, more favorable announcement effects, and better postissue operating performance when compared to ordinary convertible issuers. Third, putable convertible issuers have better postissue long-run stock return performance as compared to ordinary convertible issuers. Finally, putable convertible issuers typically have greater tax obligations and better credit ratings than ordinary convertible issuers. Overall, the results of our univariate as well as multivariate analyses provide support for the asymmetric information and tax savings hypotheses, but little support for the risk-shifting hypothesis.

When Citigroup announced that it had raised $7.5 billion of capital via the issuance of mandatory convertibles that paid 11% annual distribution, the financial press reported the opinion that the additional capital was been raised at a high price. For example, the Wall Street Journal observed that "Citi is paying a higher interest rate than companies that borrow on the highyield, or junk-bond, market; currently they pay roughly 9% for straight bonds. Typically, convertible bonds pay lower interest rates than straight bonds, although a particular bond's structure could affect the interest rate paid." 1 This negative interpretation of Citi"s convertible financing has not changed over the years. When Citicorp issued convertible securities in 1991, a New York Times' article concluded that "People used to denounce banks for charging usurious interest rates. Now Citicorp, desperate for capital, is paying such rates. The capital infusion that Citicorp obtained last week from a Saudi prince came at a heavy cost. It may have proved that it can raise capital, but … Citicorp may go on paying that rate [11 percent] long after the current crisis of confidence has passed. Not before 1996 can the company force Prince al-Waleed bin Talal to convert the preferred to common, at $16 per share. Any profits on conversion will come on top of the assured 11 percent return." 2 Raising equity via convertible securities is a roundabout procedure that can lead to erroneous conclusion in the absence of careful evaluation. How can one determine if issuing convertibles is a better alternative to the straight issuance of common equity? In this paper, we attempt to answer this question in the case of Citigroup by estimating the implied common equity price from its $7.5 billion convertible issue and comparing it to a common equity offering. In doing so, we provide a simple procedure for calculating the implied common equity proceeds of convertible issues.

This paper studies the after-tax valuation of convertible bonds in the light of Europe's participation exemption (PEX) rules and International Financial Reporting Standards (IFRS). The focus is on Italy's representative case. PEX rules exempt from company taxation capital gains realized by companies selling stocks. PEX rules raise the value of convertibles as investor companies can strategically convert the bond into stock to enjoy PEX. Historical cost-based national accounting standards imply taxation upon realization and valuable tax timing options (TTOs). 'Fair value' based IFRS entail mark-to-market taxation, which 'kills' TTOs, but investor companies can convert the bond early in order to enjoy PEX. Early conversion can be valuable.

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Convertible bonds can be difficult to value, given their hybrid nature of containing elements of both debt and equity. Further complications arise due to the frequent presence of additional options such as callability and puttability, and contractual complexities such as trigger prices and "soft call" provisions, in which the ability of the issuing firm to exercise its option to call is dependent upon the history of its stock price. This paper explores the valuation of convertible bonds subject to credit risk using an approach based on the numerical solution of linear complementarity problems. We argue that many of the existing models, such as that of Tsiveriotis and Fernandes (1998), are unsatisfactory in that they do not explicitly specify what happens in the event of a default by the issuing firm. We show that this can lead to internal inconsistencies, such as cases where a call by the issuer just before expiry renders the convertible value independent of the credit risk of the issuer, or situations where the implied hedging strategy may not be self-financing. By contrast, we present a general and consistent framework for valuing convertible bonds assuming a Poisson default process. This framework allows various models for stock price behaviour, recovery, and action by holders of the bonds in the event of a default. We also present a detailed description of our numerical algorithm, which uses a partially implicit method to decouple the system of linear complementarity problems at each timestep. Numerical examples illustrating the convergence properties of the algorithm are provided.

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.

We examine changes in equity and asset betas around convertible bond calls and report two major findings. First, calling firms exhibit an increase in asset betas following the call. We argue that the finding is consistent with the implications of the sequential financing theory but not of the backdoor equity financing theory. Second, abnormal returns at call announcements are negative only for the subsample of firms that also exhibit an increase in equity beta. We conclude that risk changes help explain the market reaction to convertible bond calls.

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate. There is strong evidence that interest rates and bond yield movements exhibit both stochastic volatility and unanticipated jumps. The presence of frequent jumps makes it natural to ask whether there is a premium for jump risk embedded in observed bond yields. This paper identifies a class of jump-diffusion models that are successful in approximating the term structure of interest rates of emerging markets. The parameters of the term structure of interest rates are reconciled with the associated bond yields by estimating the volatility and jump risk premia in highly volatile markets. Using the simulated method of moments (SMM), results suggest that all variants of models which do not take into account stochastic volatility and unanticipated jumps cannot generate the non-normalities consistent with the observed interest rates. Jumps occur (8,10) times a year in Argentina and Brazil, respectively. The size and variance of these jumps is also of statistical significance.

This paper was written while we were visiting the Stern School of Business. We are grateful for the hospitality that we received at this institution. Landskroner acknowledges the financial support of the Krueger Foundation of the Hebrew University of Jerusalem. Raviv acknowledges ...

This paper was written while we were visiting the Stern School of Business. We are grateful for the hospitality that we received at this institution. Landskroner acknowledges the financial support of the Krueger Foundation of the Hebrew University of Jerusalem. Raviv acknowledges ...

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