Effects of Callable Feature on Early Exercise Policy

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 boundary of the callable American call is identical to that of the American capped call. When the notice period requirementis imposed, the critical asset price (considered as a function of time to expiry τ) first increases with τ,reaches some maximum value, then decreases with τ. Several approaches of designing numerical algorithms for the valuation of the callable American option are also presented. This revised version was published online in November 2006 with corrections to the Cover Date.     

Are they still called late? The effect of notice period on calls of convertible bonds

When calling its convertible bonds, a company must typically give bondholders a notice period of about 30 days to decide whether to convert the bonds. This notice period affects the optimal call policy for convertible bonds. After accounting for the notice period, convertible bonds in our sample would have been optimally called when the stock was at about an 11% premium (median) relative to the conversion price. We show that after properly accounting for the call notice period and other factors, the median excess call premium is less than 4%—substantially less than the 26–44% call premium previous researchers have documented.     

The determinants of the convertible bonds call policy of Western European companies

This paper analyzes the determinants of the convertible bonds call delay of the Western European firms. This delay is analyzed comparatively to the optimal call policy suggested by Ingersoll (1977a) who argues that in a perfect market, managers should call the convertible bonds immediately when the conversion value reaches the call price. Like the previous studies in the US market, we find that the Western European companies delay the call of their convertible bonds for several weeks. This delay is explained by considering the main theoretical rationales for the convertible bonds call delays (the notice period, the call protection provisions, the cash flow advantage hypothesis, the financial distress and the signaling theory). The results are consistent with the cash flow advantage rationale but less evidence is found for the other theories.     

Effects of law on corporate financing practices—international evidence from convertible bond issues

Firms can adjust their convertibles to be more debt-like or equity-like through several contract terms. In particular, by providing call protection, a convertible issuer can assure its convertible bondholders that it will not force them to become equity holders during the call protection period. The possibility of a forced conversion instituted by an early call should be more threatening to investors in an economy where local laws are biased against shareholders. I examine call protection terms in an international sample and find evidence consistent with the hypothesis that convertible bond design varies based on the features of local law.     

Convertible Bonds Are Not Called Late

Starting with Ingersoll (1977b), the academic literature has repeatedly sought to explain why convertible bonds are called late. The findings here demonstrate there is no call delay to explain. This paper finds that most convertible bonds, given their call protection, are called as soon as possible. For those that are not, there are significant cash flow advantages to delaying. The median call delay for all convertible bonds is less than four months. If a safety premium is desired to assure the conversion value will exceed the call price at the end of call notice period, the median call period is less than a month.     

Determinants of corporate call policy for convertible bonds

For a sample of convertible bonds issued during the period 1980 through 2002, we empirically investigate the determinants of call policy. We find that the risk of a failed call over the call notice period helps explain why firms call only after conversion value exceeds call price by a substantial safety premium. We find strong evidence that cash flow considerations and a desire to mitigate agency conflicts influence call policy. We also find evidence that the decision to issue and subsequently call a convertible bond is influenced by a desire to obtain backdoor equity financing and to finance growth options. There is no evidence, however, that firms with favorable inside information are more likely to delay calls. Finally, we find that a significant portion of calls are associated with restructuring and merger activity, and with bond rating upgrades and downgrades. In these cases, there is little if any call delay.     

The role of time value in convertible bond call policy

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.     

Credit ratings and convertible bond prices: a simulation-based valuation

This study presents a simulation-based model of convertible bond prices under the assumption of stochastic interest rates. The model is developed such that the convertible bond price explicitly depends on the credit rating at the time of issuance. Key ideas explored in this study include terminating the simulated sample path immediately when the issuer defaults on the bond at time t, which is the same as the investor and the issuer optimally exercising their options and discounting the resulting cash flows at a risk-free rate. In turn, the defaulted group of sample paths belongs to the bottom xth percentile of the realized stock prices at each time, which is exogenously given by the cumulative or marginal default probability of a firm that has the same rating as the issuer. Upon calibrating the model, we can see that the moneyness of convertible bonds is strongly responsible for influencing the convertible bond price when the rating changes. Furthermore, the effects of stochastic interest rates are shown to be possibly significant when the interest rate risk’s market price is not zero.     

The buyers’ perspective on security design: Hedge funds and convertible bond call provisions

We provide evidence that security design reflects the interplay of capital supplier and security issuer preferences. While call provisions have historically been the default option in convertible security design, only a minority of post-2005 issues are callable. Because hedge funds dominate the market for new convertibles today and because convertible arbitrage is less risky without callability, the recent diminution in the frequency of call provisions in new convertible bond issues illustrates the importance of the preferences of the suppliers of capital in security design.     

Financial Distress Costs and Delayed Calls of Convertible Bonds: An Empirical Analysis

Theoretical analysis implies that optimal call policy would be to call the bonds as soon as the conversion value equals the call price. Empirical studies, however, report that firms appear to systematically delay the call and the difference between the conversion value and the call price is large at the time of the call. This study examines convertible bond calls between 1977 and 1993, with a view to explain the large difference between the conversion value and the call-price at the time of the call. A large majority of the firms calling the bonds have cash-flow incentive to call the bonds in that the after-tax interest payments are higher than the dividends on the converted shares. The large difference between the conversion value and the call price is positively related to the risk characteristics of the firm. Evidence seems to support the view that risk aversion and fear of potential financial distress may explain the large difference at the time of call between the conversion value and the call price.     

Disappearing Call Delay and Dividend‐Protected Convertible Bonds

Firms do not historically call their convertible bonds as soon as conversion can be forced. A number of explanations for the delay rely on the size of the dividends that bondholders forgo so long as they do not convert. We investigate an important change in convertible security design, namely, dividend protection of convertible bond issues. Dividend protection means that the conversion value of the convertible bond is unaffected by dividend payments and thus dividend‐related rationales for call delay become moot. We document that call delay is near zero for dividend‐protected convertible bonds.     

A contingent-claims valuation of convertible securities

This paper examines the pricing of convertible bonds and preferred stocks. The optimal policies for call and conversion of these securities are determined via the criterion of dominance. The techniques underlying the Black-Scholes Option Model are used to price convertible securities as contingent claims on the firm as a whole.     

A SEQUENTIAL SIGNALING MODEL OF CONVERTIBLE DEBT ISSUE AND CALL POLICIES

This paper offers a new explanation for why some risk‐averse firms may prefer to issue callable convertible debt. Here, the convertible debt issue and call policies are integrated into a unified financing policy. It is then shown that for firms with relatively low unsystematic risk, convertible debt issuance followed by an appropriate in‐the‐money signaling call policy reduces more unsystematic equity risk than equity, callable straight debt, or their combination. The model is modified to incorporate asymmetric information at the issue stage to explain the stock price behavior at announcements of convertible debt sales.     

Convertible Bonds and Stock Liquidity

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 firm size, book to market equity value and firm beta. I describe the effect of unlisted convertible debt on the liquidity of listed firms in the US, Korea and Singapore. The effects of conversion probability on stock liquidity are less pronounced for smaller firms, which helps explain time series variations in the liquidity premiums for smaller firms over time. The relationship between convertibles and stock liquidity is mainly attributed to the expected increase in the number of shares available for trade upon conversion and the expected change in the capital structure of the firm.     

THE CHOICE AMONG DEBT,EQUITY, AND CONVERTIBLE BONDS

The hybrid nature of convertible bonds continues to interest corporate financial managers, investors, and economists. While much theoretical and empirical research examines an issuer's choice between using straight debt and equity, little research evaluates how an issuer chooses among debt, equity, and convertible bonds. This study extends Marsh's [ 13 ] research on the differences between debt and equity issuers in the United Kingdom by examining U.S. industrial firms that issue debt, equity, or convertible bonds. It also illustrates how various distinguishing features influence the probability that each security will be issued.     

Covenants in convertible bonds: Boon or boilerplate?

This paper examines the role of restrictive covenants in convertible bonds. After controlling for standard covenant intensity determinants, an average convertible bond offering has 3.21 fewer covenants than an average straight bond offering. While covenants negatively affect straight bond yields, there is no negative association between covenants and convertible bond yields. Moreover, contrary to straight bond covenants, convertible bond covenants are set largely independently of issuer characteristics. Overall, our findings suggest that the conversion option and certain covenants are substitutes for addressing debt-related financing costs. The few covenants included in convertibles represent irrelevant boilerplate clauses.     

CONVERTIBLE BONDS: MATCHING FINANCIAL AND REAL OPTIONS

For companies whose value consists in large part of “real options”‐ growth opportunities that may (or may not) materialize‐convertible bonds may offer the ideal financing vehicle because of the matching financial options built into the securities. This paper proposes that convertible debt can be a key element in a financing strategy that aims not only to fund current activities, but to give companies access to low‐cost capital if and when their real investment options turn out to be valuable. In this sense, convertibles can be seen as the most cost‐effective solution to a sequential financing problem‐how to fund not only today's activities, but also tomorrow's growth opportunities (some of them not yet even foreseeable). For companies with real options, the ability of convertibles to match capital inflows with corporate outlays adds value by minimizing two sets of costs: those associated with having too much (particularly equity) capital (known as “agency costs of free cash flow”) and those associated with having too little (“new issue” costs). The key to the cost‐effectiveness of convertibles in funding real options is the call provision. Provided the stock price is “in the money” (and the call protection period is over), the call gives managers the option to force conversion of the bonds into equity. If and when the company's investment opportunity materializes, exercise of the call feature gives the firm an infusion of new equity (while eliminating the debt service burden associated with the convertible) that enables it to carry out its new investment plan. Consistent with this argument, the author's recent study of the investment and financing activities of 289 companies around the time of convertible calls reports significant increases in capital expenditures starting in the year of the call and extending three years after. The companies also showed increased financing activity following the call, mainly new long‐term debt issues (many of them also convertibles) in the year of the call.     

Optimal exercise of executive stock options

Valuing executive stock options is a challenging problem, because the standard risk-neutral valuation of those options is not appropriate; the executive is not allowed to trade the stock of the firm, so is not operating in a complete market. As this paper shows, an executive holding many American-style call options on his firm’s stock will optimally exercise the options bit by bit, whereas a risk-neutral valuation of the options would assume that all are exercised at the same time. Comparative statics of the optimal exercise policy show many surprising features.      

中美可转换债券比较研究

通过对中国和美国的可转换债券市场的规模、条款、风险收益特征和套利机会进行对比分析,结果表明中国可转债市场规模仍远不及美国,尤其对创新性中小企业融资需求的支持上差距更大。中国可转债的条款设计更多替发行人考虑,而较少关注投资者的需求,具有明显的扩股融资动机。从风险收益特征和套利机会来看,发现美国可转换债券市场的债性凸显,股性较弱,而中国可转换债券市场具有偏股性。