Capital Structure as a Form of Signaling: The Use of Convertible Bonds

Transcription

1 Capital Structure as a Form of Signaling: The Use of Convertible Bonds Rusi Yan Stanford University rusiyan@stanford.edu May 2009 Abstract In the face of asymmetrical information in financial markets, outside investors must rely on the firms actions in order to gain information known only to firm insiders. Such actions can be construed as signals of firm quality or internal projections of success, and capital structure can serve as one such signal. This study uses a sample of 100 convertible bonds issued from 1990 to 2007 to examine the market s reactions to changes in the capital structures of the firms. A more debt-like issuance is theorized to result in positive abnormal returns, while a more equity-like issuance should result in negative abnormal returns. I also intend to investigate whether the use of capital structure as signaling differs with firms of different sizes, since information asymmetries would not be the same. This paper finds that the conversion premium of newly issued convertible bonds has a positive, statistically significant effect on the firms abnormal returns in the 30- and 200-day periods around the date of issuance. This effect is larger for smaller firms than for larger firms. However, the conversion premium has a much smaller, insignificant effect during the 10-day period, which may be caused by errors in determining the correct date that the market learned of the issuance. I would like to thank my advisor, Professor John Shoven, for his invaluable help in this process. Without his guidance and support, this paper would not have been possible.

2 Rusi Yan 1 1. Introduction The efficient market hypothesis states that in financial markets, prices on traded assets, such as stocks or bonds, already reflect all known information, leading to informational efficiency. However, in reality, not all information is known. Information asymmetries certainly exist in financial markets in the real world, as long as there are firm insiders and outsiders. One example of this asymmetry is related to the principalagent problem discussed by Jensen. Managers at the firm supposedly act in the interests of the shareholders, but often have conflicting self-interests. In this study, the managers are an example of firm insiders, and only they know the true internal projections for the likelihood of success for firm projects. Therefore, there exists an information asymmetry between the insiders and the outside investors, including shareholders. These investors can only rely on the firm s observable actions to generate some information about the internal projections for the success of the project. Because of this information asymmetry, there is a mismatch between the insiders of the firm and the outside investors whenever the firm needs external funds to finance a project. External funding can take several forms, but common methods are debt and equity. Debt is an obligation to repay the investors in a pre-specified time and manner. Should the firm be unable to repay the loan, the debtholders can claim any assets that the firm still holds to recover their investment. If firm insiders believe that the project is likely to be highly successful, then they would wish to issue debt to limit what they need to pay back in the future. On the other hand, equity gives the new investors partial ownership in the company, allowing them to share in the firm s profits and losses. If the managers of the firm believe that the project has a lower probability of success, then they

3 Rusi Yan 2 would want to issue equity to spread the risks to the new investors and owners of the firm. The previous literature explores several competing theories about how firms make their financing decisions. The traditional theory is the Tradeoff Model, in which firms strive towards a target debt level. Debt serves to generate value for the firm through tax benefits but it increases the risk of financial distress, which implies that there is an optimal level where the firm receives the maximum value. Another theory is the Pecking Order Model, which states that firms generally follow a hierarchy in choosing their capital structure because of information asymmetry. They would first prefer financing with internal funds, and only when those are unavailable do they seek outside sources. The first source of external funds is the issuance of debt, and equity is only issued as a last resort. One particular area of interest is the use of convertible bonds, which serve as a continuous, rather than discrete, measure of firms financing decisions along the debtequity spectrum. These models will be discussed in greater detail in a following section. The objectives of this study are to examine whether firms choose their capital structure, demonstrated here through the terms of the convertible bonds, according to their internal projections of success and whether outside investors find this to be a credible signal. If a firm has a lower projection of success, then it may choose to issue more favorable terms of conversion. I also intend to examine whether firm size plays a part in the signaling process or has an effect on the strength of the signal. It is possible that the magnitude of the information asymmetries differs with firm size; larger firms will receive more coverage by the media and analysts and will be more well-known, therefore facing less information asymmetry.

4 Rusi Yan 3 Using a model similar to the one developed by Davidson, Glascock, and Schwarz (1995), I will look at the conversion price set by the issuing firm in relation to the stock price at the time of issuance, or how far out of the money the bond is. The more out-themoney bonds will signal more like debt, since more stock appreciation is needed for the investors to want to convert. The further out-the-money the bond is, the less likely it is that the stock price will ever reach the required level for conversion, so the investors would treat these bonds more like straight debt because they may never convert. Conversely, the bonds closer to being at-the-money will signal more like equity because it can become profitable to convert very quickly To begin my study of how convertible bonds can serve as a signal to firm outsiders, I provide some background information about convertible bonds in the next section, followed by a review of the previous literature. I will then discuss the data and methodology that I used, followed by the empirical results. 2. Overview of Convertible Bonds A convertible bond is a hybrid security that has features of both traditional debt and equity. The investor benefits from such a bond in different states of the world. If the firm performs well, then investors can convert to equity, often at a discount, and share in the profits of the firm. On the other hand, if the firm does not perform as well, the investors still have a bond that will pay a fixed interest. Most convertible bonds pay their interest semiannually.

5 Rusi Yan Characteristics of Convertible Bonds Convertible bonds have several key characteristics. They give the bondholders the option to exchange each bond for a specified number of shares of stock of the firm. This number is the conversion ratio. A related idea is the conversion price, or the price at which the bond can be converted to stock. The number of shares received is the principal amount of the bond divided by the conversion price. A summary of these facts is displayed in section 2.3. The conversion premium is the excess of the bond value over its conversion value. Convertible bonds are valued using the difference between the conversion price and the equity price. If the conversion price is greater than the equity price, then the bond is considered out-the-money because bondholders would not wish to convert. When the conversion price is less than the equity price, the bond is considered in-the-money, and when the conversion price is exactly equal to the equity price, the bond is at-the-money. One of the variables examined in this paper is how much the stock price would need to appreciate to become at-the-money and it becomes attractive to convert the bond. Figure 1 shows the relationship between the conversion price and the stock price.

6 Rusi Yan 5 Figure 1. Here, if the bond is convertible for 20 shares, then the equivalent conversion price is $50. At the current stock price of $42, the value upon conversion would be less than the par value of the bond, so the bond is out-the-money. The conversion premium here is the stock appreciation needed to become at-the-money. I use a sample of convertible bonds from Moody s Mergent Fixed Income Database. For the firms that issued these bonds, their bonds most frequently require the stock to appreciate percent in order to become at-the-money (see section 2.3). While convertible bonds offer the option to be converted to equity seemingly at the discretion of the investor, many issuing companies will try to force conversion. Convertible debt is often issued with a call feature, which allows the firm to repurchase the bonds for a given price before the maturity of the bond. Investors are given a limited time after notification before the securities are repurchased and if the call value is below

7 Rusi Yan 6 the conversion value, investors would prefer to convert over losing money by selling the bonds back to the firms. In such situations, investors are forced to convert to equity at a time that may not be ideal for them, particularly if the value of the stock is expected to appreciate further. For example, CNET Networks issued $125 million in senior convertible bonds in April 2004, with the stipulation that the firm may redeem some or all of the notes at any time after April Such a provision would allow the firm to force conversion after a period of protection, which gives it some measure of control over how much they need to pay investors or when stock dilution would take place. Other methods for the firm to control when investors can convert include provisions detailed in the original offering of the bond. On May 8, 2006, SanDisk issued $1 billion of senior convertible bonds due in 2013 with a 1% interest rate. In their prospectus, they specify that one of three conditions must be satisfied for conversion to take place. Investors may convert during a five day period following another five day period where the trading price per note is less than 98% of the sale price of the common stock multiplied by conversion rate. They may also convert after June 2006 if the last reported sale price of common stock for 20 out of 30 consecutive trading days exceeds 120% of the conversion price. Otherwise, the investors may only convert after specified corporate events, such as giving current stockholders the right to purchase more stocks at a discounted price below the market price. Convertible bonds can come with a variety of other features. Mandatory convertible bonds are, as the name suggests, bonds that must be converted at maturity for a fixed number of shares. Because these bonds offer fewer options and are therefore less valuable, they usually compensate investors with a higher yield. Other convertibles,

8 Rusi Yan 7 called contingent convertibles, only allow investors to convert if the stock price is a certain percentage above the conversion price, or when the bond is well in-the-money. SanDisk s offering is one such contingent convertible. Other securities have properties similar to convertible bonds, such as convertible preferred stock, which gives holders of preferred stock the option to convert to common stock. Because this paper focuses on the hybrid qualities of convertible bonds, such convertible equity issuances will not be discussed. 2.2 Issuers of Convertible Bonds Convertible bonds offer several benefits to issuers. First, they offer tax advantages like straight debt when they make interest payments. Secondly, they are often less expensive to issue because the issuing firm will have to make smaller interest payments than on straight debt, which it cannot issue with low interest. As discussed by Stein (1992), most of the firms issuing convertible bonds are not of the highest quality, which is also apparent in the data that I have collected. For these firms, it would be extremely costly to provide an even higher yield on top of the high yield they must pay on account of their ratings. However, it should be noted that the firm is still giving away something of value the option to essentially buy stock at a discount at a later date so the lower cost to the firm is in terms of cash payments only. The spreads between convertible bond yields and straight debt yields, as well as the spreads between convertible bond yields and Treasury yields can be found in the next section. In the dataset, many firms are clustered in the B/Ba rating by Moody s or the B/BB rating by Standard and Poor s, denoting that they carry greater risks. They are generally classified as junk bonds, but are among the slightly more reliable securities in

9 Rusi Yan 8 this category. This is not surprising, since most investment grade borrowers would be able to issue relatively cheap straight debt because the risk of default is so low. Convertible bonds may also be a way to raise funds without actually issuing stock. However, issuing convertible bonds can decrease the value of the firm in the long run if the investors do convert, due to the stock dilution upon conversion. There are still advantages to this strategy over issuing straight equity: the firm can defer the stock dilution using convertible bonds. If the firm s ultimate goal is to introduce more equity into its capital structure, convertibles can give it some time to complete the project that it is financing or make other adjustments before the dilution takes place. Combined with a call option, convertible bonds can also give firms the ability to control when the dilution will take place in the future. 2.3 Statistics Using a sample of 2,915 convertible bond issuances, I compare them to the straight debt issuances from the same set of firms. Table 1 displays some key characteristics about the two groups of bonds. On average, the convertible bonds have a larger total offering and a longer maturity, although the convertible bonds may be called or converted before maturity. In this sample, the average dividend paid by the issuing firms is $0.22, payable every quarter. Graphs 1 and 2 show the spread of the conversion price and the conversion ratio, while Graph 3 illustrates the stock appreciation needed to become at-the-money. A number of convertible bonds are in-the-money at issuance, which may signal more like equity. Graph 4 displays the Moody s ratings and Table 2 shows how convertible bonds compare to straight debt issuances; a greater proportion of convertible bonds are graded

10 Rusi Yan 9 as junk bonds, while more nonconvertible bonds are classified as investment grade. Graph 5 shows the maturity of convertible bonds, and it is clear that there are two modes in the distribution. Most convertible bonds are either short-term bonds of 5-10 years or long-term bonds of years, with few issuances in between. Table 1: Characteristics of Bonds for the Period Convertible Bonds Straight Debt Average Maturity years 7.98 years Average Total Offering $293.9 million $199.7 million Average Offer Price $989.3 $995.6 Most common rating B A Yield 4.92% 6.18% Interest Rate Spread from Benchmark Treasuries basis points basis points Graph 1.

11 Rusi Yan 10 Graph 2. Graph 3.

12 Rusi Yan 11 Graph 4. Graph 5.

13 Rusi Yan 12 Table 2: Moody s Ratings Ratings Convertible Bonds Straight Debt Investment Grade % % Aaa % % Aa1, Aa2, Aa % % A1, A2, A % % Baa1, Baa2, Baa % % Junk Bonds % % Ba1, Ba2, Ba % % B1, B2, B % % Caa1, Caa2, Caa % % Ca % % C % % Total % % 3. Previous Literature In the attempt to create a comprehensive model of capital structure, several competing theories have been developed to answer the question of how and when firms choose to finance with outside funds. One of the theories is the traditional Tradeoff Model, in which firms weigh the costs and benefits of issuing debt. Because the payment

14 Rusi Yan 13 of debt obligations is allowed as a deduction of taxable income, debt issuance acts as a tax-shield and essentially generates value for the firm by saving them the money they would need to pay as taxes. Modigliani and Miller (1966) found positive effects of tax shields on the market values of electric utilities companies. The other theory is the Pecking Order Model, first proposed by Donaldson in The Pecking Order Model states that firms financing policies follow a hierarchy; firms first prefer internal financing over external, then choose debt when internal financing is not available, and only choose equity as a last resort. Myers and Majluf (1984) postulate that there is no optimal debt ratio due to information asymmetry and signaling problems. However, specific industries, such as the electric utilities industry referenced by Modigliani and Miller, are also subject to regulation from outsiders. Spiegel and Spulber (1994) studied the effects of regulations in such industries on these firms choice of capital structure. They constructed a sequential game, in which the regulated firm makes its capital structure and investment decisions in anticipation of the policies and market reactions. The market then values the debt and equity of the regulated firm on the basis of the capital structure and the future regulations. Finally, the regulatory commissions set rates that depend on the firm s level of investment and capital structure. Knowing this, the firm would choose its capital structure with the future regulations in mind. The probability of bankruptcy increases with more debt, which the regulators find unattractive. In equilibrium, regulated firms generally issue more debt because it raises the regulatory rates as the regulators try to reduce the bankruptcy costs. Therefore, debt is beneficial to regulated firms because it also reduces the regulators incentives to act

15 Rusi Yan 14 opportunistically. Bradley, Jarrell, and Kim (1984) found that regulated firms such as telephone and electric and gas utilities are generally among the most highly leveraged. 3.1 Tradeoff Model In addition to the tax benefits provided by debt issuances, higher leverage increases the risk of financial distress for the firm. The Tradeoff Model suggests that there is an optimal level of debt that balances the benefits from these tax-reductions and the higher levels of risk that the firm must take on. Hovakimian, Opler, and Titman (2001) analyze the ability of firms to reach this target ratio, accounting for the fact that there may be impediments to this goal. Referencing Masulis and Korwar (1986) and Asquith and Mullins (1986), they claim that firms tend to issue equity following an increase in stock prices, implying that firms that perform well wish to reduce their leverage to reach a more optimal ratio. Other models have also found that firms periodically readjust their leverage ratios to achieve an optimal level of debt. Dynamic models of capital structure, including Fischer, Heinkel, and Zechner (1989), suggest that firms repurchase equity after an increase in stock price. Hovakimian, Opler, and Titman test the hypothesis that firms move towards the target ratio when they raise new capital or retire or repurchase existing equity. They use an estimated debt ratio as a proxy for the long run optimal debt ratio and then used the difference between this predicted ratio and the actual ratio to determine whether firms issue debt or equity. They surmised that the deficit between the target and the actual ratios would have a positive effect on the later debt issue. Empirically, they found that firms that issued equity tended to be less profitable than straight debt or convertible debt issuers. However, firms that repurchased equity had

16 Rusi Yan 15 much higher returns on assets than firms that retired debt. When firms increase their leverage ratios, they generally have higher operating incomes and these regressions showed that firms tend to move toward a target ratio when they repurchase or retire equity. However, the authors assume that firms make significant changes in their debt levels and that managers make a thorough analysis of tradeoffs and there are no agency or information problems. Harris and Raviv (1990) do incorporate the informational function of debt and allow for agency problems in their analysis of the capital structure choice. They assume that there are informational asymmetries and that managers do not always act in the best interests of their investors. These managers are reluctant to give out information or relinquish control of the firm, but Harris and Raviv speculate that debt can alleviate both of these issues. Jensen (1989) asserts that if investors are uncertain about the management s quality, they can use debt to generate information. Debt must be paid first and if the firm goes into bankruptcy, the creditors are entitled to all the remaining assets of the firm. Bulow and Shoven (1978) found that firms with longer-term debt are more likely to continue operating when facing bankruptcy decisions. Harris and Raviv surmise that debt provides the outside investors with a way to force the firm into liquidation and gives them some measure of control over the firm because the firm insiders do not wish to be liquidated. In addition, debt provides information to outsiders, because the mere ability of the firm to service debt and make payments implies that the firm has at least the income level needed to cover these debt payments. Harris and Raviv derived two systems, a static model and a dynamic model. In the static model, they assume that firms can only make one choice of the debt level, which

17 Rusi Yan 16 cannot change after the choice is made, and that firm income is unobservable. The distribution of firm income depends on firm quality, which is assumed to be independently and identically distributed. They examined how firms with differing qualities behave in their issuances. Firms with a higher liquidation value, or more tangible assets, will have higher risk of default because investors would find it more profitable to force liquidation, so the managers will choose to issue more debt to give investors greater control and more information to avoid liquidation. In the dynamic model, firms capital structure can change over time and income is still unobservable and dependent on firm quality. Here, investors beliefs about firm quality increase with every debt payment made, so the debt levels increase over time. Guedes and Thomson (1994) expanded the theory of how capital structure choices signal firm quality. Using the growth and decline of the adjustable-rate debt market in the 1980s, they tested how the type of debt served as a signal compared to the issuance of fixed-rate debt. The costs of financial distress that debt creates give managers an incentive to choose the financing strategies that will stabilize the firm s income and to adopt high-risk strategies only when the gains from signaling outweigh the increases in risk. The empirical data suggests that the firms were able to signal their quality with the debt choices. By studying the market reactions to debt announcement, they were able to conclude that the firms that chose more risky strategies signaled higher quality. 3.2 Pecking Order Model Another competing theory of capital structure is the Pecking Order Model, proposed by Donaldson in This model states that firms capital structure choices follow a hierarchy; firms first prefer internal financing, then choose debt when internal

18 Rusi Yan 17 financing is not available, and only choose equity as a last resort. Myers (1984) pointed out that the Tradeoff Model cannot explain the negative valuation effects of equity issues or other leverage-reducing events, documented by Masulis (1980). Titman and Wessels (1988) and Rajan and Zingales (1995) find strong negative correlations between debt ratios and past profitability, while tradeoff models predict a positive relationship. According to Myers and Majluf (1984), there is no optimal debt ratio, a result of information asymmetry and signaling problems. Shyam-Sunder and Myers (1999) devised a test to determine which model offered a better description of how firms choose their capital structures. They used data from Industrial Compustat files, focusing on large firms with conservative debt ratios. By requiring continuous data on flow of funds, they drop many of the smaller firms from the sample. However, the difference between large and small firms cannot be ignored, which I plan to elaborate. To test the Pecking Order hypothesis, Shyam-Sunder and Myers regressed the amount of debt issued or retired on the funds flow deficit, which is a measure of the firm s financial situation and include variables such as capital expenditures, operating cash flows, and current long-term debt outstanding. This regression estimates how a firm in a given financial situation behaves in its capital structure decisions. In contrast, the traditional Tradeoff Model states that changes in the current debt level are caused by deviations from the target debt ratio, so Shyam-Sunder and Myers regressed the change in the debt ratio on the difference between last period s debt ratio and the target ratio. However, they recognized that the target ratio is unobservable, so they used a historical mean of the debt ratio to estimate the target. In fact, Jalilvand and Harris (1984)

19 Rusi Yan 18 concluded that using a three-year moving average of debt ratios did not change their results when they tested for firms tendencies to revert towards an optimal ratio, supporting this use of a historical average. In testing the Pecking Order model, Shyam-Sunder and Myers found that debt dominated all other forms of external funding. A simple target adjustment model does provide some explanatory power, which is statistically significant. If target adjustment is included in conjunction with the Pecking Order theory, then target adjustment loses about 2/3 of its explanatory power. However, when the authors studied firms that have admitted to using either a pecking order policy or a target adjustment policy, they found that the Tradeoff Model resulted in false positives. Even when they looked at firms that disclosed a hierarchical model of capital structure, they found statistically significant results when testing the Tradeoff Model. The Pecking Order Model was correctly rejected when examining firms that declared that they were trying to pursue a target debt ratio. Therefore, Shyam-Sunder and Myers concluded that the Pecking Order Model was the more accurate theory. 3.3 Use of Convertibles One subsection of the literature examines the use of convertible bonds, a hybrid security that has characteristics of both debt and equity. Investors of convertible bonds have the option to exchange their bonds for shares of stock according to a predetermined conversion ratio. The conversion ratio is defined to be the number of shares of stock that one can receive for each bond. Many of these securities include a call feature, which allow firm managers to force conversion. Ingersoll (1977a) and Brennan and Schwarz

20 Rusi Yan 19 (1977) show that the firm should force conversion as soon as it is feasible, when the conversion price is at least as high as the call price. However, Ingersoll (1977b) finds that actual calls are delayed relative to this prediction and suggests possible explanations, including transaction costs and a delay in the notice period. These arguments do not explain the behavior of common stock returns at the announcement of convertible debt calls. Mikkelson (1981) discovered that on average, common stock returns are negatively correlated with announcements. In fact, the two day announcement period average return is %, while a 50 day control period s average return is %; this is inconsistent with the hypothesis that forced conversion is always beneficial to the shareholders. Harris and Raviv (1985) attempt to explain both the delayed calls and negative stock returns at call announcement using a sequential information signaling approach. They conclude that there is an equilibrium in which managers truthfully signal private information by calling conversion if and only if this information is negative. Intuitively, firms with more favorable information will have lower costs of foregoing the opportunity to force conversion because conversion is more likely to happen voluntarily later. The conversion ratio itself can also serve as an important signal to outside investors. Corrado and Patel (1995) determined that high conversion ratios are negatively correlated with offer announcement stock returns and that low conversion ratios are uncorrelated. Kim (1990) surmised that this conversion ratio serves as a credible signal to investors. A larger conversion ratio signals lower expected earnings, because it implies that the firm is more willing to shift risk, sharing profits if necessary. A lower conversion ratio signals that the firm is unwilling to share profits or spread risk, so it implies higher

21 Rusi Yan 20 expected earnings. Stein (1992) suggested that convertible debt is a backdoor form of equity financing the firm needs to issue equity to shift risk to the new investors, but wants to signal high growth with a form of debt. Davidson, Glascock, and Schwarz (1995) tested the signaling credibility of the price of convertible debt. They introduced a new variable: time to becoming at-themoney, or when it becomes attractive to convert to equity. If the conversion ratio is large in relation to the expected growth, then the expected time to becoming at-the-money is long. The convertible debt is therefore analogous to straight debt because investors would not want to convert their debt to equity. If the conversion ratio is small with respect to expected growth, then the expected time is short, which can be interpreted as an equity issuance since investors would want to convert sooner. They test this hypothesis by regressing the abnormal returns and cumulative predictive error on the expected time to becoming at-the-money and control variables for the firm, which include the relative size of issue, standard deviation of returns, and number of days after issuance before the security could be converted. They find that the time to becoming at-the-money is positively related to announcement period abnormal returns, including the control variables. The shorter the expected time, the more negative the abnormal returns are. This result can be interpreted to mean that a shorter time to becoming at-the-money signals like equity, because it indicates that insiders are more willing to shift risk to the new security-holders, supporting Kim s theory. Because equity conversion becomes profitable very quickly, the new investors would prefer to convert sooner, allowing the firm to acquire the equity financing that it needs. As Stein theorized,

22 Rusi Yan 21 the issuance of convertible debt serves as a backdoor means to obtain equity financing while signaling like debt. 4. Research Design Much of the literature has attempted to explain how firms operate under different models of capital structure choice and how different types of securities are perceived by investors. There has been much debate over which theory of capital structure Tradeoff Model or Pecking Order Model best fits the empirical evidence. These debates center around the behavior of firms in issuing straight debt or stock, but this approach is limited. Another tactic has been to use a security that has properties of both debt and equity: the convertible bond. A further subject of exploration in this topic is to determine how the characteristics of the firm itself affect its signaling behavior with respect to convertibles. This paper attempts to incorporate the size of the firm in a study of how its choice of capital structure can serve as a signal. Information asymmetries may be different for firms of different sizes. Larger firms may receive more attention because they enter the public sphere more often, so more information is publicly available about them. Consequently, these firms are less eager and less able to rely on signaling because the market already incorporates more information about them into market prices. On the other hand, smaller firms will need alternative ways to demonstrate their abilities and projections of success to firm outsiders. I theorize that smaller firms may need to rely more on signaling because there is less information available about them and may also have greater abilities to signal more strongly.

23 Rusi Yan 22 I extend the model developed by Davidson, Glascock, and Schwarz (1995) to include firm size and newer data. The previous study uses convertible bonds offered from 1980 to 1985, and in my study, I use bonds issued from 1990 to From the firm s point of view, if the probability of success is high, then it would set a higher conversion premium, making it less attractive for investors to convert, and they should see positive abnormal returns. On the other hand, a bond closer to being at-the-money with a lower conversion premium signals more like equity, and if the market believes this signal, then negative abnormal returns are expected. I plan to examine whether this signaling behavior is different for smaller firms because signaling is more important for them. 4.1 Data I use data collected from the Moody s Mergent Fixed Income Securities Database, including a series of convertible bonds, as well as the commodity, or the type of equity that the convertible bond may be converted to. Usually, this is the firm s common stock. The sample includes the original prices for these commodities as well. I will also include the quality of the bond ratings to control for the riskiness of the asset. I also have data from the Center for Research in Security Prices (CRSP) about the issuing companies and their daily closing prices to monitor how the market reacted when the bonds were issued, as well as to track the firms progress over time. 4.2 Abnormal Returns The abnormal return is the difference between the actual return of a security and its expected return. The return of a security i can be found using the Capital Asset Pricing Model (CAPM):

24 Rusi Yan 23 where R i is the excess return of the security: R i = " i + # i R m + $ i where R m is the excess return of the market: R i = r i " r f and r f is the risk-free rate. R m = r m " r f The actual return of a security for one period is: R i,t = V i,t "V i,t"1 + div i,t V i,t"1 where V is the security s value and div is the dividend paid. Here, I will use the closing price of the firm s stock. Following the model outlined in Corrado and Patel (1995), the abnormal returns for security j on day t are calculated: AR j,t = R j,t " (# j + $ j R m,t ). Let T 0 be the start date and T n be the end date of the estimation time frame. For this model, I used ordinary least squares estimates of α j and β j, which are calculated using the following: " # j = T n %(R m $ # µ m) (R j $ # µ j) T 0 T n % (R m $ µ # m) 2 T 0 " # j = µ # j $ %# µ # m Here, µ " j and µ " m are the sample averages of R j and R m.

25 Rusi Yan Model To see how the market reacts to a firm s choices in terms of its convertible bond conditions, I will examine how the firm s abnormal returns are affected by the conversion premium, or how much stock appreciation is needed for the bond to become at-themoney. Letting CP denote the conversion price, SP be the stock price at time of issuance, the conversion premium App for firm i at time of issuance t is calculated: App i = CP i " SP i,t SP i,t Extending Davidson, Glascock, and Schwarz (1995), I will use the following regression on the abnormal returns: where AR = abnormal returns, App = stock appreciation needed, C = control variables. AR i = a + b 1 App i + " j b j C ij Several control variables that may have confounding effects have been included. The first control is the quality rating of these convertible bonds. Different firms would have different inherent risks, and I hope to use the quality rating of these securities to control for the idiosyncratic risks of the individual firms. I construct a dummy variable for the Moody s ratings for the issuing firms, accounting for multi-collinearity. Another control variable is the relative size of issue; it is possible that the size of the security

26 Rusi Yan 25 issued can affect the strength of the signal. The relative size is measured by the issue size divided by the market value of 1 the firm s stock. 5. Results Using a random sample of 100 bonds from the Mergent data 1, I analyzed how the issuance of convertible bonds affects the abnormal returns of the issuing firms. The feature of interest is the amount of appreciation needed for the bond to become at-themoney, defined as the conversion premium. I considered time periods of 10, 30, and 200 days before and after the offering date, both together and separately. Figure 2 illustrates the time periods studied. Figure 2. In addition to splitting the data into before and after periods, I also separated the firms into the 50 largest and smallest firms by market capitalization. However, the event of interest is not the date that the convertible bond was issued, but rather the date that the public learned of the issue. Unfortunately, the data is limited to the date that the bond was actually issued, and the date that the market is informed of the issue is difficult to pin down. 1 The Mergent dataset was organized by issue ID and sample was drawn from the dataset using a random number generator.

27 Rusi Yan Empirical Results and Analysis Overall, I find that the conversion premium has a negative effect on the offering yield. Figure 3 displays the trend of how the offering yield changes with the appreciation needed for the bond to become at-the-money. An obvious negative relationship exists between the amount of stock appreciation needed and the yield that the bond offers to investors. Most of the bonds were clustered around a conversion premium of 0 to 50%, but even within this range the results are statistically significant. Figure 3. Effect of premium on yield T-statistic The negative, statistically significant effect of the conversion premium on the offering yield is slightly puzzling, because as the conversion premium increases, the convertible

28 Rusi Yan 27 bond should be more debt-like, which means that it should offer a higher yield. However, this interpretation requires that one compares the same firm or at least comparable firms. In this dataset, most of the firms are different, and they differ greatly on many qualities, such as ratings, size, and volatility. Of the few firms that do appear twice in the dataset, a positive relationship is observed. One such firm, Diamond Offshore Drilling, is displayed below. Figure 4. Offering Yield and Conversion Premium for Diamond Offshore Drilling The conversion premium also has a positive effect on the abnormal returns over all periods around the offering date. The following tables illustrate the effects of the stock appreciation needed to become at-the-money, including the control variables relative size and the rating of the bond. The values in parentheses are the t-statistics of the results, and in general, the 30 day and 200 day results are significant at least at the 5% level.

29 Rusi Yan 28 The positive effect of the conversion premium is consistent with the hypothesis that debt-like issuances act as a more positive signal than equity-like issuances. If a convertible bond has a higher conversion premium, then it is more out-the-money at the time of issuance and investors would therefore not find it profitable to convert until the stock appreciates significantly. Because a higher conversion premium would signal more like straight debt, a convertible bond issuance with a higher conversion premium should have a positive effect on the abnormal returns for the firm. As discussed in the previous literature, a debt issuance is perceived by the market as a positive event. The following tables show the effect of the conversion premium on the abnormal returns, if the conversion premium changed by one standard deviation. In Table 3, we see a positive, statistically significant effect of the conversion premium in the 30 day and 200 day ranges. The 10 day range is not significant, which will be discussed in the next section. Tables 4 and 5 show the differences between the smaller firms and the larger firms for all time periods. The same pattern of statistically significant, positive effects of the conversion premium on the abnormal returns exists in both groups. However, the effect is generally larger for the smaller firms, which is also consistent with the hypothesis that the signaling effect of capital structure can differ with firm size. As discussed in the previous sections, larger firms may be less willing or able to use capital structure as a form of signaling because more information about them is already publicly available, which the market incorporates into its decisions. In general, less is known about smaller firms, making signaling a much more important and viable means of informing the market of their expectations. These results support this theory as the

30 Rusi Yan 29 issuance of the convertible bond, through the stock appreciation needed, has a larger effect on the abnormal returns, or the market s response, for the smaller firms. The results also frequently show a negative constant in the regressions, which implies that the firms that issue these bonds generally perform worse than expected, which is also consistent with the previous literature because firms that issue convertible bonds are of intermediate quality. This supports Stein s 1992 theory that firms of medium quality would be the only ones that issue convertible debt, since high quality firms would issue straight debt and firms of low quality could not afford to issue even convertible debt. Regressions of abnormal returns on only firm quality attempt to capture the pattern of the abnormal returns if the firms had not issued a convertible bond at all, which yield mixed results. For larger firms, the constants tend to be more negative. Full results can be found in the Appendix. Table 3. Effects on Abnormal Returns for all Bonds Abnormal Constant Conv. Relative Size Rating Returns Premium 10 days before to 10 days (0.82) (0.84) (-0.18) (-0.28) after 30 days before *** to 30 days (-1.93) (4.68) (1.47) (0.51) after 200 days ** before to 200 days after -(0.87) (2.52) (-0.42) (1.03) *All values in parentheses are the t-statistics

31 Rusi Yan 30 Abnormal Returns 10 days before to 10 days after 30 days before to 30 days after 200 days before to 200 days after Table 4. Effects on Abnormal Returns for Small Firms Constant Conv. Relative Size Rating Premium (1.1) (0.79) (-0.41) (-0.76) *** (-1.11) (4.68) (0.76) (-0.21) *** (-1.35) (3.21) (-0.21) (1.26) Abnormal Returns 10 days before to 10 days after 30 days before to 30 days after 200 days before to 200 days after Table 5. Effects on Abnormal Returns for Large Firms Constant Conv. Relative Size Rating Premium (-0.07) (0.22) (0.09) (0.52) *** (-1.28) (3.47) (-1.58) (1.49) ** ** (0.68) (2.37) (-2.57) (0.47)

32 Rusi Yan Inconsistencies and Discussion There are several aspects of the results that are inconsistent with the hypothesis that the firms issuance of convertible bonds acts as a signal to outside investors who do not have the same information that firm insiders do. While a preliminary study of all the bonds yields a compatible result (Table 3), a few puzzles develop when the data is separated by time frame as well as by firm size. The initial concept is that the issuance of the convertible bond drives the movements in the abnormal returns of the firms, so it would follow that a larger effect should be seen in the period after the offering date. This is not the case when looking at all the firms or at only the smaller firms. Table 6. Effects on Abnormal Returns Before Offering Date Abnormal Constant Conv. Relative Size Rating Returns Premium 10 days before to offering (0.29) (-0.29) (-0.14) (0.64) date 30 days before *** *** *** to offering (-2.66) (2.87) (2.6) (1.33) date 200 days *** ** before to offering date (-2.79) (2.03) (1.7) (1.32)

33 Rusi Yan 32 Table 7. Effects on Abnormal Returns After Offering Date Abnormal Constant Conv. Relative Size Rating Returns Premium Offering date to 10 days (0.96) (1.74) (-0.11) (-1.27) after Offering date *** to 30 days (0.61) (3.25) (-1.22) (-0.99) after Offering date to 200 days after (1.37) (1.23) (-1.95) (0.08) Tables 6 and 7 show the regression results for all firms in the periods before the offering date and after the offering date, respectively. The most significant effects of the conversion premium are found in the 30 day periods. The overall effect is split almost evenly between the before and after periods, which is counter-intuitive because the original hypothesis suggests that there should be a stronger effect in the time period after the offering date if the convertible bond issuance is the driving force of changes in the abnormal returns.

34 Rusi Yan 33 Table 8. Time-Separated Effects on Abnormal Returns For Small and Large Firms Effect of Small Firms Large Firms Conversion Premium Before After Before After 10 days 30 days 200 days (0.36) (0.78) (-0.75) (1.59) *** *** (5.36) (0.43) (0.2) (4.78) *** ** (4.23) (0.2) (0.13) (2.4) *Constants and effects of relative size and rating are omitted. These can be found in the Appendix. Separating the data further, there is a noticeable difference between large and small firms when examining the patterns in the effect of the conversion premium, displayed in Table 8. While all the results show a positive effect of the conversion premium on the abnormal returns and are generally consistent with the signaling hypothesis, the relative weights of the time periods before and after are not. For larger firms, the outcome is more compatible with theory; most of the effects take place after the offering date. In addition to being larger, the effects in the after period are also more significant than the effects in the before period. This suggests that the market was reacting to the issuance of the convertible bond and the changes in the abnormal returns reflect this reaction. However, the results for the smaller firms tell a different story because it is the period before the offering date that dominates. The effect of the conversion premium is both larger and more statistically significant than the same effects in the period after the offering date. This is also counter-intuitive because it implies that the market is reacting to the terms of the convertible bond before the bond is issued. It is also worth noting that

35 Rusi Yan 34 overall, the effects are much larger for the 30 day and 200 day periods than for the 10 day period, suggesting that markets do not incorporate new information quickly and efficiently. One possible explanation for this aberration is the difficulty in pinpointing exactly when the market learned of the bond issuance, which is the actual date of interest. Investors are often given 24 hours before the offering date to learn about the bond and its issuing firm, as well as to express interest in purchasing the bond when it is actually offered to the public. However, some firms may wish to begin marketing their issuances well in advance of this 24-hour window, which creates a larger discrepancy between when the public learns about the issuance and when the bond is actually issued, displayed in Figure 5. If the market became aware of the issuance at any time in the shaded region, then the results that were classified into the before period actually belonged in the after period, and the 10 day time period in the study did not capture the true 10 day bracket around the market s discovery. Figure 5. This discrepancy could be larger and more important for smaller firms for the same reason that signaling itself could be more important; there is less information available about them. A smaller firm may be required to introduce itself and its bond in advance in order to convince outsiders to invest in a way that a larger, more well-known firm would

36 Rusi Yan 35 not need to. Therefore, the offering date may be a more incorrect measure for smaller firms than for larger firms. Another source of error could be the actual leakage of private information. It is possible that firm outsiders are aware of the potential issuance far earlier than 10 days before the announcement and are acting on private information. This does not suggest a lack of signaling, but rather that the signal occurred at a different time than the period under investigation. 6. Conclusion Using data from the Mergent Fixed Income Securities Database, this paper investigates the use of capital structure as a form of signaling by firms when faced with information asymmetry. By regressing the abnormal returns of the firms stock prices on the conversion premium, this study hopes to capture the market s reactions to the announcement of a convertible issue. The amount of stock appreciation needed is a continuous measure of where the convertible bond exists on the debt-equity spectrum, and this paper tries to capture its effect on how outside investors perceive the issuance. I find that a larger conversion premium, or more stock appreciation needed, has a positive effect on the abnormal returns, which is consistent with the theory that debt issuances are perceived more positively. The effect is most prominent in the 30 and 200 day periods and is also statistically significant. In addition, the effect is slightly larger for the smaller firms in the sample. This indicates that it is possible that smaller firms rely on signaling more than their larger counterparts, perhaps due to a greater information asymmetry for the smaller firms. Several puzzles emerged in this study, particularly the timing of the effect of the conversion premium. There appears to be no large, significant effect in the 10 day period