CONVERTIBLE DEBT AND RISK-SHIFTING INCENTIVES. Abstract. I. Introduction

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1 The Journal of Financial Research Vol. XXXII, No. 4 Pages Winter 2009 CONVERTIBLE DEBT AND RISK-SHIFTING INCENTIVES Assaf Eisdorfer University of Connecticut Abstract I argue that convertible debt, in contrast to its perceived role, can produce shareholders risk-shifting incentives. When a firm s capital structure includes convertible debt, every investment decision affects not only the distribution of the asset value but also the likelihood that the debt will be converted and thereby the distribution of the firm s leverage. This suggests that managers can engage in riskincreasing projects if a higher asset risk generates a more favorable distribution of leverage. Empirical evidence using 30 years of data supports my argument. JEL Classifications: G31, G32, G33 I. Introduction One of the primary reasons identified in the literature for issuing convertible debt is mitigating the risk-shifting (asset substitution) problem. Following the work of Jensen and Meckling (1976) and Galai and Masulis (1976), Green (1984) shows that because convertible debt reverses the convex shape of levered equity over the upper range of the firm s value, it reduces the incentive of shareholders to engage in risk-increasing projects. Studies extending Green s work show that the ability of convertible debt to reduce risk-shifting incentives may vary under different frameworks (e.g., Barnea, Haugen, and Senbet 1985; Frierman and Viswanath 1993; Chesney and Gibson-Asner 2001; Ozerturk Forthcoming), yet they all agree that providing bondholders with conversion rights helps mitigate the risk-shifting problem. In this article, however, I argue and find that the presence of convertible debt can produce shareholders risk-increasing incentives. When a firm s capital structure includes convertible debt, every project undertaken affects not only the distribution of the value of the firm s assets but also the likelihood that the debt will be converted and thereby the distribution of the firm s leverage. Because the capital structure of a firm affects its value, managers should take into consideration the effect of new projects on the expected leverage. This suggests that managers can have incentives to engage in risk-increasing projects if a higher asset risk generates a more desirable distribution of leverage. I thank Jayant Kale (the editor), David Mauer (the referee), Michael Barclay, Joseph Golec, Thomas O Brien, Clifford Smith, and Jerold Warner for valuable comments and suggestions. 423

2 424 The Journal of Financial Research Assume, for instance, that a firm s current debt, including convertible debt, represents the firm s optimal leverage. Thus, converting a significant portion of the debt to common equity will result in a suboptimal leverage. This will reduce the firm s value either because of the costs associated with suboptimal capital structure (e.g., tax-based costs, agency costs) or the costs of immediate financing to readjust the leverage to its target level. 1 Assume further that the conversion option is slightly in the money, which means that the debt is expected to be converted. Increasing the asset volatility in this case will lower the likelihood of conversion (i.e., higher probability that the conversion option will fall out of the money) and therefore will reduce the expected conversion costs. In a similar way, if the firm s debt after conversion is closer to its target leverage (i.e., debt conversion is desirable), riskincreasing incentives will arise when the conversion option is out of the money. That is, the presence of convertible debt can produce risk-increasing incentives when conversion is either costly or beneficial. I find empirical support for my argument. First, when the conversion option is in the money and conversion is expected to be costly, it is more likely to observe an increase in asset volatility that reduces the likelihood of conversion and therefore the expected costs upon conversion. When debt conversion is expected to be beneficial, however, no such relation is found. Second, when the likelihood of conversion increases and conversion is costly, there is a positive relation between the expected costs and the change in asset volatility. Similarly, when the likelihood of conversion decreases and conversion is beneficial, there is a positive relation between the expected benefits and the change in asset volatility. Third, as debt conversion decisions are more predictable when the asset volatility is low, changes in asset volatility that are driven by conversion cost and benefit considerations are larger at the lower level of volatility. Fourth, as opposed to the expected negative consequences of agency-based risk-shifting behavior, increasing firm risk to decrease the likelihood of costly conversion has a positive effect on firm value. II. The Effect of Convertible Debt on Risk-Shifting Incentives The risk-shifting (asset substitution) problem identified by Jensen and Meckling (1976) and Galai and Masulis (1976) suggests that shareholders in highly levered firms can have incentives to increase firm risk, as they enjoy the benefits if things go well, whereas the bondholders bear the costs if things go poorly. Green (1984) 1 Smith (1986) discusses the fixed costs associated with capital structure adjustments. Lee et al. (1996) estimate that direct costs of issuing debt and equity range between 2% and 13% of the total proceeds. Altinkilic and Hansen (2000) characterize the cost functions associated with debt and equity issuance. Leary and Roberts (2004) find that financing costs affect the frequency at which firms rebalance their capital structure.

3 Convertible Debt 425 argues that providing bondholders with conversion rights helps mitigate the riskshifting problem. That is, as the incentive to convert bonds to common shares increases with firm value, and as conversion dilutes the equity held by the current shareholders, the presence of convertible debt makes risky projects with high upside potential less attractive to shareholders. Mathematically, Green shows that because convertible debt reverses the convex shape of the equity value over the upper range of the firm value, it reduces shareholders incentive to increase firm risk. Whereas Green s (1984) argument that convertible debt mitigates riskshifting incentives is based on the equity-dilution effect of debt conversion, I argue that other consequences of debt conversion can produce incentives to increase firm risk. Specifically, changing the asset risk can affect the likelihood that the debt will be converted and thereby the future leverage of the firm. As the level of leverage affects firm value, managers can have an incentive to increase asset risk if it will result in more favorable leverage. Put differently, managers can use the asset volatility as a tool to affect the conversion decision, future leverage, and thus firm value. The following two-date setup illustrates my argument. At date 0, the value of the firm s total assets is composed of common equity and debt, where part of the debt can be converted to common equity at date 1. Let K be the conversion threshold; that is, the debt will be converted only if the asset value at date 1 is higher than K. Assume that the value of the asset at date 0, A, is slightly higher than K (i.e., the conversion option is in the money) and that the current volatility of the asset is very low. This means that the value of the asset will not change significantly between dates 0 and 1, and thus the debt is likely to be converted. Assume further that converting the debt will result in a too small leverage ratio, which will impose costs on the firm, either the costs associated with operating under suboptimal capital structure (e.g., tax-based costs) or the costs of immediate financing to readjust the leverage to its target level. Let C>0be the leverage-change conversion costs. That is, the expected value of the firm is A C. Suppose that the firm can costlessly and without delay take actions that increase asset volatility such that the asset value at date 1 will be either A + δ or A δ with equal probability, and that A δ <K;that is, the debt will be converted only at the high asset value. This means that while keeping the expected asset value at A, the firm reduces the likelihood of conversion and thereby the expected conversion costs. Specifically, the firm value is 1 2 (A + δ C) (A δ) = A 1 C>A C. Increasing volatility therefore can have a positive effect 2 on firm value in the presence of convertible debt. This analysis has several implications. First, when conversion results in a too small leverage ratio, the incentive to increase risk arises only when the conversion option is in the money. If the conversion option is out of the money, the firm will be better off with low asset volatility, under which the debt is less likely to be converted. Second, the presence of convertible debt can generate risk-increasing incentives when debt conversion is beneficial rather than costly, that is, when the

4 426 The Journal of Financial Research firm s leverage after conversion is closer than that before conversion to its target level. In this case, if the asset value at date 0 is lower than the conversion threshold (i.e., the debt is not likely to be converted), increasing asset volatility will increase the likelihood of beneficial conversion. Third, as the conversion decision is more predictable when asset volatility is lower, the incentive to increase asset risk (in either case where conversion is costly or beneficial) is stronger over the lower range of asset volatility. Fourth, as the purpose of increasing firm risk is to generate a more favorable capital structure (by either decreasing the likelihood of a costly conversion or increasing the likelihood of a beneficial conversion), risk-increasing behavior that is driven by conversion considerations should have a positive effect on firm value. (This result is in contrast to the consequences of other cases of risk-changes, as discussed later.) These arguments therefore yield the following hypotheses: H1: If conversion is costly, asset volatility will increase if the conversion option is in the money. If conversion is beneficial, asset volatility will increase if the conversion option is out of the money. H2: When the conversion option is moving in the money and conversion is costly, there is a positive relation between conversion costs and subsequent changes in asset volatility. When the conversion option is moving out of the money and conversion is beneficial, there is a positive relation between conversion benefits and subsequent changes in asset volatility. H3: Changes in asset volatility that are driven by conversion considerations are larger at the lower level of volatility. H4: Changes in asset volatility that are driven by conversion considerations have a positive effect of firm value. These hypotheses address the direct implications of the incentives to increase firm risk to affect conversion decisions, specifically, the effect of the moneyness of the conversion option on changes in asset volatility. As changing volatility might have other purposes and consequences, however, testing the hypotheses requires a discussion on how the implications of the conversion-based risk-increasing incentives identified in this study interact with those of other risk-increasing incentives, primarily the well-documented risk-shifting problem, and thereby the ability of convertible debt to mitigate the problem. The risk-shifting problem implies that increasing asset risk can benefit shareholders as a result of the wealth transfer from the current bondholders, yet it can also impose costs on shareholders due to a higher price of new debt

5 Convertible Debt 427 issued. In either case, these shareholders considerations to change asset risk will arise in highly levered firms in which the value of debt is more sensitive to asset risk. The incentive to change firm risk to encourage or prevent conversion should also be stronger for highly levered firms, as the potential change in leverage induced by conversion increases with the level of leverage. Yet, as the effects of the level of leverage on the two types of risk-shifting incentives are not necessarily of the same magnitude, the empirical tests should control for firm leverage. Further note that the risk-shifting problem is a conflict of interest between shareholders and bondholders, whereas the risk-increasing incentive identified in this study does not represent an agency problem. Therefore, to control for the former effect, the empirical tests should take into account the potential for shareholder bondholder agency conflicts. Proxies for potential agency conflicts, in particular, the risk-shifting problem, include investment opportunity set (Smith and Watts 1992; Gaver and Gaver 1993), firm size (Diamond 1993), and debt maturity (Barnea, Haugen, and Senbet 1980). In addition, the effect of agency-based risk-shifting behavior on the value of debt is stronger over the upper level of asset risk, under which the firm experiences a higher default risk. In contrast, as discussed previously, adopting risk-increasing behavior to change the likelihood of debt conversion is more effective at the lower level of asset risk. Looking at the level of asset volatility in assessing risk-increasing incentives due to debt conversion considerations (hypothesis 3) therefore reduces the effect of the traditional risk-shifting incentives. Finally, a positive shock to firm risk is typically associated with a reduction in firm value. That is, shareholders risk-shifting incentives represent an agency conflict that may result in making poor corporate decisions that decrease firm value. In addition, an increase in firm risk can indicate a higher cost of capital, which results in a lower present value of future earnings. However, as discussed previously, increasing firm risk to affect conversion decisions should lead to a higher firm value. Hypothesis 4 therefore separates the effect of the conversionbased risk-increasing behavior from other risk-related effects. III. Data and Variables Testing the hypotheses requires estimation of firm-level asset value, asset volatility, conversion option, and expected costs and benefits of conversion. Asset Value and Asset Volatility I estimate the market value of the firm s total assets and the volatility of the assets using the following two equations. The first equation, based on Merton (1974),

6 428 The Journal of Financial Research expresses the value of the firm s equity as the value of a call option on the firm s total assets, using the Black and Scholes (1973) formula: V E = V A N(d 1 ) Fe rt N(d 2 ), (1) where V E is the equity value; V A is the asset value; N( ) is the cumulative function of a standard normal distribution; d 1 = [ln(v A /F) + (r + σ 2 A /2)T ]/[σ A T ]; d2 = d 1 σ A T;σA is the asset volatility; F is the face value of debt; r is the risk-free rate; and T is the time to maturity of debt. The second equation, which is derived from Ito s lemma, represents the relation between equity volatility (σ E ) and asset volatility: σ E = V A N(d 1 )σ A V E. (2) The unobservable V A and σ A are calculated using estimates of the remaining inputs. V E is measured by the stock price multiplied by the number of shares outstanding. F is measured by the total liabilities of the firm. r is measured by the one-year Treasury bill yield. T is measured by the average maturity of the firm s debt, based on a partition to short- and long-term debt. 2 Short-term debt is defined as debt that matures within one year, and long-term debt as debt with a maturity of over one year. 3 Following Barclay and Smith (1995), who find the median of long-term debt to be approximately five years, and assuming a conditional uniform distribution of maturity, the average debt maturity is measured by: T ˆ = 1 (0.5STD + 5LTD), (3) TD where TD, STD, and LTD are the book values of total, short-term, and long-term debt. The mean debt maturity estimate produced by equation (3) (reported later in Table 1) is comparable with that reported in Barclay and Smith, as well as with that in Stohs and Mauer (1996) who calculate actual average maturities using corporate bond data. Finally, σ E is measured by the realized monthly stock return volatility in the subsequent year. Solving simultaneously equations (1) and (2) for each firm in each year generates firm-level time series estimates of asset value and asset volatility. 4 2 Crosbie and Bohn (2002) and Hillegeist et al. (2004) use debt maturity of one year for all firms in similar equations for modeling default risk. 3 I do not use the year-specific maturity data provided in Compustat because it has many missing and unreliable values (for more details on these data, see Barclay and Smith 1995). 4 As there are no closed-form solutions to V A and σ A, I solve the two-equation system numerically. The initial values used are V E + F and σ E, as they should be sufficiently close to V A and σ A, respectively, to ensure a quick convergence to the solutions.

7 Convertible Debt 429 This procedure to estimate asset value and volatility is used in the literature mostly in assessing bankruptcy risk (also known as the KMV approach; see Crosbie and Bohn 2002; Leland 2004). We should note that this approach has several limitations: it assumes a single class of zero-coupon debt with a single maturity date and ignores the presence of frictions such as taxes and transaction costs, which may affect the accuracy of the estimates. These drawbacks, however, seem less significant for the purpose of my study because I use only firm-specific changes in asset volatility (rather than levels). That is, assuming that there are no substantial year-to-year changes in debt maturity structure, tax schedule, transaction costs, and so on, in the same firm, ignoring these factors is not likely to have a significant effect on the accuracy of the results, and even in the presence of such changes, they will not induce bias unless they are systematically related to the moneyness of the conversion option. Yet to ensure that the results are robust to the estimation procedure of asset volatility, I examine the main hypotheses using an additional measure, which is based on unlevering equity volatility (see Section V). Conversion Option The conversion option is in the money (i.e., the asset value is higher than the conversion threshold) when the expected payoff to the convertible bondholders after conversion is higher than that before conversion. Let NC value be the share of the convertible bondholders in the firm s debt before conversion and C value be the share of the convertible bondholders in the firm s equity after conversion, where the values of debt and equity are based on the contingent claim model of Merton (1974) as described previously. These values are estimated as follows: C value = NC value = CD TD (V A V E ) (4) [ ) ] V A,F, r,σ A,T, (5) #CSRC #CS + #CSRC f ( 1 CD TD where CD is the book value of convertible debt, #CS is the number of common shares, #CSRC is the number of common shares reserved for conversion, and f [ ] is the Black and Scholes (1973) call option value formula. Given these estimates, I assume that the conversion option is in the money if C value > NC value. Note that this criterion does not take into account expected stock dividends and bond coupon payments that can affect the value of the conversion option. Because the dividend and coupon advantages are not necessarily perfectly matched in every firm, the criterion I use might produce noisy estimates, which may affect the classification of the moneyness of the conversion options, especially where the option is very close to at the money. To reduce this potential problem, I reexamine the main hypotheses by classifying the conversion option to be in the money only

8 430 The Journal of Financial Research if C value is higher by at least 5% than NC value, and vice versa for the out-ofthe-money conversion option (see Section V). Costs and Benefits of Conversion The extent to which debt conversion is costly or beneficial is based on the deviations from target leverage before and after potential conversion. The preconversion deviation from the target leverage is estimated by the absolute value of the difference between the firm s leverage, including convertible debt and the industry leverage. 5 The postconversion deviation is estimated by the absolute value of the difference between the firm s leverage excluding convertible debt and the industry leverage. The conversion costs are therefore estimated as: Conv Costs = NCD Ind Lvg V TD Ind Lvg A V, (6) A where NCD is the book value of the firm s non-convertible debt, and Ind Lvg is the median leverage in the industry in the same year. 6 Thus, conversion is expected to be costly if the value of equation (6) is positive, whereas conversion is expected to be beneficial if the value is negative. A numerical example illustrates this measure. Let V A = 100, TD = 30, NCD = 20, and Ind Lvg = That is, the current leverage ratio of the firm is 0.3, which is higher by 0.02 from the target (industry) leverage of 0.28, though upon conversion the leverage ratio will reduce to 0.2, which is lower by 0.08 than target leverage. Thus, converting the debt will increase the deviation from target leverage by 0.06, or equivalently, the conversion costs are: =0.06. Assume now instead that the target leverage 100 is In this case, converting the debt will decrease the deviation from target leverage by 0.04, which means conversion benefits, as implied by the negative value of equation (6): = Sample Descriptives Data are obtained from the Center for Research in Security Prices (CRSP) and Compustat from 1970 to For a firm to be included in the full sample, it must have the variables required for computing the asset value and asset volatility; for a firm to be included in the convertible debt subsample, it must also have the variables associated with conversion, including book value of convertible debt and number 5 For robustness, I also use a generated target leverage derived from a regression model (see Section V). 6 The median leverage in the industry in each year is based on the four-digit Standard Industrial Classification (SIC) code. If the four-digit industry contains fewer than five observations, I use the threedigit industry, and if that contains fewer than five observations, I use the two-digit industry. See Lang, Ofek, and Stulz (1996) for similar industry-adjustment procedures.

9 Convertible Debt 431 TABLE 1. Descriptive Statistics. Firms with Straight Debt Only Firms with Convertible Debt (N = 51,805) (N = 6,817) Mean Median Mean Median Book leverage Excess leverage Convertible debt/total debt Market-to-book Asset value 1, Asset volatility Equity volatility C value/nc value Debt maturity Note: The table presents descriptive statistics for firm-years with and without convertible debt, where convertible debt is assumed if it accounts for at least 5% of the total debt. The results are based on 58,622 firm-years from 1970 to Book leverage is the ratio of the book value of total debt to the book value of total assets. Excess leverage is the difference between the firm leverage and the industry leverage, as defined in Section III. Market-to-book is the equity market value divided by the equity book value. Asset value (presented in million dollars) and asset volatility are calculated by solving equations (1) and (2). Equity volatility is the realized monthly stock return volatility in the subsequent year. NC value and C value are the values of the claims held by the convertible bondholders before and after conversion, as defined in equations (4) and (5). Debt maturity is estimated by a weighted average of the short- and long-term debt of the firm, as defined in equation (3). The table indicates whether the means and medians in the convertible debt sample are significantly different from those in the straight debt sample. Significant at the 1% level. Significant at the 5% level. Significant at the 10% level. of shares reserved for conversion. After including all firms traded on the NYSE, AMEX, and Nasdaq that satisfy these conditions, the full sample contains 58,622 firm-year observations, representing data on 8,290 different firms. The convertible debt subsample contains 6,817 firm-years, representing 1,766 firms. Table 1 presents descriptive statistics for the sample. Firms with convertible debt typically have higher leverage than firms with only straight debt (averages of 0.34 and 0.25, respectively). This difference most likely reflects the role of convertible debt as a substitute for both straight debt and common equity. 7 The average of the C value/nc value ratio is 1.12, suggesting that conversion options are in the money on average. The market-to-book ratio is higher for firms with convertible debt. This finding is expected as the market-to-book ratio proxies for the investment opportunity set and as convertible debt is used to control for investment-based agency conflicts (i.e., risk shifting and information asymmetry). Debt maturity is longer for firms with convertible debt. This result is consistent 7 Lewis, Rogalski, and Seward (1999) construct a security choice model that determines whether convertible debt substitutes straight debt or common equity.

10 432 The Journal of Financial Research with Alderson, Betker, and Stock (2006), who document that convertible debt has relatively long maturity. IV. Results Hypothesis 1 I examine whether expected costs and benefits of conversion have implications for the effect of convertible debt on asset volatility. Table 2 presents regressions of firm-specific market-adjusted change in asset volatility in a given year (both in absolute and percentage terms) on a dummy variable that indicates whether the conversion option is in the money in that year. 8 Specifically, for a given year t, the absolute change in asset volatility is the difference between asset volatility at the end of year t and asset volatility at the end of year t 1, and the percentage change in volatility is absolute change divided by asset volatility at the end of year t 1. The marketadjusted change in asset volatility at year t is the difference between the firm s change in asset volatility and the change in the volatility of the CRSP value-weighted market index at year t. (Using an equal-weighted average yields similar results). The sample contains all firm-years with convertible debt, and the results are presented separately for the cases where conversion is expected to be costly and when conversion is expected to be beneficial. That is, conversion is assumed to be costly if the value of equation (6) is positive, which means that converting the debt will increase the deviation from target leverage, and conversion is assumed to be beneficial if the value of equation (6) is negative, implying a smaller deviation from target leverage after conversion. Following the discussion in Section II, firm size, market-to-book ratio (as a measure of investment opportunities), leverage, and debt maturity are included in all regressions as control variables. As the tests in this study rely on long time series firm-level data, the Newey West (1987) procedure, modified for panel data, is used to correct for heteroskedasticity and serial correlation. 9 When conversion is expected to be costly, a significantly larger increase in asset volatility occurs when the conversion option is in the money, that is, when there is a substantial likelihood of conversion (t-statistics between 2.09 and 3.23). These results support hypothesis 1, indicating that when conversion is costly and is expected to occur, it is more likely to observe an increase in asset volatility that reduces the likelihood of conversion. When conversion is expected to be beneficial, the likelihood of conversion has no significant effect on future changes in asset volatility. This result can be 8 I assume that firms can increase asset volatility without a significant time delay; for robustness, I examine the results where the change in volatility is measured in a longer period (see Section V). 9 The number of lags used in the Newey West procedure is one less than the number of years for each firm.

11 Convertible Debt 433 TABLE 2. Regressions of Change in Asset Volatility on the Likelihood of Conversion for Cases of Conversion Costs and Benefits. Panel A. Conversion Costs (N = 4,042) Intercept I in-the-money Size MB Leverage Maturity R 2 σ A Coefficient t-statistic ( 13.88) (2.09) Coefficient t-statistic ( 4.48) (2.40) (3.27) ( 2.34) ( 0.80) (2.75) σ A Coefficient t-statistic ( 7.66) (3.05) Coefficient t-statistic ( 2.93) (3.23) (1.63) ( 2.29) ( 0.62) (2.18) Panel B. Conversion Benefits (N = 2,578) Intercept I out-of-the-money Size MB Leverage Maturity R 2 σ A Coefficient t-statistic (0.10) ( 0.06) Coefficient t-statistic ( 1.09) ( 0.01) ( 3.78) (1.70) (0.63) (3.14) % σ A Coefficient t-statistic (0.66) ( 0.10) Coefficient t-statistic ( 1.41) (0.08) ( 2.25) (2.14) (0.89) (2.35) Note: The sample contains firm-years in which the convertible debt accounts for at least 5% of the total debt. Results are presented separately for firm-years in which conversion is expected to be costly and beneficial (based on the deviation from the optimal leverage before and after conversion, as defined in equation (6)). The dependent variable is market-adjusted change in asset volatility (both in absolute and percentage terms), calculated by the difference between the firm s change in asset volatility in a given year and the value-weighted average change in volatility in the same year. The independent variables are a dummy variable that equals 1 if the conversion option is in the money (out of the money) for the conversion costs (benefits) groups, and the following control variables: size, estimated by the natural log of the market value of the firm s total assets (as measured by solving equations (1) and (2)); market-to-book ratio (MB), estimated by the equity market value divided by the equity book value; leverage, estimated by the ratio of the book value of total debt to the book value of total assets; and maturity, estimated by a weighted average of the short- and the long-term debt of the firm, as defined in equation (3). The table presents regression coefficients and t-statistics (in parentheses), based on Newey West standard errors, computed from 1970 to Significant at the 1% level. Significant at the 5% level. Significant at the 10% level. related to several factors. First, when the conversion is beneficial to the firm, the conversion threshold is lower than when conversion is costly (this is because conversion benefits increase the value of conversion); thus, risk-increasing incentives are more likely to arise when the asset value is relatively low. This means that other

12 434 The Journal of Financial Research factors may affect the ability of the firm to increase risk, such as debt covenants and a better monitoring system. Second, in the case of conversion benefits, volatility is increased to encourage conversion (and not to prevent one as in the case of conversion costs). As most convertible bond issues contain call provisions (see Korkeamaki and Moore 2004), the debt can be converted by forcing conversion, with no need to change the firm s risk. The regressions in Table 2 provide a first indication that expected conversion costs can generate risk-increasing incentives. Yet, as the results are based on all firm-years with convertible debt, firm-specific time series effects can induce noise to the coefficient estimates. Assume, for example, that a certain firm has the same amount of convertible debt and likelihood of conversion in two consecutive years, which results in risk-increasing incentives. In this case, the firm might increase risk in the first year to a sufficient level and therefore does not need to do so in the second year. Thus, a positive change in asset risk will be observed only in one of the two years. To address this effect, I reexamine the results in Table 2 on a sample of firms with new issues of convertible debt. To eliminate the effect of existing convertible debt, and to capture only significant issues of debt, a new issue is assumed when the fraction of convertible debt in the total debt increases from 0% to more than 25% in the past year. 10 The results reported in Table 3 are consistent with Table 2. When conversion is costly and the conversion option is in the money, there is a significant, larger increase in asset volatility (t-statistics between 1.81 and 2.75), and as in Table 2, when conversion is beneficial, the likelihood of conversion has no effect on asset risk. The results in Tables 2 and 3 also indicate that the moneyness of the conversion option has an important economic effect on changes in firm risk, especially when debt conversion is costly; specifically, when the conversion option is in the money, the absolute change in volatility is higher by 2.0% to 4.3% than when the conversion option is out of the money. Hypothesis 2 Table 4 assesses how changes in the likelihood of conversion affect the relation between costs and benefits of conversion and changes in asset volatility. That is, I examine whether the effect of conversion costs on risk changes is strengthened when the conversion option moves in the money and whether the effect of conversion benefits on risk changes is strengthened when the conversion option moves out of the money. I estimate the following regression on a sample of all firm-years in which conversion is expected to be costly: σ A = β 0 + β 1 CC + β 2 I (+) CC + β 3 I ( ) CC + CONTROLS + ε (7) 10 The choice of 25% is arbitrary; the results are robust to other cutoffs between 10% and 40%.

13 Convertible Debt 435 TABLE 3. Regressions of Change in Asset Volatility on the Likelihood of Conversion for Cases of Conversion Costs and Benefits in the Presence of New Convertible Debt. Panel A. Conversion Costs (N = 453) Intercept I in-the-money Size MB Leverage Maturity R 2 σ A Coefficient t-statistic ( 6.85) (1.81) Coefficient t-statistic ( 2.83) (2.16) (1.14) ( 0.92) (1.29) (1.19) % σ A Coefficient t-statistic ( 5.16) (2.26) Coefficient t-statistic ( 3.87) (2.75) (1.72) ( 0.39) (0.47) (2.43) Panel B. Conversion Benefits (N = 481) Intercept I out-of-the-money Size MB Leverage Maturity R 2 σ A Coefficient t-statistic ( 1.15) (0.09) Coefficient t-statistic ( 0.38) (0.33) ( 1.08) (0.26) (0.00) (0.98) % σ A Coefficient t-statistic (0.02) ( 0.36) Coefficient t-statistic ( 0.87) ( 0.19) ( 0.97) (0.65) (0.50) (1.18) Note: The sample contains firms with new issues of convertible debt. A new issue is assumed when the share of convertible debt in the total debt increases from 0% to more than 25% in the past year. Results are presented separately for firm-years in which conversion is expected to be costly and beneficial (based on the deviation from the optimal leverage before and after conversion, as defined in equation (6)). The dependent variable is market-adjusted change in asset volatility (both in absolute and percentage terms) following new issues. The independent variables are a dummy variable that equals 1 if the conversion option is in the money (out of the money) for the conversion costs (benefits) groups, and a set of control variables, as defined in Table 2. The table presents regression coefficients and t-statistics (in parentheses), based on Newey West standard errors, computed from 1970 to Significant at the 1% level. Significant at the 5% level. Significant at the 10% level. and the following regression for all firm-years in which conversion is expected to be beneficial: σ A = γ 0 + γ 1 CB + γ 2 I (+) CB + γ 3 I ( ) CC + CONTROLS + ν, (8) where CC is the conversion costs, estimated by the positive value of equation (6); CBis the conversion benefits, estimated by the negative value of equation (6); and

14 436 The Journal of Financial Research TABLE 4. Regressions of Change in Asset Volatility on an Interactive Term between Conversion Costs (Benefits) and the Change in the Likelihood of Conversion. Panel A. Conversion Costs (N = 887) Intercept CC I (+) CC I ( ) CC Size MB Leverage Maturity R 2 σa Coefficient t-statistic (1.32) ( 0.94) (3.12) Coefficient t-statistic (1.00) (0.60) ( 3.86) Coefficient t-statistic (1.26) (0.13) (2.63) ( 3.17) ( 2.33) ( 0.52) ( 0.38) (0.21) % σa Coefficient t-statistic (3.53) ( 0.37) (1.98) Coefficient t-statistic (3.15) (0.74) ( 3.50) Coefficient t-statistic (1.82) (0.15) (1.80) ( 2.85) ( 2.67) ( 0.51) (1.32) (0.97) (Continued)

15 Convertible Debt 437 TABLE 4. Continued. Panel B. Conversion Benefits (N = 825) Intercept CB I (+) CB I ( ) C B Size MB Leverage Maturity R 2 σa Coefficient t-statistic ( 17.77) ( 0.56) ( 1.43) Coefficient t-statistic ( 17.69) ( 1.80) (1.45) Coefficient t-statistic ( 5.15) ( 0.35) ( 0.98) (1.82) (7.09) ( 2.36) ( 0.07) (0.47) % σa Coefficient t-statistic ( 12.90) (0.23) ( 0.41) Coefficient t-statistic ( 13.05) ( 0.69) (2.67) Coefficient t-statistic ( 2.52) (0.02) ( 0.34) (2.32) (0.70) (1.60) ( 0.61) (0.55) Note: The sample contains firm-years in which the convertible debt accounts for at least 5% of the total debt. Results are presented separately for firm-years in which conversion is expected to be costly and beneficial. The dependent variable is market-adjusted change in asset volatility (both in absolute and percentage terms). The independent variables are: CC and CB are the measures of conversion costs and benefits, respectively, as estimated by equation (6); I (+) and I ( ) are dummy variables that indicate whether the conversion option moves in the money and out of the money, respectively, based on the C value/nc value ratio, as defined in Section III; and the remaining control variables are defined in Table 2. The table presents regression coefficients and t-statistics (in parentheses), based on Newey West standard errors, computed from 1970 to Significant at the 1% level. Significant at the 5% level. Significant at the 10% level.

16 438 The Journal of Financial Research I (+) (I ( ) ) is a dummy variable that equals 1 if the conversion option had moved in the money (out of the money) in the past year, and 0 otherwise. 11 Hypothesis 2 is therefore consistent with positive β 2 and γ 3, and negative β 3 and γ 2. The results of the first regression strongly support the hypothesis. When the conversion option is moving in the money (increasing the likelihood of conversion), higher conversion costs are associated with positive changes in asset volatility (t-statistics between 1.80 and 3.12), and when the conversion option is moving out of the money (decreasing the likelihood of conversion), higher costs are associated with negative changes in asset volatility (t-statistics between 2.85 and 3.86). The results of the second regression show that the relation between conversion benefits and changes in asset volatility is stronger when the conversion option is moving out of the money (t-statistics between 1.45 and 2.67), whereas no significant relation is found when the conversion option is moving in the money. In economic terms, when conversion is costly and the conversion option is moving in the money, a 1 standard deviation increase in conversion costs increases the change in asset volatility by 2.8% to 6.4%. Similarly, when conversion is beneficial and the conversion option is moving out of the money, a 1 standard deviation increase in conversion benefits increases the change in asset volatility by 2.2% to 3.0%. The results in Table 4 are therefore consistent with the second hypothesis, providing further indication that the presence of convertible debt can produce riskincreasing incentives. Hypothesis 3 Table 5 examines whether the relation between conversion costs and benefits and changes in asset volatility is stronger at a lower level of firm risk. I regress the change in asset volatility on an interaction variable between conversion costs and benefits and the likelihood of conversion (similar to the regressions in Table 4) for subsamples of low and high asset volatility. Panel A shows that the positive effect of the change in the conversion likelihood (i.e., when the conversion option moves in the money) on the relation between conversion costs and volatility changes is stronger when the initial firm risk is low. Panel B shows that when conversion is expected to be beneficial, the effect of the change in conversion likelihood on the relation between conversion benefits and volatility changes is also stronger in the low-risk subgroups, although it is insignificant. These results support hypothesis 3, providing further evidence that expected conversion costs can generate risk-increasing incentives whereas conversion benefits have a lesser effect on firm risk. 11 To avoid trivial changes in asset value, changes in the C value/nc value ratio of less than 5% are excluded.

17 Convertible Debt 439 TABLE 5. Regressions of Change in Asset Volatility on an Interactive Term between Conversion Costs (Benefits) and the Change in the Likelihood of Conversion for Low and High Firm Risk. Panel A. Conversion Costs (N = 887) Intercept CC I (+) CC Size MB Leverage Maturity R 2 σa Low volatility (3.43) ( 0.93) (2.89) ( 4.39) (2.63) ( 0.96) ( 0.29) High volatility (0.46) ( 0.19) (1.42) ( 2.34) (1.55) ( 0.97) (0.13) % σa Low volatility (2.76) ( 0.39) (2.26) ( 2.79) (0.87) (0.20) ( 0.48) High volatility ( 0.21) ( 1.55) (1.29) ( 2.08) (0.58) ( 0.76) (1.16) Panel B. Conversion Benefits (N = 825) Intercept CB I ( ) C B Size MB Leverage Maturity R 2 σa Low volatility ( 1.03) ( 2.12) (1.44) (0.97) (0.90) ( 0.53) ( 1.46) High volatility ( 3.54) (0.48) (0.93) (3.65) (0.06) ( 1.73) (0.30) % σa Low volatility ( 1.08) (0.33) (1.95) (0.18) (1.71) ( 0.85) (0.19) High volatility ( 1.28) (0.14) (1.60) ( 1.37) (1.22) ( 0.96) (0.87) Note: The sample contains firm-years in which the convertible debt accounts for at least 5% of the total debt. Results are presented separately for firm-years in which conversion is expected to be costly and beneficial. Each subsample is divided into two equal-sized subgroups based on the asset volatility in the previous year. The dependent variable is market-adjusted change in asset volatility (both in absolute and percentage terms). The independent variables are: CC and CBare the measures of conversion costs and benefits, respectively, as estimated by equation (6); I (+) and I ( ) are dummy variables that indicate whether the conversion option moves in the money and out of the money, respectively, based on the C value/nc value ratio, as defined in Section III; and the remaining control variables are defined in Table 2. The table presents regression coefficients and t-statistics (in parentheses) based on Newey West standard errors, computed from 1970 to Significant at the 1% level. Significant at the 5% level. Significant at the 10% level.

18 440 The Journal of Financial Research Hypothesis 4 I evaluate how changes in firm risk that are associated with conversion considerations affect firm value. Table 6 presents regressions of a given year asset returns (both raw returns and market-adjusted returns) 12 on the change in asset volatility in the same year and on an interaction variable between the change in volatility and a dummy variable that indicates the incentive to increase risk due to conversion considerations. That is, the dummy variable equals 1 either when debt conversion is costly and the conversion option is in the money (results reported in Panel A) or when conversion is beneficial and the conversion option is out of the money (Panel B), and 0 otherwise. The results first indicate a significant negative effect of change in firm risk on firm value (t-statistics between 6.41 and 11.00), which is consistent with the conventional models of asset pricing and with the expected consequences of the agency-based shareholders risk-shifting behavior, as discussed in Section II. The presence of debt conversion-based risk-increasing incentives, however, produces the opposite effect, as predicted by the argument of this study. When debt conversion is costly and the conversion option is in the money, an increase in firm risk has a relative positive effect on firm value, as indicated by the coefficient of the interactive variable (t-statistics between 2.71 and 3.20). This finding supports hypothesis 4, suggesting that when facing expected debt conversion that will impose costs on the firm, managers have an incentive to increase firm risk to reduce the likelihood of conversion and thus to increase firm value. Economically, when conversion is costly and the conversion option is in the money, a 1 standard deviation increase in the change in asset volatility increases the asset return by approximately 6.5%. When debt conversion is beneficial, however, the moneyness of the conversion option has no significant effect on the relation between changes in firm risk and firm value. V. Robustness Tests I examine the robustness of the main results with respect to six aspects. The first two concern the estimation procedure. The main regression results in this study are based on ordinary least squares (OLS) estimation, where the standard errors are corrected for heteroskedasticity and serial correlation using the Newey West (1987) procedure. I use two alternative methods. The first is a feasible generalized least squares (FGLS) regression that allows for a heteroskedastic and firm-specific autocorrelation variance covariance matrix of the errors. The second method is a fixed 12 Raw asset return is measured by the annual percentage change in asset value; market-adjusted asset return is the difference between the firm s raw return in a given year and the value-weighted average return of the market in the same year.

19 Convertible Debt 441 TABLE 6. Regressions of Asset Return on an Interactive Term between the Change in Asset Volatility and the Incentive to Increase Firm Risk Due to Conversion Considerations. Panel A. Conversion Costs (N = 56,679) Intercept σa Iin-the-money σa Size MB Leverage Maturity R 2 Raw return Coefficient t-statistic (48.40) ( 10.70) (3.07) Coefficient t-statistic (4.27) ( 11.00) (3.20) (11.97) ( 18.95) (0.78) (7.30) Market-adjusted return Coefficient t-statistic ( 77.26) ( 6.83) (2.71) Coefficient t-statistic ( 15.48) ( 6.68) (2.74) ( 2.59) ( 1.00) ( 2.81) (2.39) Panel B. Conversion Benefits (N = 56,679) Intercept σa Iout-of-the-money σa Size MB Leverage Maturity R 2 Raw return Coefficient t-statistic (48.42) ( 10.44) ( 0.58) Coefficient t-statistic (4.25) ( 10.73) ( 0.50) (11.95) ( 18.92) (0.79) (7.32) Market-adjusted return Coefficient t-statistic ( 77.23) ( 6.57) ( 0.78) Coefficient t-statistic ( 15.49) ( 6.41) ( 0.83) ( 2.60) ( 0.98) ( 2.79) (2.40) Note: The dependent variable is the firm s asset return in a given year, where raw return is the annual percentage change in asset value, and market-adjusted return is the difference between the firm s raw return and the value-weighted average return in the same year. The independent variables are the market-adjusted change in asset volatility and an interactive variable between the change in asset volatility and a dummy variable that indicates the incentive to increase firm risk due to conversion considerations; in Panel A, the dummy variable equals 1 if conversion is expected to be costly and the conversion option is in the money, and in Panel B, the dummy variable equals 1 if conversion is expected to be beneficial and the conversion option is out of the money. The regressions also include a set of control variables, as defined in Table 2. The table presents regression coefficients and t-statistics (in parentheses) based on Newey West standard errors, computed from 1970 to Significant at the 1% level.

20 442 The Journal of Financial Research industry effects regression that eliminates potential effects of industry-specific properties on changes in asset risk. This regression includes dummy variables for each two-digit SIC code in the sample, where White (1980) standard errors are used to adjust for heteroskedasticity. The third robustness test addresses the estimate of the deviation from target leverage, which determines the magnitude of costs and benefits of conversion. Throughout the article I use the median leverage in the industry as a measure of target leverage. For robustness, I estimate target leverage using a pooled regression of firm s actual leverage on a set of variables that are found in prior studies to explain cross-sectional variation in observed leverage ratios (see, e.g., Barclay, Smith, and Watts 1995; Hovakimian, Opler, and Titman 2001). The explanatory variables are: log of firm size; market-to-book ratio; net property, plant, and equipment (PP&E), scaled by total assets; earnings before interest, tax, and depreciation (EBITD), scaled by total assets; research and development expense, scaled by sales; and selling expenses, scaled by total assets. The target leverage is therefore measured by the fitted value of the regression model. The fourth test uses a different measure of asset volatility. Instead of the contingent-claim-based measure, I estimate asset volatility by unlevering the volatility of the firm s equity, excluding convertible debt. That is, σ A = V A NCD V A σ E, using the same notations as in Section III. Although this measure is more easily computed than the measure used throughout the article, it has one main drawback: it ignores the risk of the firm s debt. 13 The fifth test concerns the timing of the change in asset volatility. In all regressions the change in volatility is measured during the year where the moneyness of the conversion option is determined. To account for possible time delays in changing asset volatility, I examine the results where the change in volatility is measured in a two-year period, the current year and the subsequent year. Finally, as discussed in Section III, I use a modified criterion for the moneyness of the conversion options; that is, the option is assumed to be in the money (out of the money) if the share of the convertible bondholders in the firm s equity after conversion is higher (lower) by at least 5% than their share in the firm s debt before conversion. Panels A, B, and C of Table 7 replicate the results in Tables 2, 3, and 4, respectively, using the procedures described previously, where only the coefficients and t-statistics of the primary independent variables are reported. The results based on the FGLS estimation in Panels A and B are, for the most part, significantly stronger than those reported in Tables 2 and 3 for cases of conversion costs, 13 The results remain similar when using the change in the unadjusted equity volatility as a proxy for the change in asset volatility.