# Stock price response to calls of convertible bonds: still a puzzle?

The liquidity hypothesis predicts' negative abnormal returns around the conversion-forcing call announcements of convertible bonds,
followed by a price recovery. We find the former but not the latte. The
liquidity hypothesis also implies that the abnormal returns during the
announcement and the post-announcement periods should be related to
proxies for the stock's liquidity. Again, our findings do not
support these implications of the liquidity hypothesis. We conclude that
the reason for the negative abnormal returns around the announcement of
a conversion-forcing call needs further examination.

**********

Several studies have documented negative abnormal returns around conversion-forcing call announcements (COFCAs) of convertible bonds followed by positive abnormal returns. These studies attribute this pattern to liquidity pressures, and this explanation is referred to as "the liquidity hypothesis" by Mazzeo and Moore (1992). We examine the robustness of the evidence in support of the liquidity hypothesis in two ways. First, we examine the cross-sectional relation between the abnormal returns (during and after the COFCAs) and illiquidity proxies. The liquidity hypothesis implies that abnormal returns during the announcement period should be negatively related to illiquidity proxies, i.e., the less liquid the security is, the more negative the abnormal return. It also implies that the post-announcement positive abnormal returns should be negatively related to the announcement abnormal returns, or positively related to the illiquidity proxies, or both. We confirm the negative abnormal returns during the COFCA window. However, we find that neither the COFCA window abnormal returns nor the post-announcement abnormal returns are statistically related to illiquidity proxies. Moreover, we do not find a statistically significant relationship between the post-announcement abnormal returns and the announcement abnormal returns.

Second, our findings indicate that the abnormal returns following COFCAs are sensitive to the choice of the estimation period for the market-model parameters. Thus, we obtain abnormal returns by using an alternative measure of abnormal returns that follows the buy-and-hold procedure developed by Barber and Lyon (1997) and Lyon, Barber, and Tsai (1999). The buy-and-hold abnormal returns also do not exhibit a price recovery. This finding reinforces our conclusion that empirical support for the liquidity hypothesis is not robust.

Previous studies consider asymmetric information as another explanation for the negative abnormal returns around COFCAs. Thus, we also include proxies for asymmetric information in our cross-section regressions. However, we do not find a relation that is consistent with the predictions of the asymmetric information hypothesis.

The paper is organized as follows. In Section I we review relevant previous studies and present the contributions of this paper. Section II describes our data and empirical design. Section III reports the results and Section IV concludes.

I. Literature Review

Mikkelson (1981), Ofer and Natarajan (1987), Cowan, Nayar, and Singh (1993) and others find that forced conversion of convertible bonds is associated with negative abnormal equity returns. (1) Harris and Raviv (1985), Kim and Kallberg (1998), and Cowan, Nayar, and Singh (2000) present asymmetric-information models suggesting that forcing a conversion is a negative signal for the value of the company. When managers receive such a signal, they force conversion to conserve their company's cash flow. When managers receive a good signal, they distinguish their companies by not forcing a conversion and instead let bondholders elect to convert voluntarily when the positive information is revealed. Thus, the asymmetric information hypothesis implies that the market should react negatively to COFCAs. Additionally, if the negative information conveyed by COFCAs is immediately impounded in security prices, then we should not observe abnormal returns during the post-announcement period.

Alexander and Stover (1980) and Ofer and Natarajan (1987) find long-term negative abnormal performance (in terms of equity returns and accounting measures) that support the asymmetric-information explanation. However, Ofer and Natarajan (1987) note that a long-term (post-announcement) abnormal equity return is also an indication of either market inefficiency or an inappropriate benchmark. Cowan, Nayar, and Singh (1990) demonstrate that using the pre-announcement period as an estimating period introduces a downward bias in the estimated post-announcement abnormal returns because COFCAs usually follow stock price increases. Consistent with market efficiency, Cowan, Nayar, and Singh (1990) find no long-term (post-announcement) abnormal returns when they use post-announcement data to estimate the market model parameters.

In subsequent research, Campbell, Ederington, and Vankudre (1991), Mazzeo and Moore (1992), Byrd and Moore (1996), Ederington and Goh (2001) and Bechmann (2004) use a post-announcement estimation period and find negative abnormal returns around the COFCAs, followed by positive abnormal returns. Ederington and Goh (2001) find that insiders buy equity before the announcements and analysts increase their earnings forecasts. Thus, they conclude that the price decline is due to liquidity price pressures rather than asymmetric information. In an imperfect (or a relatively thin) market, the increase in the number of outstanding shares induces an initial price decline and a subsequent price recovery as the market absorbs the new shares. (2)

In this paper we argue that the liquidity hypothesis also implies that the magnitude (i.e., the absolute value) of the initial price decline should be positively related to illiquidity proxies. Additionally, the post-announcement returns should be positively related to the magnitude of the initial price decline and/or to illiquidity proxies. However, we show that the negative price decline around the announcement date and the abnormal returns following the announcement date are not related to traditional illiquidity proxies. Thus, our paper raises doubts whether the negative abnormal returns around COFCAs should be attributed to liquidity price pressures.

II. Data and Empirical Design

This section describes our data sources and the procedures we use to obtain our sample. It also describes the statistical procedures and variables we use.

A. Data

Our sample has two sources. First, Ederington and Goh (2001) have kindly made available a sample of 298 forced conversions between December 1984 and November 1993. This sample is the one they use in Ederington and Gob (2001). Second, we use Standard and Poor's Bond Guide to update this sample to December 2002 and increase its size to 537 conversions.

We use Factiva to collect the announcement dates, and exclude six observations where we cannot find an announcement in any daily newspaper or newswire. We further reduce the sample to exclude two foreign firms and 20 firms from regulated industries such as utilities and financial institutions. We exclude another 97 firms for which we cannot find any apparent forced-conversion, either because the stock price at the time of the corporate announcement is lower than the conversion price or because we cannot find the actual conversion price. We eliminate an additional 11 observations because the announcement indicates that the bond in question is not a traditional convertible bond. Three of these bonds are either exchangeable to the equity of another firm or to more than one class of equity. The remaining eight are liquid yield option notes. We delete another nine firms because of insufficient stock return data. These deletions result in a final sample of 392 firms.

For the full sample, we obtain data on issue size, conversion ratio, and final maturity of the issues from Factiva, and the daily returns, market capitalization of equity, and the returns on the market indexes from CRSE For each of the firms we also obtain from Hasbrouck's web site two measures of liquidity (or illiquidity) that Hasbrouck (2004, 2005) discusses. (3) We obtain accounting data for these firms from Compustat, including the data we need to identify the appropriate matched firms. We use Institutional Brokers' Estimate System (IBES) to obtain the standard deviation of analysts' earnings forecasts for each firm in the sample. The final sample size we use in each of our empirical tests varies according to data availability. Finally, we use the Eventus Software (Cowan, 2005a, 2005b) to estimate abnormal returns and associated statistics to test for significance.

B. Event Study Method

To begin our analysis, we use the traditional market model to estimate the abnormal returns. We estimate the market model for firm i as

[R.sub.i,t] = [[alpha].sub.i] + [[beta].sub.i][R.sub.m,t] + [[epsilon].sub.i.t] (1)

where [R.sub.i,t] is its return on day t and [R.sub.m,t] is the corresponding return on the CRSP market index.

We estimate our abnormal returns using the CRSP value-weighted market index and, alternatively, the CRSP equally weighted index. After we estimate the parameters of the market model, we estimate the abnormal return for each day for each firm as

[AR.sub.i,t] = ([R.sub.i,t] - [[alpha].sub.i] - [[beta].sub.i][R.sub.m,t]). (2)

We denote the announcement date as t = 0 and average these abnormal returns for each event day across firms. Next, we compute the cumulative abnormal returns (CARs) for the windows of interest by summing the average abnormal returns for those windows.

As we discuss above, the results from event studies around calls of convertible bonds are very sensitive to the estimation period of the market model. We first evaluate whether any difference between the results of our study and the corresponding results in previous studies could be due to a difference in the data set rather than to the empirical procedure. Thus, we examine both the announcement and post-announcement abnormal returns by using estimation periods before (as do Ofer and Natarajan, 1987) and after the announcement (as do Ederington and Goh, 2001).

Our standard pre-announcement estimation period is t = -250 to t = -101. The estimation period ends at t = -101 so that we can compare our results to previous studies and use the abnormal returns between t = -100 and t = -1 as an indicator for overvaluation prior to the forced conversion. Our post-announcement estimation period is t = LCD+21 to t = LCD+170, where LCD is the last day on which bondholders may convert their bonds. We note that for several bonds in our sample, the last conversion date differs from the call, i.e., redemption, date. We use the former date, since we expect the liquidity pressure would manifest itself between the announcement date and last possible conversion date.

To replicate Ederington and Goh's (2001) estimation procedure, we use days t = 251 to t = 506 as an alternative post-announcement estimation period. We report results for this latter estimation period only when using this estimation period yields estimates that differ from those we obtain using our standard estimation periods. Using the post-announcement estimation period decreases our maximum sample size from 392 to 389.

We estimate the CARs for various event windows and use several alternative procedures to test whether the CARs are significantly different from zero. First, we use the standard Patell (1976) test, which we refer to as the Z-statistic. This test assumes cross-sectional independence. Second, we report the standardized cross-sectional test introduced by Boehmer, Musumeci, and Poulsen (1991), which (following Cowan, 2005b) we denote as SCS Z. Unlike the Patell test, this test allows for a possible increase in variance on an event date. Finally, we also estimate the generalized sign Z, which is a test of the hypothesis that the fraction of positive returns during the event window equals the corresponding fraction during the estimation period (see Cowan, 1992). This nonparametric test complements the above two parametric tests and provides robustness for the significance of our test results.

C. Alternative Measures for Abnormal Returns

Because previous studies show that the abnormal returns following COFCAs are sensitive to the period used to estimate the coefficients of the market model, we check the robustness of our results by using the buy-and-hold method. We first match each company in our sample with a company that has equity capitalization and market-to-book value within plus or minus 20%. Because we do not find an appropriate match for all the firms in our sample, our sample size reduces to 354 observations. We then use the buy-and-hold return method provided by Eventus (see Cowan, 2005a), which is based on Lyon, Barber, and Tsai (1999), to measure the abnormal returns of our sample firms. We define the buy-and-hold abnormal return as the difference between the holding-period returns of the sample and matched firms as

[BHAR.sub.i](I, J) = [BHR.sub.i](I, J) - [BHR.sub.m,i](I, J) (3)

where [BHR.sub.i](I, J) is the buy-and-hold return for security i between days I and J and the [BHR.sub.m,i] (I, J) is the corresponding buy-and-hold return for its matched firm.

We calculate the holding-period returns for each firm as the difference between the product of the one plus the daily returns for the dates that we include in the holding period and one. Our inferences for the BHAR are based on the standardized cross-sectional t-statistic as given by Brown and Warner (1985).

D. Cross-Sectional Analysis of the Cumulative Abnormal Returns

We conduct cross-sectional analyses of the cumulative abnormal returns during the announcement window and a post-announcement window to ascertain whether there is empirical support for the liquidity hypothesis, the asymmetric information hypothesis, or both. We use both the market model (post-announcement estimation period with a value-weighted market index) and the matched-sample buy-and-hold methods to estimate the relevant abnormal returns. We estimate our regressions using OLS and, because of heteroskedasticity, report White (1980) t-statistics, which are heteroskedasticity-consistent.

1. Dependent Variables

We examine the CARs during several windows around the call announcement, and during several post-announcement short-term windows. We denote as CAR(0, 1) the cumulative abnormal return during an event window which includes the announcement day and the following day that we obtain by using the market model. We let CAR(2, 21) denote the cumulative abnormal return during the 20 business days that follow the announcement window (i.e., days 2 to 21). Because the length of the period during which bondholders can convert their bond varies across observations, we also use a post-announcement window that starts on day 2 and ends on the last day that bondholders can convert their bonds. We denote this window as CAR(2, LCD). We calculate these abnormal returns by using the value-weighted market index and a post-announcement estimation period of LCD+21 to LCD+170. Using either an equal weighted index, or a post-announcement estimation period of t = 251 to t = 506, or both, does not qualitatively affect the results we obtain from the cross-sectional analyses. When we obtain abnormal returns using the buy-and-hold return method, we denote the corresponding variables as BHAR(0, 1), BHAR(2, 21) and BHAR(2, LCD), respectively.

We note that the buy-and-hold method is commonly used for long-term abnormal return analysis. For completeness, we use both the market model and the buy-and-hold methods for all event windows. Under both procedures, we find statistically significant positive abnormal returns prior to the announcement and statistically significant negative abnormal returns around the announcement date. Hence, we use abnormal returns generated by both procedures in our cross-sectional analysis.

2. Independent Variables

We use illiquidity proxies and control variables as our independent variables in the cross-sectional analysis.

a. Illiquidity Proxies

Our first illiquidity proxy, denoted as Gibbs, is the Gibbs sampler estimate of trading costs that is proposed by Hasbrouck (2004, 2005). This proxy estimates the average trading price deviation from the equilibrium price. We also use, and denote as ilq, the inverse of the Amivest measure. The Amivest measure is the ratio of the volume to the absolute return. We also check for the robustness of these measures by using several alternative measures: 1) Amihud's (2002) illiquidity measure, which is the standard deviation of the scaled daily price range defined as the difference between the highest and lowest prices of the day scaled by the closing price; 2) the volatility of daily returns, using returns from t = -251 to t = -31; and 3) the reciprocal of the price as of t = -2. Since the results are not qualitatively different from the estimates that are reported in this paper, we do not report them. However, the results are available on request.

According to the liquidity hypothesis, price declines around the COFCAs result from either an unexpectedly large infusion of shares or the short-sale of shares in illiquid markets (Bechmann, 2004). In other words, the impact of dilution is contingent on the degree of illiquidity. For example, if the shares are completely liquid, dilution should not be associated with abnormal returns.

To capture the dependence between illiquidity and the impact of dilution, we include as an independent variable an interaction effect between our illiquidity proxies and the stock dilution that is caused by the call. We measure the infusion of new shares by the dilution of the stock, and denote this measure by the variable DILUTION. We define this variable as the product of the conversion rate and the par value of the called convertible debt in thousands of dollars divided by the number of shares prior to the COFCA. We denote the product of DILUTION and Gibbs as DGibbs and the product of DILUTION and ilq is denoted as Dilq. According to the liquidity hypothesis the abnormal returns around the announcement date should be negatively related to these interaction variables, but the post-announcement buy-and-hold abnormal return should be positively related to the interaction variables.

We also perform our tests using DILUTION either as an additional independent control variable or as substitute for DGibbs and Dilq. The results are not qualitatively different from that formally reported and are available on request.

b. Control Variables

Because several authors propose asymmetric information as the reason for the negative abnormal returns during the announcement period, we use the diversity of analysts' earnings forecasts as our proxy for the degree of asymmetric information. We calculate the standard deviation of the analysts' annual earnings forecasts in the fiscal year that precedes the announcement. We denote this variable as SEPS and use it as a proxy for the degree of asymmetric information.

According to the asymmetric information hypothesis, firms call their convertible bonds if managers consider the stock overvalued. We use the abnormal returns in the (-60, -1) pre-announcement window as a proxy for the degree of overvaluation. We denote this variable as CAR(-60, -1) when we use the market-model method (post-announcement estimation) and as BHAR(-60, -1) when we use the buy-and-hold method. We check the robustness of this pre-announcement window by also using the (-100, -1) pre-announcement window as a proxy for the degree of overvaluation.

According to the asymmetric information hypothesis, the abnormal returns during the announcement window should be negatively related to SEPS and the overvaluation proxies [CAR(-60, -1) or BHAR(-60, -1)]. The asymmetric information hypothesis also implies that in an efficient market, the post-announcement abnormal returns should not be significantly different from zero and should not be related to SEPS and the overvaluation proxies.

As an additional control variable, we include the logarithm of the equity market capitalization of the firm, which we denote as lsize. Usually, the coverage of firms by analysts is directly related to firm size. Thus, the equities of large firms are less likely to exhibit large abnormal returns. Consequently, we expect that the abnormal returns on equities of large firms will be closer to zero than the abnormal returns on equities of small firms.

Cowan, Nayar, and Singh (2000) use an asymmetric information signaling model to demonstrate that low value firms will use underwriters to guarantee forced conversions. They conclude that underwriters should be used when the conversion option is less deep in the money. Their model also predicts that the magnitude of the stock price decline following the call announcement should be negatively related to the value of the conversion option. Singh, Cowan and Nayar (1991) show that abnormal returns are negatively related to the use of an underwriter to guarantee the success of a forced conversion, and that the use of an underwriter is negatively related to the value of the conversion option. Thus, we include as a control variable, OPTPREM, which we calculate as the difference between the stock price at the time of the announcement and the conversion price, divided by the conversion price. We expect a positive coefficient for OPTPREM.

Underwriters can protect their position by shorting the underlying stock, thus adding to the liquidity pressure around the announcement date. Bechmann (2004) demonstrates that the hedging motive will decline with the moneyness of the conversion option. Hence, a positive coefficient on OPTPREM is also consistent with the liquidity hypothesis. However, according to the liquidity hypothesis, the post-announcement abnormal return should be negatively related to OPTPREM. In contrast, according to the asymmetric information explanation delineated above, we should expect neither a significant post-announcement abnormal return nor a relation between the post-announcement abnormal return and OPTPREM.

Finally, the liquidity hypothesis implies a negative relation between the post-announcement abnormal returns and the announcement abnormal returns. Thus, when the dependent variable in our cross-sectional analysis is the post-announcement abnormal return, we also include the abnormal return around the announcement period as an independent variable.

The sample size for our cross-sectional regressions is reduced by the lack of data availability on liquidity, the standard deviation of analysts' earnings forecasts, and the dilution impact of the conversion-forcing call. The sample size for the cross-section regressions varies between 253 and 389 observations.

E. Descriptive Statistics of the Independent Variables Used in the Cross-sectional Analysis

Table I, Panel A, provides the summary statistics of our key independent variables, and Panel B presents their correlation coefficients. For the sample in our cross-sectional regressions, the mean of the standard deviation of analysts' earnings forecasts (SEPS) is $0.1413, and the median is $0.0482. The average size of the company is almost $2.9 billion, and the median is $764 million. The smallest firm has an equity capitalization of approximately $25 million, and the largest firm has an equity capitalization of approximately $134 billion. The mean value of OPTPREM is 0.645, and the median is 0.407. The mean percentage increase of common shares due to the call is 8.8% and the median is 4.32%.

Table I, Panel B, reports the correlations between our variables. We also include the correlation between estimates of our abnormal returns using both the market-model and the buy-and-hold methods. These variables include BHAR(-100, -1), BHAR(-60, -1), CAR(-100, -1), and CAR(-60, -1), respectively. We note that in general, when we use the two procedures, the correlation between the respective abnormal returns is quite high.

III. Results

In this section, we present the results of our empirical tests.

A. Market Reaction to Announcements of Calls of Convertible Bonds

To verify that the composition of our sample is not the reason for any difference between our results and those in previous studies, we use the traditional event study method to estimate the abnormal returns during several pre-announcement, announcement, and post-announcement windows. We repeat these estimates using pre- and post-announcement estimation periods.

Table II presents the estimates when we follow earlier studies and use a pre-announcement estimation period (t = -250 to t = -101). The estimates in Panel A are based on the equally weighted index, and those in Panel B are based on the value-weighted index. The estimates are qualitatively similar to those in previous studies that use a pre-announcement estimation period (see, for example, Ofer and Natarajan, 1987). The pre-announcement abnormal returns are positive and significantly different from zero and the abnormal returns during the announcement period and post-announcement periods are negative and significantly different from zero.

We repeat these tests by using a post-announcement estimation period (t = LCD+21 to t = LCD+170, where LCD is the last day on which bondholders may convert their bonds to equity). As we report in Table III, the announcement window abnormal returns are negative and similar to those obtained using the pre-announcement estimation period, while the pre-announcement abnormal returns are even more positive than their counterparts in Table II. However, the post-announcement abnormal returns for (2, 21) and (2, LCD) are not significantly different from zero. The results presented in Table III are not consistent with Mazzeo and Moore (1992), Datta and Iskandar-Datta (1996), and Ederington and Gob (2001) who find, consistent with the predictions of the liquidity hypothesis, a post-announcement positive abnormal return.

We also conduct the analysis using the post-announcement period between t = 251 and t = 506, as in Ederington and Goh (2001). In this case, we find post-announcement positive drift, consistent with the results that are presented in previous studies. Hence, the finding of post-announcement positive drift is not robust and is sensitive to the empirical method used.

The lack of robustness of the results to the empirical method motivates us to use a procedure that involves neither a pre- nor a post-announcement period as the estimation period. Thus, we re-estimate the abnormal returns using the buy-and-hold procedure that Barber and Lyon (1997) and Lyon, Barber, and Tsai (1999) suggest. In Table IV we report the corresponding estimates when we use as benchmarks the buy-and-hold returns on firms that are matched to our sample firms by size and market-to-book value. The results of Table IV are similar to those reported in Table III. Hence, the results reported in Table IV reinforce our conclusion that the price recovery following the announcement date is not robust and is sensitive to the empirical method used.

We note that because we do not find appropriate matched firms for all of our sample firms, our sample size using the buy-and-hold method is smaller than the sample size using the traditional market model method. To check whether we introduce a bias because the buy-and-hold sample is smaller than the full sample, we re-estimate the traditional market model method by using the smaller sample that is used by the buy-and-hold method. We find that the abnormal returns using the market model method are similar to those obtained using the full sample. Thus, any difference between the two methods should not be due to the difference in samples.

B. Cross-Sectional Regressions

In Table V, we report the estimates from regressions in which the dependent variable is the post-announcement abnormal return, and the independent variable is the abnormal return during the announcement window. Panel A shows the estimates from two regressions that vary in the windows for the dependent variables. In this panel, the independent variable is CAR(0, 1), the abnormal returns for the window (0, 1). In the first regression, the dependent variable, CAR(2, 21) is the abnormal returns for the window (2, 21). In the second regression, the dependent variable is CAR(2, LCD), the abnormal return during a window that starts on day 2 and ends on the last conversion date, (i.e., the last day that holders of the bond may convert the bond into equity). Panel B reports the corresponding estimates when we use the buy-and-hold method instead of the market model to estimate the abnormal returns. Unlike the results obtained by Mazzeo and Moore (1992), we find no statistically significant relation between the post-announcement abnormal returns and the announcement window abnormal return in all four specifications. Hence, these findings do not provide support for a price recovery, which is a direct implication of the liquidity hypothesis.

In Table VI, we present our cross-sectional regressions where we estimate the relation between the cumulative abnormal returns during the two-day call announcement window and our illiquidity and asymmetric information proxies. Our dependent variable in Panel A is CAR(0, 1) and our dependent variable in Panel B is BHAR(0, 1). Panel A shows that CAR(0, 1) is not significantly related to any of the illiquidity proxies in either the univariate or multivariate specifications. Panel B reports that BHAR(0, 1) is negatively related to DGibbs at the 10% level and BHAR(-60, -1) at the 5% level in the univariate specification. These results are consistent with the liquidity premium and the asymmetric information hypotheses. However, the results are not robust, since BHAR(0, 1) is not significantly related to any of the illiquidity or asymmetric information proxies in the multivariate specifications.

Table VI also reports significant positive coefficients on OPTPREM in the univariate specifications. However, interpreting a positive coefficient as being consistent with the liquidity hypothesis depends on finding a negative relation between OPTPREM and the post-announcement abnormal return. But as we report in Table VII, we do not find a negative relation between the post-announcement abnormal returns and the option premium variable. Hence, we interpret the positive coefficient on OPTPREM in Table VI as being consistent with the Cowan, Nayar, and Singh (2000) asymmetric information model. We also note that the positive coefficient associated with OPTPREM is no longer statistically significant in the multivariate specification. Thus, the estimated coefficients for our liquidity proxies reported in Table VI do not support the liquidity hypothesis.

We note that the relation between BHAR(0, 1) and BHAR(-60, -1), which is significant in the univariate specification, is not significant in the multivariate specification. We also note that because of missing variables, we base our multivariate regressions on fewer observations than the univariate regression. Thus, we re-estimate a univariate regression with BHAR(-60, -1) as the independent variable using only the observations we include in all the multivariate regressions. This regression results in a nonsignificant coefficient for BHAR(-60, -1) and an adjusted R-square below 1%.

Table VII presents the estimates of cross-sectional regressions where the dependent variables represent the abnormal returns between t = 2 and t = LCD. In Panel A, the dependent variable is CAR(2, LCD). We note that in all specifications, the coefficients of SEPS, which controls for possible impacts of asymmetric information, are negative and significantly different from zero. In addition, the coefficients of isize in the univariate and in two of the multivariate regressions are also negative and significantly different from zero. However, in the absence of a corresponding impact on the announcement-window abnormal returns, the significant impacts of SEPS and lsize on post-announcement abnormal returns are not consistent with the implications of the asymmetric information hypothesis. We note that the coefficients of OPTPREM and CAR(0, 1) are not significantly different from zero.

In Panel B, the dependent variable is BHAR(2, LCD). The coefficients of OPTPREM are significant and positive at the 10% level in two multivariate specifications. Thus, when the dependent variable is the announcement window abnormal return in Table VI, the positive coefficients on OPTPREM should not necessarily be interpreted as supporting the liquidity hypothesis. Furthermore, BHAR(2, LCD) is not significantly related to any other independent variable, including the announcement abnormal return, BHAR(0, 1). Thus, the results in Table VII do not provide any support for the liquidity hypothesis. (4)

We perform several robustness tests. First, we replicate the tests using CAR(2, 21) and BHAR(2, 21), the 20-day abnormal returns for the post-announcement windows that start two days after the announcement day as dependent variables. Second, we note that several of our independent variables are skewed to the right. Consequently, we transform some of our variables to reduce the potential impact of a few extreme observations or measurement errors. We substitute the coefficient of variation of the earnings forecasts for SEPS, the logarithm of (1+OPTPREM) for OPTPREM, and the logarithm of ilq for ilq. Third, we find that one company, CBS, had a dilutive impact of 500%. Hence, we re-estimate all of the regressions, deleting this observation. Fourth, we analyze the abnormal returns with the market model, using the t = 251 to t = 506 estimation period of Ederington and Goh (2001). Fifth, we re-estimate our cross-sectional regression analysis, using an equal-weighted market index to compute the abnormal returns. The results we obtain for all of these robustness tests are not qualitatively different from those we report.

IV. Conclusion

The liquidity hypothesis attributes the negative abnormal returns around the conversion-forcing calls announcements (COFCAs) of convertible bonds and the subsequent price recovery to liquidity pressures. The liquidity hypothesis implies that this price recovery should be inversely related to the initial price decline, and that the abnormal returns during the announcement and post-announcement windows should be related to proxies of the stock's illiquidity.

We confirm the existence of negative abnormal returns around COFCAs. However, we find that when we control for other factors that might impact the abnormal return, these negative abnormal returns are not statistically related to any of the conventional illiquidity proxies. Nor do we find a statistical relation between the post-announcement abnormal returns and the announcement abnormal returns.

We demonstrate that the post-announcement positive abnormal returns that are documented in previous studies are sensitive to the estimation procedure. The absence of post-announcement abnormal returns is consistent with the efficient markets hypothesis. We also find no consistent empirical support for alternative hypotheses such as the asymmetric information, interest tax loss, and investment options hypotheses. We conclude that the negative market reaction to COFCAs needs further examination.

The views' expressed in this paper are solely that of the authors and not of the OCC or the U.S. Department of the Treasury. We thank William T. Moore, Avri Ravid, John Wald, and the anonymous referee for their helpful comments on earlier drafts, We also thank Arnold Cowan in advising us in the use of Eventus, and Louis Ederington and Jeremy Goh for allowing us to use their data. In addition, we acknowledge partial funding support from the David K. Whitcomb Center for Research in Financial Services. Rutgers University.

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Cowan, A.R., N. Nayar, and A.K. Singh, 1993, "Calls of Out-of-the-Money Convertible Bonds," Financial Management 22, 106-16.

Cowan, A.R., N. Nayar, and A.K. Singh, 2000, "Underwriting and Calls of Convertible Bonds," Decision Sciences 31, 57-77.

Datta, S. and M. Iskandar-Datta, 1996, "New Evidence on the Valuation Effects of Convertible Bond Calls," Journal of Financial and Quantitative Analysis 31, 295-307.

Ederington, L.H, G.L. Caton, and C.J. Campbell, 1997, "To Call or Not to Call Convertible Debt," Financial Management 26, 22-31.

Ederington, L.H. and J.C. Gob, 2001, "Is a Convertible Bond Call Really Bad News'?" Journal of Business 74, 459-76.

Graham, J.R., 1996, "Debt and the Marginal Tax Rate," Journal of Financial Economies 41, 41-73.

Harris, M. and A. Raviv, 1985, "A Sequential Signaling Model of Convertible Debt Call Policy," Journal of Finance 40, 1263-81.

Hasbrouck, J., 2004, "Liquidity in the Futures Pits: Inferring Market Dynamics from Incomplete Data," Journal of Financial and Quantitative Analysis 39, 305-26.

Hasbrouck, J., 2005, "Trading Costs and Returns for US Equities: The Evidence from Daily Data," New York University Working Paper.

Howe, J.S., J. Lin, and A.K. Singh, 1998, "Clientele Effects and Cross-Security Market Making: Evidence from Calls of Convertible Preferred Securities," Financial Management 27, 41-52.

Kadapakkam, P. and A.P. Tang, 1996, "Stock Reaction to Dividend Savings of Convertible Preferred Calls: Free Cash Flow or Price Pressure Effects?" Journal of Banking & Finance 20, 1759-73.

Kim, Y.O. and J. Kallberg, 1998, "Convertible Calls and Corporate Taxes under Asymmetric Information," Journal of Banking & Finance 22, 19-40.

Lyon, J.D., B.M. Barber, and C. Tsai, 1999, "Improved Methods for Tests of Long-Run Abnormal Stock Returns," Journal of Finance 54, 165-201.

Mayers, D., 1998, "Why Firms Issue Convertible Bonds: The Matching of Financial and Real Investment Options," Journal of Financial Economics 47, 83-102.

Mazzeo, M.A. and W.T. Moore, 1992, "Liquidity Costs and Stock Price Response to Convertible Security Calls," Journal of Business 65, 353-69.

Mikkelson, W.H., 1981, "Convertible Calls and Security Returns," Journal of Financial Economics 9, 237-264.

Mikkelson, W.H., 1985, "Capital Structure Changes and Decreases in Stockholder's Wealth: A Cross-Sectional Study of Convertible Security Calls," in B.M. Friedman, Ed., Corporate Capital Structure in the United States, Chicago, IL, University of Chicago Press for NBER.

Mitchell, M., T. Pulvino, and E. Stafford, 2004, "Price Pressure around Mergers," Journal of Finance 59, 31-63.

Ofer, A.R. and A. Natarajan, 1987, "Convertible Call Policies: An Empirical Analysis of an Information-Signaling Hypothesis," Journal of Financial Economics 19, 91-108.

Patell, J.M., 1976, "Corporate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Tests," Journal of Accounting Research 14, 246-274.

Singh, A.K., A.R. Cowan, and N. Nayar, 1991, "Underwritten Calls of Convertible Bonds," Journal of Financial Economics 29, 173-96.

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(1) For a review of the optimal time to call a convertible bond, see Ederington, Caton, and Campbell (1997).

(2) A similar interpretation is given by Kadapakkam and Tang (1996) and Howe, Lin, and Singh (1998) for stock price reactions around the announcement of the forced conversion of preferred stocks, and by Mitchell, Pulvino, and Stafford (2004) for the abnormal returns around merger announcements. Alderson and Betker (2003) suggest that price pressures might partially explain the negative stock reaction to forced warrant exercise.

(3) See http://pages.stern.nyu.edu/~jhasbrou/.

(4) The literature has offered additional explanations for the impact of a conversion-forcing call, most notably are the investment option hypothesis (see Mayers, 1998) and the loss of tax shields (see Mikkelson, 1985). In alternative specifications we include also variables that should be associated with the abnormal returns according to these hypotheses. These variables include the Market-to-Book ratio as a measure of the investment option, John Graham's estimate of the effective tax rate (see, Graham 1996) and the difference between the aggregate after corporate tax interest payment of the convertible bond and the dividend payment from the additional equity generated by the conversion scaled by the market capitalization of equity for t = -1. We do not report the results from these specifications because the coefficients of these variables are not significantly different from zero, and because including them does not qualitatively affect the coefficients that are reported in Tables VI and VII.

Ivan E. Brick, Oded Palmon, and Dilip K. Patro *

* Ivan E. Brick is Professor of Finance and Economics at Rutgers University, in Newark and New Brunswick, NJ. Oded Palmon is Professor of Finance and Economics at Rutgers University, in Newark and New Brunswick, NJ. Dilip K. Patro is a Senior Financial Economist at the Office of the Comptroller of the Currency in Washington, DC.

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Several studies have documented negative abnormal returns around conversion-forcing call announcements (COFCAs) of convertible bonds followed by positive abnormal returns. These studies attribute this pattern to liquidity pressures, and this explanation is referred to as "the liquidity hypothesis" by Mazzeo and Moore (1992). We examine the robustness of the evidence in support of the liquidity hypothesis in two ways. First, we examine the cross-sectional relation between the abnormal returns (during and after the COFCAs) and illiquidity proxies. The liquidity hypothesis implies that abnormal returns during the announcement period should be negatively related to illiquidity proxies, i.e., the less liquid the security is, the more negative the abnormal return. It also implies that the post-announcement positive abnormal returns should be negatively related to the announcement abnormal returns, or positively related to the illiquidity proxies, or both. We confirm the negative abnormal returns during the COFCA window. However, we find that neither the COFCA window abnormal returns nor the post-announcement abnormal returns are statistically related to illiquidity proxies. Moreover, we do not find a statistically significant relationship between the post-announcement abnormal returns and the announcement abnormal returns.

Second, our findings indicate that the abnormal returns following COFCAs are sensitive to the choice of the estimation period for the market-model parameters. Thus, we obtain abnormal returns by using an alternative measure of abnormal returns that follows the buy-and-hold procedure developed by Barber and Lyon (1997) and Lyon, Barber, and Tsai (1999). The buy-and-hold abnormal returns also do not exhibit a price recovery. This finding reinforces our conclusion that empirical support for the liquidity hypothesis is not robust.

Previous studies consider asymmetric information as another explanation for the negative abnormal returns around COFCAs. Thus, we also include proxies for asymmetric information in our cross-section regressions. However, we do not find a relation that is consistent with the predictions of the asymmetric information hypothesis.

The paper is organized as follows. In Section I we review relevant previous studies and present the contributions of this paper. Section II describes our data and empirical design. Section III reports the results and Section IV concludes.

I. Literature Review

Mikkelson (1981), Ofer and Natarajan (1987), Cowan, Nayar, and Singh (1993) and others find that forced conversion of convertible bonds is associated with negative abnormal equity returns. (1) Harris and Raviv (1985), Kim and Kallberg (1998), and Cowan, Nayar, and Singh (2000) present asymmetric-information models suggesting that forcing a conversion is a negative signal for the value of the company. When managers receive such a signal, they force conversion to conserve their company's cash flow. When managers receive a good signal, they distinguish their companies by not forcing a conversion and instead let bondholders elect to convert voluntarily when the positive information is revealed. Thus, the asymmetric information hypothesis implies that the market should react negatively to COFCAs. Additionally, if the negative information conveyed by COFCAs is immediately impounded in security prices, then we should not observe abnormal returns during the post-announcement period.

Alexander and Stover (1980) and Ofer and Natarajan (1987) find long-term negative abnormal performance (in terms of equity returns and accounting measures) that support the asymmetric-information explanation. However, Ofer and Natarajan (1987) note that a long-term (post-announcement) abnormal equity return is also an indication of either market inefficiency or an inappropriate benchmark. Cowan, Nayar, and Singh (1990) demonstrate that using the pre-announcement period as an estimating period introduces a downward bias in the estimated post-announcement abnormal returns because COFCAs usually follow stock price increases. Consistent with market efficiency, Cowan, Nayar, and Singh (1990) find no long-term (post-announcement) abnormal returns when they use post-announcement data to estimate the market model parameters.

In subsequent research, Campbell, Ederington, and Vankudre (1991), Mazzeo and Moore (1992), Byrd and Moore (1996), Ederington and Goh (2001) and Bechmann (2004) use a post-announcement estimation period and find negative abnormal returns around the COFCAs, followed by positive abnormal returns. Ederington and Goh (2001) find that insiders buy equity before the announcements and analysts increase their earnings forecasts. Thus, they conclude that the price decline is due to liquidity price pressures rather than asymmetric information. In an imperfect (or a relatively thin) market, the increase in the number of outstanding shares induces an initial price decline and a subsequent price recovery as the market absorbs the new shares. (2)

In this paper we argue that the liquidity hypothesis also implies that the magnitude (i.e., the absolute value) of the initial price decline should be positively related to illiquidity proxies. Additionally, the post-announcement returns should be positively related to the magnitude of the initial price decline and/or to illiquidity proxies. However, we show that the negative price decline around the announcement date and the abnormal returns following the announcement date are not related to traditional illiquidity proxies. Thus, our paper raises doubts whether the negative abnormal returns around COFCAs should be attributed to liquidity price pressures.

II. Data and Empirical Design

This section describes our data sources and the procedures we use to obtain our sample. It also describes the statistical procedures and variables we use.

A. Data

Our sample has two sources. First, Ederington and Goh (2001) have kindly made available a sample of 298 forced conversions between December 1984 and November 1993. This sample is the one they use in Ederington and Gob (2001). Second, we use Standard and Poor's Bond Guide to update this sample to December 2002 and increase its size to 537 conversions.

We use Factiva to collect the announcement dates, and exclude six observations where we cannot find an announcement in any daily newspaper or newswire. We further reduce the sample to exclude two foreign firms and 20 firms from regulated industries such as utilities and financial institutions. We exclude another 97 firms for which we cannot find any apparent forced-conversion, either because the stock price at the time of the corporate announcement is lower than the conversion price or because we cannot find the actual conversion price. We eliminate an additional 11 observations because the announcement indicates that the bond in question is not a traditional convertible bond. Three of these bonds are either exchangeable to the equity of another firm or to more than one class of equity. The remaining eight are liquid yield option notes. We delete another nine firms because of insufficient stock return data. These deletions result in a final sample of 392 firms.

For the full sample, we obtain data on issue size, conversion ratio, and final maturity of the issues from Factiva, and the daily returns, market capitalization of equity, and the returns on the market indexes from CRSE For each of the firms we also obtain from Hasbrouck's web site two measures of liquidity (or illiquidity) that Hasbrouck (2004, 2005) discusses. (3) We obtain accounting data for these firms from Compustat, including the data we need to identify the appropriate matched firms. We use Institutional Brokers' Estimate System (IBES) to obtain the standard deviation of analysts' earnings forecasts for each firm in the sample. The final sample size we use in each of our empirical tests varies according to data availability. Finally, we use the Eventus Software (Cowan, 2005a, 2005b) to estimate abnormal returns and associated statistics to test for significance.

B. Event Study Method

To begin our analysis, we use the traditional market model to estimate the abnormal returns. We estimate the market model for firm i as

[R.sub.i,t] = [[alpha].sub.i] + [[beta].sub.i][R.sub.m,t] + [[epsilon].sub.i.t] (1)

where [R.sub.i,t] is its return on day t and [R.sub.m,t] is the corresponding return on the CRSP market index.

We estimate our abnormal returns using the CRSP value-weighted market index and, alternatively, the CRSP equally weighted index. After we estimate the parameters of the market model, we estimate the abnormal return for each day for each firm as

[AR.sub.i,t] = ([R.sub.i,t] - [[alpha].sub.i] - [[beta].sub.i][R.sub.m,t]). (2)

We denote the announcement date as t = 0 and average these abnormal returns for each event day across firms. Next, we compute the cumulative abnormal returns (CARs) for the windows of interest by summing the average abnormal returns for those windows.

As we discuss above, the results from event studies around calls of convertible bonds are very sensitive to the estimation period of the market model. We first evaluate whether any difference between the results of our study and the corresponding results in previous studies could be due to a difference in the data set rather than to the empirical procedure. Thus, we examine both the announcement and post-announcement abnormal returns by using estimation periods before (as do Ofer and Natarajan, 1987) and after the announcement (as do Ederington and Goh, 2001).

Our standard pre-announcement estimation period is t = -250 to t = -101. The estimation period ends at t = -101 so that we can compare our results to previous studies and use the abnormal returns between t = -100 and t = -1 as an indicator for overvaluation prior to the forced conversion. Our post-announcement estimation period is t = LCD+21 to t = LCD+170, where LCD is the last day on which bondholders may convert their bonds. We note that for several bonds in our sample, the last conversion date differs from the call, i.e., redemption, date. We use the former date, since we expect the liquidity pressure would manifest itself between the announcement date and last possible conversion date.

To replicate Ederington and Goh's (2001) estimation procedure, we use days t = 251 to t = 506 as an alternative post-announcement estimation period. We report results for this latter estimation period only when using this estimation period yields estimates that differ from those we obtain using our standard estimation periods. Using the post-announcement estimation period decreases our maximum sample size from 392 to 389.

We estimate the CARs for various event windows and use several alternative procedures to test whether the CARs are significantly different from zero. First, we use the standard Patell (1976) test, which we refer to as the Z-statistic. This test assumes cross-sectional independence. Second, we report the standardized cross-sectional test introduced by Boehmer, Musumeci, and Poulsen (1991), which (following Cowan, 2005b) we denote as SCS Z. Unlike the Patell test, this test allows for a possible increase in variance on an event date. Finally, we also estimate the generalized sign Z, which is a test of the hypothesis that the fraction of positive returns during the event window equals the corresponding fraction during the estimation period (see Cowan, 1992). This nonparametric test complements the above two parametric tests and provides robustness for the significance of our test results.

C. Alternative Measures for Abnormal Returns

Because previous studies show that the abnormal returns following COFCAs are sensitive to the period used to estimate the coefficients of the market model, we check the robustness of our results by using the buy-and-hold method. We first match each company in our sample with a company that has equity capitalization and market-to-book value within plus or minus 20%. Because we do not find an appropriate match for all the firms in our sample, our sample size reduces to 354 observations. We then use the buy-and-hold return method provided by Eventus (see Cowan, 2005a), which is based on Lyon, Barber, and Tsai (1999), to measure the abnormal returns of our sample firms. We define the buy-and-hold abnormal return as the difference between the holding-period returns of the sample and matched firms as

[BHAR.sub.i](I, J) = [BHR.sub.i](I, J) - [BHR.sub.m,i](I, J) (3)

where [BHR.sub.i](I, J) is the buy-and-hold return for security i between days I and J and the [BHR.sub.m,i] (I, J) is the corresponding buy-and-hold return for its matched firm.

We calculate the holding-period returns for each firm as the difference between the product of the one plus the daily returns for the dates that we include in the holding period and one. Our inferences for the BHAR are based on the standardized cross-sectional t-statistic as given by Brown and Warner (1985).

D. Cross-Sectional Analysis of the Cumulative Abnormal Returns

We conduct cross-sectional analyses of the cumulative abnormal returns during the announcement window and a post-announcement window to ascertain whether there is empirical support for the liquidity hypothesis, the asymmetric information hypothesis, or both. We use both the market model (post-announcement estimation period with a value-weighted market index) and the matched-sample buy-and-hold methods to estimate the relevant abnormal returns. We estimate our regressions using OLS and, because of heteroskedasticity, report White (1980) t-statistics, which are heteroskedasticity-consistent.

1. Dependent Variables

We examine the CARs during several windows around the call announcement, and during several post-announcement short-term windows. We denote as CAR(0, 1) the cumulative abnormal return during an event window which includes the announcement day and the following day that we obtain by using the market model. We let CAR(2, 21) denote the cumulative abnormal return during the 20 business days that follow the announcement window (i.e., days 2 to 21). Because the length of the period during which bondholders can convert their bond varies across observations, we also use a post-announcement window that starts on day 2 and ends on the last day that bondholders can convert their bonds. We denote this window as CAR(2, LCD). We calculate these abnormal returns by using the value-weighted market index and a post-announcement estimation period of LCD+21 to LCD+170. Using either an equal weighted index, or a post-announcement estimation period of t = 251 to t = 506, or both, does not qualitatively affect the results we obtain from the cross-sectional analyses. When we obtain abnormal returns using the buy-and-hold return method, we denote the corresponding variables as BHAR(0, 1), BHAR(2, 21) and BHAR(2, LCD), respectively.

We note that the buy-and-hold method is commonly used for long-term abnormal return analysis. For completeness, we use both the market model and the buy-and-hold methods for all event windows. Under both procedures, we find statistically significant positive abnormal returns prior to the announcement and statistically significant negative abnormal returns around the announcement date. Hence, we use abnormal returns generated by both procedures in our cross-sectional analysis.

2. Independent Variables

We use illiquidity proxies and control variables as our independent variables in the cross-sectional analysis.

a. Illiquidity Proxies

Our first illiquidity proxy, denoted as Gibbs, is the Gibbs sampler estimate of trading costs that is proposed by Hasbrouck (2004, 2005). This proxy estimates the average trading price deviation from the equilibrium price. We also use, and denote as ilq, the inverse of the Amivest measure. The Amivest measure is the ratio of the volume to the absolute return. We also check for the robustness of these measures by using several alternative measures: 1) Amihud's (2002) illiquidity measure, which is the standard deviation of the scaled daily price range defined as the difference between the highest and lowest prices of the day scaled by the closing price; 2) the volatility of daily returns, using returns from t = -251 to t = -31; and 3) the reciprocal of the price as of t = -2. Since the results are not qualitatively different from the estimates that are reported in this paper, we do not report them. However, the results are available on request.

According to the liquidity hypothesis, price declines around the COFCAs result from either an unexpectedly large infusion of shares or the short-sale of shares in illiquid markets (Bechmann, 2004). In other words, the impact of dilution is contingent on the degree of illiquidity. For example, if the shares are completely liquid, dilution should not be associated with abnormal returns.

To capture the dependence between illiquidity and the impact of dilution, we include as an independent variable an interaction effect between our illiquidity proxies and the stock dilution that is caused by the call. We measure the infusion of new shares by the dilution of the stock, and denote this measure by the variable DILUTION. We define this variable as the product of the conversion rate and the par value of the called convertible debt in thousands of dollars divided by the number of shares prior to the COFCA. We denote the product of DILUTION and Gibbs as DGibbs and the product of DILUTION and ilq is denoted as Dilq. According to the liquidity hypothesis the abnormal returns around the announcement date should be negatively related to these interaction variables, but the post-announcement buy-and-hold abnormal return should be positively related to the interaction variables.

We also perform our tests using DILUTION either as an additional independent control variable or as substitute for DGibbs and Dilq. The results are not qualitatively different from that formally reported and are available on request.

b. Control Variables

Because several authors propose asymmetric information as the reason for the negative abnormal returns during the announcement period, we use the diversity of analysts' earnings forecasts as our proxy for the degree of asymmetric information. We calculate the standard deviation of the analysts' annual earnings forecasts in the fiscal year that precedes the announcement. We denote this variable as SEPS and use it as a proxy for the degree of asymmetric information.

According to the asymmetric information hypothesis, firms call their convertible bonds if managers consider the stock overvalued. We use the abnormal returns in the (-60, -1) pre-announcement window as a proxy for the degree of overvaluation. We denote this variable as CAR(-60, -1) when we use the market-model method (post-announcement estimation) and as BHAR(-60, -1) when we use the buy-and-hold method. We check the robustness of this pre-announcement window by also using the (-100, -1) pre-announcement window as a proxy for the degree of overvaluation.

According to the asymmetric information hypothesis, the abnormal returns during the announcement window should be negatively related to SEPS and the overvaluation proxies [CAR(-60, -1) or BHAR(-60, -1)]. The asymmetric information hypothesis also implies that in an efficient market, the post-announcement abnormal returns should not be significantly different from zero and should not be related to SEPS and the overvaluation proxies.

As an additional control variable, we include the logarithm of the equity market capitalization of the firm, which we denote as lsize. Usually, the coverage of firms by analysts is directly related to firm size. Thus, the equities of large firms are less likely to exhibit large abnormal returns. Consequently, we expect that the abnormal returns on equities of large firms will be closer to zero than the abnormal returns on equities of small firms.

Cowan, Nayar, and Singh (2000) use an asymmetric information signaling model to demonstrate that low value firms will use underwriters to guarantee forced conversions. They conclude that underwriters should be used when the conversion option is less deep in the money. Their model also predicts that the magnitude of the stock price decline following the call announcement should be negatively related to the value of the conversion option. Singh, Cowan and Nayar (1991) show that abnormal returns are negatively related to the use of an underwriter to guarantee the success of a forced conversion, and that the use of an underwriter is negatively related to the value of the conversion option. Thus, we include as a control variable, OPTPREM, which we calculate as the difference between the stock price at the time of the announcement and the conversion price, divided by the conversion price. We expect a positive coefficient for OPTPREM.

Underwriters can protect their position by shorting the underlying stock, thus adding to the liquidity pressure around the announcement date. Bechmann (2004) demonstrates that the hedging motive will decline with the moneyness of the conversion option. Hence, a positive coefficient on OPTPREM is also consistent with the liquidity hypothesis. However, according to the liquidity hypothesis, the post-announcement abnormal return should be negatively related to OPTPREM. In contrast, according to the asymmetric information explanation delineated above, we should expect neither a significant post-announcement abnormal return nor a relation between the post-announcement abnormal return and OPTPREM.

Finally, the liquidity hypothesis implies a negative relation between the post-announcement abnormal returns and the announcement abnormal returns. Thus, when the dependent variable in our cross-sectional analysis is the post-announcement abnormal return, we also include the abnormal return around the announcement period as an independent variable.

The sample size for our cross-sectional regressions is reduced by the lack of data availability on liquidity, the standard deviation of analysts' earnings forecasts, and the dilution impact of the conversion-forcing call. The sample size for the cross-section regressions varies between 253 and 389 observations.

E. Descriptive Statistics of the Independent Variables Used in the Cross-sectional Analysis

Table I, Panel A, provides the summary statistics of our key independent variables, and Panel B presents their correlation coefficients. For the sample in our cross-sectional regressions, the mean of the standard deviation of analysts' earnings forecasts (SEPS) is $0.1413, and the median is $0.0482. The average size of the company is almost $2.9 billion, and the median is $764 million. The smallest firm has an equity capitalization of approximately $25 million, and the largest firm has an equity capitalization of approximately $134 billion. The mean value of OPTPREM is 0.645, and the median is 0.407. The mean percentage increase of common shares due to the call is 8.8% and the median is 4.32%.

Table I, Panel B, reports the correlations between our variables. We also include the correlation between estimates of our abnormal returns using both the market-model and the buy-and-hold methods. These variables include BHAR(-100, -1), BHAR(-60, -1), CAR(-100, -1), and CAR(-60, -1), respectively. We note that in general, when we use the two procedures, the correlation between the respective abnormal returns is quite high.

III. Results

In this section, we present the results of our empirical tests.

A. Market Reaction to Announcements of Calls of Convertible Bonds

To verify that the composition of our sample is not the reason for any difference between our results and those in previous studies, we use the traditional event study method to estimate the abnormal returns during several pre-announcement, announcement, and post-announcement windows. We repeat these estimates using pre- and post-announcement estimation periods.

Table II presents the estimates when we follow earlier studies and use a pre-announcement estimation period (t = -250 to t = -101). The estimates in Panel A are based on the equally weighted index, and those in Panel B are based on the value-weighted index. The estimates are qualitatively similar to those in previous studies that use a pre-announcement estimation period (see, for example, Ofer and Natarajan, 1987). The pre-announcement abnormal returns are positive and significantly different from zero and the abnormal returns during the announcement period and post-announcement periods are negative and significantly different from zero.

We repeat these tests by using a post-announcement estimation period (t = LCD+21 to t = LCD+170, where LCD is the last day on which bondholders may convert their bonds to equity). As we report in Table III, the announcement window abnormal returns are negative and similar to those obtained using the pre-announcement estimation period, while the pre-announcement abnormal returns are even more positive than their counterparts in Table II. However, the post-announcement abnormal returns for (2, 21) and (2, LCD) are not significantly different from zero. The results presented in Table III are not consistent with Mazzeo and Moore (1992), Datta and Iskandar-Datta (1996), and Ederington and Gob (2001) who find, consistent with the predictions of the liquidity hypothesis, a post-announcement positive abnormal return.

We also conduct the analysis using the post-announcement period between t = 251 and t = 506, as in Ederington and Goh (2001). In this case, we find post-announcement positive drift, consistent with the results that are presented in previous studies. Hence, the finding of post-announcement positive drift is not robust and is sensitive to the empirical method used.

The lack of robustness of the results to the empirical method motivates us to use a procedure that involves neither a pre- nor a post-announcement period as the estimation period. Thus, we re-estimate the abnormal returns using the buy-and-hold procedure that Barber and Lyon (1997) and Lyon, Barber, and Tsai (1999) suggest. In Table IV we report the corresponding estimates when we use as benchmarks the buy-and-hold returns on firms that are matched to our sample firms by size and market-to-book value. The results of Table IV are similar to those reported in Table III. Hence, the results reported in Table IV reinforce our conclusion that the price recovery following the announcement date is not robust and is sensitive to the empirical method used.

We note that because we do not find appropriate matched firms for all of our sample firms, our sample size using the buy-and-hold method is smaller than the sample size using the traditional market model method. To check whether we introduce a bias because the buy-and-hold sample is smaller than the full sample, we re-estimate the traditional market model method by using the smaller sample that is used by the buy-and-hold method. We find that the abnormal returns using the market model method are similar to those obtained using the full sample. Thus, any difference between the two methods should not be due to the difference in samples.

B. Cross-Sectional Regressions

In Table V, we report the estimates from regressions in which the dependent variable is the post-announcement abnormal return, and the independent variable is the abnormal return during the announcement window. Panel A shows the estimates from two regressions that vary in the windows for the dependent variables. In this panel, the independent variable is CAR(0, 1), the abnormal returns for the window (0, 1). In the first regression, the dependent variable, CAR(2, 21) is the abnormal returns for the window (2, 21). In the second regression, the dependent variable is CAR(2, LCD), the abnormal return during a window that starts on day 2 and ends on the last conversion date, (i.e., the last day that holders of the bond may convert the bond into equity). Panel B reports the corresponding estimates when we use the buy-and-hold method instead of the market model to estimate the abnormal returns. Unlike the results obtained by Mazzeo and Moore (1992), we find no statistically significant relation between the post-announcement abnormal returns and the announcement window abnormal return in all four specifications. Hence, these findings do not provide support for a price recovery, which is a direct implication of the liquidity hypothesis.

In Table VI, we present our cross-sectional regressions where we estimate the relation between the cumulative abnormal returns during the two-day call announcement window and our illiquidity and asymmetric information proxies. Our dependent variable in Panel A is CAR(0, 1) and our dependent variable in Panel B is BHAR(0, 1). Panel A shows that CAR(0, 1) is not significantly related to any of the illiquidity proxies in either the univariate or multivariate specifications. Panel B reports that BHAR(0, 1) is negatively related to DGibbs at the 10% level and BHAR(-60, -1) at the 5% level in the univariate specification. These results are consistent with the liquidity premium and the asymmetric information hypotheses. However, the results are not robust, since BHAR(0, 1) is not significantly related to any of the illiquidity or asymmetric information proxies in the multivariate specifications.

Table VI also reports significant positive coefficients on OPTPREM in the univariate specifications. However, interpreting a positive coefficient as being consistent with the liquidity hypothesis depends on finding a negative relation between OPTPREM and the post-announcement abnormal return. But as we report in Table VII, we do not find a negative relation between the post-announcement abnormal returns and the option premium variable. Hence, we interpret the positive coefficient on OPTPREM in Table VI as being consistent with the Cowan, Nayar, and Singh (2000) asymmetric information model. We also note that the positive coefficient associated with OPTPREM is no longer statistically significant in the multivariate specification. Thus, the estimated coefficients for our liquidity proxies reported in Table VI do not support the liquidity hypothesis.

We note that the relation between BHAR(0, 1) and BHAR(-60, -1), which is significant in the univariate specification, is not significant in the multivariate specification. We also note that because of missing variables, we base our multivariate regressions on fewer observations than the univariate regression. Thus, we re-estimate a univariate regression with BHAR(-60, -1) as the independent variable using only the observations we include in all the multivariate regressions. This regression results in a nonsignificant coefficient for BHAR(-60, -1) and an adjusted R-square below 1%.

Table VII presents the estimates of cross-sectional regressions where the dependent variables represent the abnormal returns between t = 2 and t = LCD. In Panel A, the dependent variable is CAR(2, LCD). We note that in all specifications, the coefficients of SEPS, which controls for possible impacts of asymmetric information, are negative and significantly different from zero. In addition, the coefficients of isize in the univariate and in two of the multivariate regressions are also negative and significantly different from zero. However, in the absence of a corresponding impact on the announcement-window abnormal returns, the significant impacts of SEPS and lsize on post-announcement abnormal returns are not consistent with the implications of the asymmetric information hypothesis. We note that the coefficients of OPTPREM and CAR(0, 1) are not significantly different from zero.

In Panel B, the dependent variable is BHAR(2, LCD). The coefficients of OPTPREM are significant and positive at the 10% level in two multivariate specifications. Thus, when the dependent variable is the announcement window abnormal return in Table VI, the positive coefficients on OPTPREM should not necessarily be interpreted as supporting the liquidity hypothesis. Furthermore, BHAR(2, LCD) is not significantly related to any other independent variable, including the announcement abnormal return, BHAR(0, 1). Thus, the results in Table VII do not provide any support for the liquidity hypothesis. (4)

We perform several robustness tests. First, we replicate the tests using CAR(2, 21) and BHAR(2, 21), the 20-day abnormal returns for the post-announcement windows that start two days after the announcement day as dependent variables. Second, we note that several of our independent variables are skewed to the right. Consequently, we transform some of our variables to reduce the potential impact of a few extreme observations or measurement errors. We substitute the coefficient of variation of the earnings forecasts for SEPS, the logarithm of (1+OPTPREM) for OPTPREM, and the logarithm of ilq for ilq. Third, we find that one company, CBS, had a dilutive impact of 500%. Hence, we re-estimate all of the regressions, deleting this observation. Fourth, we analyze the abnormal returns with the market model, using the t = 251 to t = 506 estimation period of Ederington and Goh (2001). Fifth, we re-estimate our cross-sectional regression analysis, using an equal-weighted market index to compute the abnormal returns. The results we obtain for all of these robustness tests are not qualitatively different from those we report.

IV. Conclusion

The liquidity hypothesis attributes the negative abnormal returns around the conversion-forcing calls announcements (COFCAs) of convertible bonds and the subsequent price recovery to liquidity pressures. The liquidity hypothesis implies that this price recovery should be inversely related to the initial price decline, and that the abnormal returns during the announcement and post-announcement windows should be related to proxies of the stock's illiquidity.

We confirm the existence of negative abnormal returns around COFCAs. However, we find that when we control for other factors that might impact the abnormal return, these negative abnormal returns are not statistically related to any of the conventional illiquidity proxies. Nor do we find a statistical relation between the post-announcement abnormal returns and the announcement abnormal returns.

We demonstrate that the post-announcement positive abnormal returns that are documented in previous studies are sensitive to the estimation procedure. The absence of post-announcement abnormal returns is consistent with the efficient markets hypothesis. We also find no consistent empirical support for alternative hypotheses such as the asymmetric information, interest tax loss, and investment options hypotheses. We conclude that the negative market reaction to COFCAs needs further examination.

The views' expressed in this paper are solely that of the authors and not of the OCC or the U.S. Department of the Treasury. We thank William T. Moore, Avri Ravid, John Wald, and the anonymous referee for their helpful comments on earlier drafts, We also thank Arnold Cowan in advising us in the use of Eventus, and Louis Ederington and Jeremy Goh for allowing us to use their data. In addition, we acknowledge partial funding support from the David K. Whitcomb Center for Research in Financial Services. Rutgers University.

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(1) For a review of the optimal time to call a convertible bond, see Ederington, Caton, and Campbell (1997).

(2) A similar interpretation is given by Kadapakkam and Tang (1996) and Howe, Lin, and Singh (1998) for stock price reactions around the announcement of the forced conversion of preferred stocks, and by Mitchell, Pulvino, and Stafford (2004) for the abnormal returns around merger announcements. Alderson and Betker (2003) suggest that price pressures might partially explain the negative stock reaction to forced warrant exercise.

(3) See http://pages.stern.nyu.edu/~jhasbrou/.

(4) The literature has offered additional explanations for the impact of a conversion-forcing call, most notably are the investment option hypothesis (see Mayers, 1998) and the loss of tax shields (see Mikkelson, 1985). In alternative specifications we include also variables that should be associated with the abnormal returns according to these hypotheses. These variables include the Market-to-Book ratio as a measure of the investment option, John Graham's estimate of the effective tax rate (see, Graham 1996) and the difference between the aggregate after corporate tax interest payment of the convertible bond and the dividend payment from the additional equity generated by the conversion scaled by the market capitalization of equity for t = -1. We do not report the results from these specifications because the coefficients of these variables are not significantly different from zero, and because including them does not qualitatively affect the coefficients that are reported in Tables VI and VII.

Ivan E. Brick, Oded Palmon, and Dilip K. Patro *

* Ivan E. Brick is Professor of Finance and Economics at Rutgers University, in Newark and New Brunswick, NJ. Oded Palmon is Professor of Finance and Economics at Rutgers University, in Newark and New Brunswick, NJ. Dilip K. Patro is a Senior Financial Economist at the Office of the Comptroller of the Currency in Washington, DC.

Table I. Descriptive Statistics This table provides the summary statistics of all of our independent variables for December 1984-December 2002. SEPS is the standard deviation of analysts' earnings forecasts. The term lsize is the natural logarithm of equity market capitalization where capitalization is in terms of thousands of dollars. Gibbs is Gibbs sampler estimate of trading costs. DILUTION measures the dilution of the stock as the result of the call, which we define as the product of the conversion rate and the par value of the called convertible debt in thousands of dollars divided the number of shares that will become outstanding after the conversion. The variable ilq is the ratio of the absolute return to volume which is the inverse of the Amivest measure. OPTPREM is a measure of the moneyness of the conversion option, which we calculate as the difference between the stock price at the time of the announcement and the conversion price divided by the conversion price. In panel B, BHAR(-100, -1) and BHAR(-60, -1) are the buy-and-hold abnormal returns for days (-100, -1), and (-60, -1), respectively. Similarly, CAR(-100, -1) and CAR(-60, -1) are the market-model abnormal returns for days (-100, -1), and (-60, -1), respectively. N is the number of observations. Panel A: Summary Statistics Variable N Mean Median Std Dev Minimum Maximum SEPS 309 0.1413 0.0482 0.2493 0.0000 2.3282 lsize 383 13.5458 13.5462 1.5035 10.1481 18.7159 Gibbs 367 0.1267 0.0983 0.1013 0.0277 0.8079 Dilution 368 0.0888 0.0432 0.3275 0.0001 5.7980 ilq 381 11.1744 2.7689 25.0539 0.0097 246.4362 OPTPREM 387 0.6445 0.4072 0.9353 0.0052 10.0102 Panel B: Correlation Matrix CAR CAR BHAR BHAR (-100, -1) (-60, -1) (-100, -1) (-60, -1) CAR (-100, -1) 1.000 N 389 CAR (-60, -1) 0.811 *** 1.000 N 389 389 BHAR (-100, -1) 0.499 *** 0.464 *** 1.000 N 352 352 352 BHAR (-60, -1) 0.414 *** 0.626 *** 0.825 *** 1.000 N 352 352 352 352 Gibbs -0.051 -0.02 0.033 0.037 N 367 367 331 331 DGibbs -0.057 -0.027 -0.034 -0.011 N 348 348 314 314 ilq 0.021 0.056 -0.015 0.000 N 381 381 345 345 Dilq -0.008 -0.041 -0.067 -0.081 N 361 361 327 327 OPTPREM 0.060 0.093 * 0.118 ** 0.128 N 387 387 350 350 lsize -0.07 -0.064 -0.024 -0.041 N 383 383 347 347 SEPS 0.072 0.114 ** 0.002 0.061 N 309 309 282 282 Dilution -0.052 -0.030 -0.052 -0.034 N 368 368 333 333 Gibbs DGibbs ilq Dilq CAR (-100, -1) N CAR (-60, -1) N BHAR (-100, -1) N BHAR (-60, -1) N Gibbs 1.000 N 367 DGibbs 0.233 1.000 N 348 348 ilq -0.115 -0.039 1.000 N 367 348 381 Dilq -0.032 0.043 0.428 *** 1.000 N 348 348 361 361 OPTPREM 0.295 -0.038 -0.089 * -0.104 ** N 365 348 379 361 lsize 0.391 *** 0.086 -0.56 *** -0.38 *** N 361 348 375 361 SEPS 0.121 0.541 *** -0.035 0.027 N 291 279 302 289 Dilution 0.197 *** 0.978 *** -0.056 0.109 ** N 348 348 361 361 OPTPREM lsize SEPS Dilution CAR (-100, -1) N CAR (-60, -1) N BHAR (-100, -1) N BHAR (-60, -1) N Gibbs N DGibbs N ilq N Dilq N OPTPREM 1.000 N 387 lsize 0.272 *** 1.000 N 381 383 SEPS 0.092 0.072 1.000 N 308 308 309 Dilution -0.08 0.044 0.561 *** 1.000 N 368 368 295 368 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table II. Abnormal Returns Around Announcements of Conversion of Convertible Bonds Using a Pre-Announcement Estimation Period and the Market Model Our original sample includes 392 announcements of calls of convertible bonds between December 1984 and December 2002. The table reports results from a market model using the CRSP equally weighted and value-weighted indexes. The estimation period is between t = -250 and t = -101. LCD is the last day for conversion. Pos:Neg is the ratio of positive to negative CARs. Z is the standard Patell (1976) test that accounts for non-i.i.d. distributions of abnormal returns. SCZ-Z is the Boehmer, Musumeci and Poulsen (1991) standardized cross-sectional Z. Sign Z is the generalized sign test developed in Cowan (1992), indicating whether the proportion of positive to negative abnormal returns is significantly different from one. Panel A: Equally Weighted Index Window N CAR Pos: Neg Z (-100,-1) 392 7.17% 224:168 4.617 *** (-60,-1) 392 5.37% 221:171 4.617 *** (0, +1) 392 -1.02% 145:247 -5.953 *** (0, +21) 392 -2.09% 170:222 -3.205 *** (0, LCD) 388 -2.45% 161:227 -4.129 *** (+2, +21) 392 -1.07% 186:206 -1.614 (+2, LCD) 388 -1.57% 166:222 -2.743 *** Panel B: Value Weighted Index (-100, -1) 392 11.95% 258:134 7.328 *** (-60, -1) 392 9.10% 266:126 7.535 *** (0, +1) 392 -0.88% 139:253 -5.242 *** (0, +21) 392 -1.61% 176:216 -2.272 ** (0, LCD) 388 -2.35% 165:223 -3.390 *** (+2, +21) 392 -0.74% 191:201 -0.826 (+2, LCD) 388 -1.63% 168:220 -2.155 ** Panel A: Equally Weighted Index Window SCS Z Sign Z (-100,-1) 4.634 *** 4.184 *** (-60,-1) 4.542 *** 3.880 *** (0, +1) -4.866 *** -3.815 *** (0, +21) -3.328 *** -1.284 (0, LCD) -4.404 *** -2.014 * (+2, +21) -1.662 * 0.336 (+2, LCD) -2.939 *** -1.517 Panel B: Value Weighted Index (-100, -1) 7.673 *** 7.538 *** (-60, -1) 8.062 *** 8.347 *** (0, +1) -4.278 *** -4.508 *** (0, +21) -2.343 * -0.763 (0, LCD) -3.606 *** -1.694 * (+2, +21) -0.842 0.756 (+2, LCD) -2.299 ** -1.356 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table III. Abnormal Returns Around Announcements of Conversion of Convertible Bonds Using a Post-Announcement Estimation Period and the Market Model Our original sample includes 392 announcements of calls of convertible bonds between December 1984 and December 2002. The table reports results from a market model using the CRSP equally weighted and value-weighted indexes. LCD is the last day for conversion. The estimation period is between t = LCD + 21 and t = LCD + 170. Pos:Neg is the ratio of positive to negative CARs. Z is the standard Patell (1976) test that accounts for non-i.i.d. distributions of abnormal returns. SCZ-Z is the Boehmer, Musumeci and Poulsen (1991) standardized cross-sectional Z. Sign Z is the generalized sign test developed in Cowan (1992), indicating whether the proportion of positive to negative abnormal returns is significantly different from one. Panel A: Equally Weighted Index Window N CAR Pos: Neg Z (-100, -1) 389 12.48% 259:130 7.130 *** (-60, -1) 389 8.38% 260:129 6.356 *** (0, +1) 389 -0.91% 144:245 -5.033 *** (0, +21) 389 -0.91% 184:205 -1.764 * (0, LCD) 389 -1.17% 182:207 -2.208 ** (+2, +21) 389 0.00% 191:198 -0.358 (+2, LCD) 389 -0.33% 185:204 -0.859 Panel B: Value-Weighted Index (-100, -1) 389 16.77% 291:98 -9.686 *** (-60, -1) 389 11.83% 287:102 9.183 *** (0, +1) 389 -0.75% 143:246 -4.248 *** (0, +21) 389 -0.41% 188:201 -0.931 (0, LCD) 389 -1.66% 185:204 -1.436 (+2, +21) 389 0.33% 202:187 0.293 (+2, LCD) 389 -1.00% 186:203 -0.301 Panel A: Equally Weighted Index Window SCS Z Sign Z (-100, -1) 8.338 *** 7.574 *** (-60, -1) 7.070 *** 7.676 *** (0, +1) -4.402 *** -4.103 *** (0, +21) -2.238 ** -0.042 (0, LCD) -2.859 *** -0.245 (+2, +21) -0.461 0.669 (+2, LCD) -1.136 0.06 Panel B: Value-Weighted Index (-100, -1) 11.981 *** 10.658 *** (-60, -1) 11.015 *** 10.252 *** (0, +1) -3.747 *** -4.364 *** (0, +21) -1.196 0.204 (0, LCD) -1.915 * -0.101 (+2, +21) 0.382 1.625 (+2, LCD) -0.409 0.001 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table IV. Buy-and-Hold Abnormal Returns Using Control Firms as Benchmarks We match benchmark firms to sample firms by size and market-to-book value (within 20%). Pos:Neg is the ratio of positive to negative BHARs. LCD is the last day for conversion. The t-statistic is the cross-sectional standard deviation t-test as discussed in Brown and Warner (1985). Sign Z is the generalized sign test developed in Cowan (1992), indicating whether the proportion of positive to negative abnormal returns is significantly different from one. Window N BHAR Pos: Neg t-statistic Sign Z (-100, -1) 354 13.93% 257:97 13.022 *** 9.488 *** (-60, -1) 354 8.80% 257:97 10.617 *** 9.488 *** (0, +1) 354 -0.48% 136:218 -3.181 *** -3.395 *** (0, +21) 354 -0.22% 175:179 -0.439 0.757 (0, LCD) 354 -0.46% 160:194 -0.815 -1.297 (+2, +21) 354 0.28% 182:172 0.576 1.503 (+2, LCD) 354 -0.04% 180:174 -0.081 0.83 *** Significant at the 0.01 level. Table V. Regression Results for the Post-Announcement Window Abnormal Returns on Announcement Window Abnormal Returns This table provides the coefficient estimates from OLS tests in which the dependent variable is a post-announcement abnormal return and the independent variable is a corresponding announcement window abnormal return. The coefficient is followed by the heteroskedasticity- consistent White (1980) t-values in parenthesis. CAR (0, 1) is the two-day (t = -1,0) cumulative abnormal return based on the market model. BHAR (0, 1) is the corresponding buy-and-hold abnormal return. CAR(2, 21) is the post-announcement market-model-based cumulative abnormal return for (2, 21). BHAR(2, 21) is the corresponding buy-and- hold abnormal return. CAR(2, LCD) is the post-announcement market- model-based cumulative abnormal return for (2, LCD). BHAR(2, LCD) is the corresponding buy-and-hold cumulative abnormal return. LCD is the last day for conversion. Panel A: Market-Model Abnormal Returns CAR(2, 21) CAR(2, LCD) Intercept 0.002808 -0.00993 (0.57) (-1.03) 2AR (0, 1) -0.07116 0.03 (-0.31) (0.12) V 389 387 Adj R-Square -0.0019 -0.0026 Panel B: Buy-and-Hold Abnormal Returns BHAR(2, 21) BHAR(2, LCD) Intercept 0.001824 -0.00079 (0.41) (-0.19) BHAR (0, 1) -0.18296 -0.09509 (-0.90) (-0.50) N 354 354 Adj. [R.sup.2] 0.0006 -0.0018 Table VI. Cross-Sectional Regression Results for the Announcement Window Abnormal Returns This table provides the coefficient estimates from OLS tests. The dependent variable in Panel A is CAR(0, 1), the cumulative abnormal return from t = 0 to 1 based on the market model. The dependent variable in Panel B is BHAR(0, 1), the buy-and-hold abnormal return from (0, 1). The set of independent variables comprises the following. Gibbs is the Hasbrouck (2005) Gibbs sampler estimate of trading costs; lsize is the logarithm of the firm's equity market capitalization; CAR(-60, -1) is the cumulative abnormal return for (-60, -1) based on the market model; BHAR(-60, -1) is the buy-and-hold abnormal return for (-60, -1); SEPS is the standard deviation of analysts' earning forecasts; DGibbs is the product of DILUTION and Gibbs: The variable ilq is the inverse of the Amivest measure; Dilq is the product of DILUTION and ilq; and OPTPREM is the difference between the market price of a share and the conversion price, divided by the conversion price. Underneath each coefficient is the White (1980) t-statistic. Panel A. Dependent Variable is CAR(0, 1) Intercept -0.0062 -0.007 *** -0.008 *** -0.008 *** (-1.63) (-3.22) (-3.41) (-3.31) Gibbs -0.0054 -- -- -- (-0.17) DGibbs -- -0.0037 -- -- (-0.72) ilq -- -- 0.0000 -- (0.12) Dilq -- -- -- -0.0003 (-0.22) lsize -- -- -- -- CAR (-60, -1) -- -- -- -- SEPS -- -- -- -- OPTPREM -- -- -- -- Adj. [R.sup.2] -0.0026 -0.0028 -0.0026 -0.0027 N 367 350 381 363 Panel B: Dependent Variable is BHAR(0, 1) Intercept -0.0054 * -0.0046 *** -0.0049 *** -0.0047 *** (-1.93) (-2.93) (-3.22) (-2.99) Gibbs 0.0069 -- -- -- (0.33) DGibbs -- -0.0049* -- -- I1q - -- 0.0000 -- (0.02) Dilq -- -- -- -0.0007 (-0.83) Lsize -- -- -- -- BHAR (-60, -1) -- -- -- -- SEPS -- -- -- -- OPTPREM -- -- -- -- Adj. [R.sup.2] -0.0023 -0.0026 -0.0029 -0.0021 N 334 319 348 332 Panel A. Dependent Variable is CAR(0, 1) Intercept -0.0034 -0.0051 ** -0.008 *** -0.010 *** (-0.16) (-2.3) (-3.16) (-4.3) Gibbs -- -- -- -- DGibbs -- -- -- -- ilq -- -- -- -- Dilq -- -- -- -- lsize -0.0003 -- -- -- (-0.2) CAR (-60, -1) -- -0.0203 -- -- (-1.64) SEPS -- -- 0.0013 -- (0.19) OPTPREM -- -- -- 0.0038 * (1.68) Adj. [R.sup.2] -0.0025 0.0100 -0.0032 0.005 N 383 389 309 387 Panel B: Dependent Variable is BHAR(0, 1) Intercept -0.0097 -0.0029 ** -0.0051 ** -0.0067 *** (-0.69) (-2.04) (-2.84) (-4.06) Gibbs -- -- -- -- DGibbs -- -- -- -- I1q -- -- -- -- Dilq -- -- -- -- Lsize 0.0004 -- -- -- (0.37) BHAR (-60, -1) -- -0.0223 ** -- -- (-2.37) SEPS -- -- 0.0055 -- (0.97) OPTPREM -- -- -- 0.0028 ** (2.11) Adj. [R.sup.2] -0.0024 0.0256 -0.0011 0.007 N 350 354 284 353 Panel A. Dependent Variable is CAR(0, 1) Intercept -0.0198 -0.0024 -0.0132 0.0061 (-0.95) (-0.11) (-0.53) (0.23) Gibbs -0.0428 -- -- -- (-1.12) DGibbs -- -0.0154 -- -- (-1.28) ilq -- -- 0.0000 -- (0.26) Dilq -- -- -- -0.003 (-1.04) lsize 0.0014 -0.0004 0.0005 -0.0009 (0.89) (-0.22) (0.28) (-0.50) CAR (-60, -1) -0.0326 ** -0.0306 ** -0.0300 ** -0.0276 ** (-2.50) (-2.25) (-2.45) (-2.10) SEPS 0.0068 0.0112 0.0057 0.0073 (0.93) (1.06) (0.83) (1) OPTPREM 0.0030 0.0040 0.0018 0.0034 (1.39) (1.57) (1.01) (1.43) Adj. [R.sup.2] 0.0339 0.0192 0.0183 0.0143 N 289 278 300 288 Panel B: Dependent Variable is BHAR(0, 1) Intercept -0.0218 -0.017 -0.0175 -0.0143 (-1.4) (-1.06) (-0.98) (-0.76) Gibbs -0.0122 -- -- -- (-0.49) DGibbs -- -0.0132 -- -- (-1.36) I1q -- -- 0.0000 -- (0.09) Dilq -- -- -- 0.0000 (-0.01) Lsize 0.0013 0.0008 0.0009 0.0006 (1.15) (0.70) (0.69) (0.45) BHAR (-60, -1) -0.0158 -0.0171 -0.0158 -0.0158 (-0.95) (-0.94) (-1.05) (-1.01) SEPS 0.0035 0.0079 0.0034 0.0035 (0.58) (0.87) (0.59) (0.56) OPTPREM 0.0026 0.0031 0.0023 0.0029 (1.59) (1.42) (1.59) (1.52) Adj. [R.sup.2] 0.0076 0.007 0.0047 0.0027 N 264 255 275 265 *** Significant at the 0.01 level. ** Significant at the 0.05 level. * Significant at the 0.10 level. Table VII. Cross-Sectional Regression Results for the Post-Announcement Abnormal Return This table provides the coefficient estimates from OLS tests. In Panel A, the dependent variables are CAR(2, LCD), which are the cumulative abnormal return based on the market model from t = 2 to the last conversion date. In Panel B, the dependent variable is BHAR(2, LCD), the buy-and-hold abnormal return for the same period. The set of independent variables comprises the following: Gibbs, is the Hasbrouck (2005) Gibbs sampler estimate of trading costs; lsize is the logarithm of the firm's equity market capitalization; CAR(-60, -1) and CAR(0, 1), which are the cumulative abnormal returns for (-60, -1) and (0, 1), respectively, based on the market model; BHAR(-60, -1) and BHAR(0, 1), which are the buy-and-hold abnormal returns for (-60, -1) and (0, 1), respectively; SEPS is the standard deviation of analysts' earning forecasts; DGibbs is the product of DILUTION and Gibbs: the variable ilq is the inverse of the Amivest measure; Dilq is the product of DILUTION and ilq; and OPTPREM is the difference between the market price of a share and the conversion price divided by the conversion price. Underneath each coefficient is the White (1980) t-statistic. Panel A: Dependent variable is CAR(2, LCD) Intercept -0.0213 -0.0075 -0.0123 -0.0089 (-1.50) (-0.96) (-1.02) (-0.75) Gibbs 2.2052 -- -- -- (1.05) DGibbs -- -7.3517 -- -- (-0.44) ilq -- -- 0.0003 -- (1.2) Dilq -- -- -- 0.0036 (0.58) Nize -- -- -- -- CAR -- -- -- -- (-60,-1) CAR -- -- -- -- (0, 1) SEPS -- -- -- -- OPTPREM -- -- -- -- Adj. [R.sup.2] -0.0017 -0.0024 -0.0013 -0.0024 N 366 349 380 362 Panel B: Dependent Variable is BHAR(2, LCD) Intercept 0.0033 -0.0005 0.0010 0.0002 (0.49) (-0.11) (0.22) (0.04) Gibbs -0.0369 -- -- -- (-0.84) DGibbs -- 0.0041 -- -- (0.87) ilq -- -- -0.0001 -- (-0.37) Dilq -- -- -- 0.0025 (0.99) lsize -- -- -- -- BHAR -- -- -- -- (-60,-1) BHAR -- -- -- -- (0, 1) SEPS -- -- -- -- OPTPREM -- -- -- -- Adj. [R.sup.2] -0.0006 -0.0031 -0.0025 -0.0016 N 332 317 346 330 Panel A: Dependent variable is CAR(2, LCD) Intercept 0.1432 ** -0.0151 -0.0099 -0.0091 (2.37) (-0.96) (-1.03) (-0.51) Gibbs -- -- -- -- DGibbs -- -- -- -- ilq -- -- -- -- Dilq -- -- -- -- Nize -0.0113 ** -- -- -- (-2.37) CAR -- 0.0449 -- -- (-60,-1) (0.64) CAR -- -- 0.0284 -- (0, 1) (0.12) SEPS -- -- -- -0.0453 ** (-2.23) OPTPREM -- -- -- -- Adj. [R.sup.2] 0.0043 -0.0001 -0.0026 -0.0007 N 382 388 387 307 Panel B: Dependent Variable is BHAR(2, LCD) Intercept 0.0457 0.0011 -0.0008 -0.0003 (1.08) (0.26) (-0.19) (-0.05) Gibbs -- -- -- -- DGibbs -- -- -- -- ilq -- -- -- -- Dilq -- -- -- -- lsize -0.0034 -- -- -- (-1.11) BHAR -- -0.0168 -- -- (-60,-1) (-0.48) BHAR -- -- -0.0951 -- (0, 1) (-0.5) SEPS -- -- -- -0.0036 (-0.27) OPTPREM -- -- -- -- Adj. [R.sup.2] 0.0012 -0.001 -0.0018 -0.0035 N 348 355 355 282 Panel A: Dependent variable is CAR(2, LCD) Intercept -0.0071 0.1364 * 0.1400 ** (-0.51) (1.73) (2.07) Gibbs -- -1.5245 -- (-0.42) DGibbs -- -- 8.0463 (0.49) ilq -- -- -- Dilq -- -- -- Nize -- -0.0116 * -0.0118 ** -1.86 (-2.00) CAR -- 0.1229 0.0835 (-60,-1) (1.38) (1.08) CAR -- 0.0401 0.1405 (0, 1) (0.12) (0.44) SEPS -- -0.0485 * -0.0616 ** (-1.66) (-2.05) OPTPREM -0.0046 0.0064 0.0055 (-0.61) (0.62) (0.48) Adj. [R.sup.2] -0.0022 0.0013 -0.0067 N 386 287 276 Panel B: Dependent Variable is BHAR(2, LCD) Intercept -0.0019 0.0421 0.0694 (-0.41) (0.81) (1.33) Gibbs -- -0.0601 -- (-1.2) DGibbs -- -- 0.0213 (0.96) ilq -- -- -- Dilq -- -- -- lsize -- -0.0033 -0.0055 (-0.83) (-1.40) BHAR -- 0.0119 0.0029 (-60,-1) (0.35) (0.09) BHAR -- -0.0881 0.0274 (0, 1) (-0.37) -0.12 SEPS -- 0.0048 -0.0095 (0.33) (-0.46) OPTPREM 0.0027 0.0092 * 0.0082 (0.67) (1.83) (1.19) Adj. [R.sup.2] -0.0018 -0.0002 -0.009 N 351 262 253 Panel A: Dependent variable is CAR(2, LCD) Intercept 0.0744 0.0798 (1.04) (1.12) Gibbs -- -- DGibbs -- -- ilq 0.0004 -- (1.16) Dilq -- 0.0150 (1.26) Nize -0.0075 -0.0074 (-1.34) (-1.28) CAR 0.1159 0.0806 (-60,-1) (1.41) (1.04) CAR 0.0196 0.1141 (0, 1) (0.06) (0.34) SEPS -0.0525 * -0.0576 ** (-1.83) (-2.01) OPTPREM 0.0057 0.0053 (0.6) (0.44) Adj. [R.sup.2] 0.0019 -0.0055 N 298 286 Panel B: Dependent Variable is BHAR(2, LCD) Intercept 0.0467 0.0568 (0.81) (0.89) Gibbs -- -- DGibbs -- -- ilq 0.0000 -- (-0.08) Dilq -- -0.0019 (-0.27) lsize -0.0041 -0.0046 (-0.96) (-0.98) BHAR 0.0424 0.0364 (-60,-1) (1.09) (0.91) BHAR -0.0910 0.0032 (0, 1) (-0.38) -0.01 SEPS -0.0034 -0.0082 (-0.24) (-0.54) OPTPREM 0.0080 0.0075 (1.67) (1.17) Adj. [R.sup.2] 0.0021 -0.0033 N 273 263 ** Significant at the 0.05 level. * Significant at the 0.10 level.

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Author: | Brick, Ivan E.; Palmon, Oded; Patro, Dilip K. |
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Publication: | Financial Management |

Geographic Code: | 1USA |

Date: | Jun 22, 2007 |

Words: | 10090 |

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