Accounting and Finance 45 (2005) 635–651
Changes in risk characteristics of firms issuing hybrid
securities: case of convertible bonds
Atul Rai
University of Alabama in Huntsville, Huntsville, AL, 35899, USA
Abstract
The present paper examines changes in risk characteristics of a firm when it issues
convertible bonds by studying the change in beta before and after the issuance
of convertible bonds. Using a sample of 149 firms, strong evidence was found of
change in beta, along with significant heterogeneity across firms. On average, the beta
of a firm issuing convertible bonds declines, although 40 per cent of firms showed
an increase in beta. A cross-sectional regression shows that after controlling for
the reversion-to-mean phenomenon, the change in beta is significantly related to
potential dilution of equity as well as to increase in debt, but is not significantly
related to either the change in bond rating of a firm or to the stated use of funds from
issuance.
Key words: Convertible bonds; Security offerings; Beta; Equity dilution; Bond rating
JEL classification: B41, C14, G10, G12, G14, M41
doi: 10.1111/j.1467-629X.2005.00148.x
1. Introduction
Convertible bonds combine aspects of both debt and common equity, thereby
presenting unique challenges for financial analysis. The current accounting treatment
of convertible bonds does not provide any guidance.1 At the time of issuance, a
convertible bond is treated like a straight-bond. The convertible feature of the bond is
The author gratefully acknowledges contributions of Tom Abbott, Ivan Brick, Dorla Evans,
Robert Faff (Editor), April Klein, seminar participants at Western Finance Association Annual Meetings, Southwest Federation of Academic Disciplines Meetings, Midwestern Finance
Association Meetings, Florida State University, Rutgers University, University of Alabama in
Huntsville, and two anonymous referees to an earlier version of the present paper.
Received 28 April 2003; accepted 7 December 2004 by Robert Faff (Editor).
1 Refer
to Financial Accounting Standards Board, Emerging Issue Task Force Issue No. 98-5.
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completely ignored. Also, subsequent to issuance, a convertible bond is treated like
a straight-bond and recognized at amortized cost. The conversion feature is ignored
again. However, for the purpose of calculating diluted earnings per share (EPS),
the basic EPS is adjusted to reflect the potential convertibility of the convertible
bond.2 Because of the global nature of the convertible bonds market, the International
Accounting Standard Board (2003b) issued International Accounting Standard 32,
which required that the equity component and the debt component of a convertible
bond be disclosed separately.3
Prior research has investigated the rationale for issuing convertible bonds and has
provided various explanations. For example, Jensen and Meckling (1976) argued
that convertible bonds mitigate asset substitution problems. They might also reduce
underinvestment problems, as suggested by Myers (1977), Green (1984) and Jen
et al. (1997). Convertible bonds also reduce asymmetric information between the
firm and its debt-holders, as suggested by Brennan and Kraus (1987) and Brennan
and Schwartz (1988). Stein (1992) has suggested that convertible bonds are used as
back-door equity financing when adverse-selection problems make a conventional
stock issue unattractive. Recent research suggests that convertible debt is useful for
sequential financing of a project (see Mayers, 1998; Cornelli and Yosha, 2003; Chang
et al., 2004). Many of these studies implicitly argue that issuance of convertible bonds
signals a change in the composition of projects undertaken by these firms. A natural
implication of these arguments is that the risk structure of firms issuing convertible
bonds changes. Investigation of this issue is important for investors for optimal
allocation of their capital. It is also important for policy-makers in determining the
fair-value based accounting treatment of these bonds.
In the present paper, we examine the change in risk characteristics of firms
issuing convertible bonds by measuring the change in beta of these firms. We
also investigate possible reasons for changes in beta. Prior published literature has
not examined changes in the systematic risk of firms issuing convertible bonds.
Our results extend the work of Lewis et al. (2002), who examined the change in
cost of capital and idiosyncratic risk of firms issuing convertible bonds, but did
not examine changes in the systematic risk of these firms. They found that although the cost of capital decreased for the issuing firms, their idiosyncratic risk
increased. Ambiguous nature of their results warrants further investigation of this
issue.
The remainder of the present paper is organized as follows. Section 2 provides
theoretical background to analyse effects of issuing convertible bonds on the systematic risk of a firm. Section 3 describes prior empirical evidence regarding convertible
bonds issues. Section 4 describes data and conducts an empirical examination of the
change in the beta of a company. Section 5 concludes the paper.
2 Refer to Financial Accounting Standards Board, Emerging Issue Task Force Issue No. 02-15.
3 See
also IASB (2003a), International Accounting Standard 39.
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2. Theoretical background
To see how the issuance of convertible bonds might change the systematic risk
of a firm, consider the beta for a levered firm. Specifically, under the simplifying
assumptions of no taxes and risk-free debt, the beta of a levered firm and beta of an
unlevered firm are related as follows:
βl = (1 + L)βu ,
or
βl = (1 + L)βu + Lβu ,
(1)
where β l is beta of levered firm (estimated using market model), L is the financial
leverage of the firm = debt/equity and β u is beta of unlevered firm with same cash
flow. Therefore, the change in beta can result from either the change in financial
leverage or the change in the unlevered beta (i.e. changes in the investment policies
of the firm) or both.
2.1. Changes in financial leverage
The effects of issuing pure securities on financial leverage are straightforward.
Unfortunately, because a convertible bond is a hybrid security, its impact on financial
leverage is not as clear-cut. If funds from issuance are used to finance new projects,
they can conceivably increase or decrease leverage depending upon relative values
of their debt-like and equity-like component claims and the firm’s financial structure
before issuance (see Dann and Mikkelson, 1984). However, if funds are used to retire
debt (equity), then leverage will decrease (increase). In these cases, the effect on
financial leverage is unambiguous because the firm is replacing ‘pure’ securities with
‘mixed’ ones.
2.2. Changes in unleveraged beta
Changes in unleveraged beta primarily result from changes in the underlying
investment policies of the firm. Agency costs between equity owners and bond
holders can be significantly reduced through the issuance of convertible bonds (see
Jensen and Meckling, 1976; Green, 1984). By providing the convertible debt-holders
with an option to participate in the profits from riskier projects, equity holders make
a credible commitment not to undertake extraordinarily risky projects. Agency costs,
therefore, provide a theoretical reason to expect a shift in the investment policy of
the firm away from more risky projects and towards less risky projects as a result
of issuing convertible bonds. This is often referred to as ‘risk-shifting hypothesis’
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in published literature pertaining to issuance of convertible bonds. This hypothesis
predicts that beta of a firm issuing convertible bonds should decrease.
Stein (1992) proposes a back-door equity financing hypothesis and argues that
convertible bonds reduce agency costs of adverse selection inherent in direct equity
issues. Lewis et al. (1999) find empirical support for both Stein’s ‘back-door equity
hypothesis’ and Green’s ‘risk-shifting hypothesis’ contingent upon the perception of
investors whether the convertible bond is more like equity or straight debt. Back-door
equity financing hypothesis also predicts that beta of the firm issuing convertible
bonds should decline.
Mayers (1998) argues that firms issue convertible bonds to reduce costs of raising
capital. He proposes a ‘sequential-financing’ hypothesis. According to this hypothesis, the risk level of the firm issuing convertible bonds should be optimal after issuance.
If a firm has a project that might be completed or extended in stages contingent upon
future profit assessment, then convertible bonds provide lower cost financing alternatives to a firm in comparison to repeated forays into the capital market to raise equity.
The call option feature of convertible bonds allows managers to avoid additional
issuance costs if the project were to be financed by sequential equity issues, or to
avoid overinvestment if straight debts were issued at every stage of a project. Cornelli
and Yosha (2003) argue that this feature is very useful for venture capitalists. Chang
et al. (2004) provides empirical support for a sequential-financing hypothesis using
a sample of convertible bonds issued in Taiwan. Sequential-financing hypothesis
suggests that beta of firms issuing convertible bonds is optimal after the issuance.
Therefore, the change in beta upon issuance might be in either direction, depending
upon whether the beta was above or below the optimal level.
In summary, the impact of issuing convertible bonds on stock beta is ambiguous.
Inference about the change in beta from the three hypotheses in the previous paragraph
is based on the assumption that funds from the issuance of convertible bonds were
used to finance new projects. Other factors that are likely to play an important role in
determining the direction and magnitude of the changes include: relative size and
riskiness of the issue; probability of conversion; call provisions; intended use of the
funds and the inherent riskiness of the enterprise; as well as other characteristics of
the particular issue and/or firm. The observed change in beta will reflect cumulative
effect of these individual factors, and remains essentially an empirical question.
3. Previous empirical evidence
As noted earlier, prior research has not examined changes in beta of a firm issuing convertible bonds. However, many studies have documented negative returns for
stockholders at the time of issuance of convertible bonds. These returns are less negative than negative returns found for firms issuing equity (see Dann and Mikkelson,
1984; Eckbo, 1986; Mikkelson and Partch, 1986; Hansen and Crutchley, 1990;
Abhyankar and Dunning, 1999). Several studies have documented that returns are
more negative for higher rated bonds and firms with lower Value Line ratings (see
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Mikkelson and Partch, 1986; Davidson et al., 1995; Mehta and Khan, 1995). Firms
that use funds from issuance of convertible bonds for capital expenditure rather than
to retire debt had higher returns (Abhyankar and Dunning, 1999). Firms announcing
private placement of convertible bonds had positive returns at the time of announcement (Fields and Mais, 1991). These studies are summarized here.
Dann and Mikkelson (1984) examined 132 public announcements of issue of
convertible bonds. They found significant negative returns for stockholders during
a 2 day period (day −l and day 0) as well as for the entire announcement period
of 121 days (day −60 to day +60). Mikkelson and Partch (1986) used a sample of
33 convertible bond offerings, which consisted of 266 other security offerings as
well. Relating the ratings of the convertible bond issue with abnormal returns, they
found that higher rated convertible bonds had larger negative returns (−3.72 per cent),
whereas lower rated convertible bond issues had less negative returns (−0.14 per cent)
for a 2 day period around the announce date.
Mehta and Khan (1995) extended the work of Mikkelson and Partch (1986) by considering an enlarged sample size (166 firms) and found similar negative returns. They
also related abnormal returns with ratings of the bond. For investment grade, speculative grade and non-rated convertible bonds, the 3 day abnormal returns were −2.061,
−1.258 and −3.744 per cent, respectively. These results are similar to Mikkelson
and Partch (1986). Davidson et al. (1995) investigated whether the conversion ratio
signals a desire by managers to share risk, therefore implying low prospects for future earnings. For a sample of 147 firms, they also found significant negative equity
returns for firms announcing issuance of convertible debt. Partitioning their sample
based on value-line ratings, they found that returns are more negative for firms with
lower ratings by value-line.
Abhyankar and Dunning (1999) also found significant negative returns for a sample
of 118 announcements of convertible debt issues in the UK. However, conditioning
the issue on the usage of funds raised, they found lower returns when funds were
used for refinancing existing debt and higher returns when they were used for capital
expenditure. They also found negative returns to privately placed convertible bonds.
Fields and Mais (1991), however, had found positive returns when firms announced
issuance of privately placed convertible debt. They argued that private placement is
usually to more informed investors (like banks) and, therefore, information asymmetry is reduced when convertible bonds are privately placed, which results in positive
returns.
4. Results
4.1. Statistical background
Betas obtained from an ordinary least square (OLS) estimate of the market model
provide consistent estimates of the underlying fixed parameters. In this instance, the
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assumption of non-stochastic regressors is clearly violated and only asymptotic results
can be proven. Under fairly general assumptions, these estimators are asymptotically
normal:
B1i ∼ AN β1i , σ1i2 ,
(2)
B2i ∼ AN β2i , σ2i2 ,
where B 1 i (B 2 i ) is (OLS) estimate of pre-issuance (post-issuance) beta, β 1 i (β 2 i )
is true pre-issuance (post-issuance) beta, and σ1i2 (σ2i2 ) is variance of pre-issuance
(post-issuance) beta.
From this, it is easy to show that the change in the estimated betas provides a consistent estimate of the true change in beta and has an asymptotic normal distribution
with variance equal to the sum of the variance of each estimate. Note that because
the estimation of pre- and post-betas are constructed from independent observations,
the covariance term is zero. That is:
Bi = B2i − B1i ∼ AN β2i − β1i , σ1i2 + σ2i2 .
(3)
Because σ 1 i and σ 2 i are not known, their OLS estimates will be used as:
S1i = standard error of B1i ,
S2i = standard error of B2i .
From this result, we can construct statistical tests for a variety of hypotheses concerning the true change in beta.
4.2. Data
The data consist of a sample of 158 firms issuing convertible bonds over the period
from 1976 to 1988 that were available on Registered Offering Statistics (ROS) data
files of the Securities and Exchange Commission (SEC).4 Of these, 149 firms had
security returns data in the Center for Research in Security Prices (CRSP) database
for a period beginning 150 trading days before the date of issuance and ending
151 trading days after issuance.5 Data were also collected for the value-weighted
4 ROS data files were maintained by the SEC from 1970 to December 1988. Subsequently, the
SEC ceased to maintain this data; therefore, the data are limited to 1988.
5 We also calculated beta using the announcement date as the anchor point to divide the time
period for estimating pre- and post-betas. Results were essentially the same. For reporting
purposes, we selected issuance date because economic changes in firms are likely to take place
after funds have been received from issuance, rather than at the time of announcement of
proposed issuance itself.
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641
market index for the same period.6 Using the date of issuance as t = 0, we estimated
a market model for pre-issuance (t = −150 to −16) and post-issuance (t = +16 to
+151) periods.7 For each firm, we estimated pre- and post-issuance market betas (B 1 i
and B 2 i , respectively) and their estimated standard errors (S 1 i and S 2 i , respectively).
In addition, data on the bond ratings of each issue was collected from Standard and
Poor’s Bond Guide. The data on the intended use of the funds were collected from
the Wall Street Journal announcements.
4.3. Hypothesis testing
H 1 : Changes in beta are non-zero.
The first hypothesis (in the null form) is that the change in beta is zero for each
firm; that is:
βi = 0 ∀i.
(4)
Tables 1 and 2 provide distribution and summary statistics of pre- and post-issuance
betas as well as changes in beta. Both pre- and post-issuance betas of the sample
firms are, on average, greater than 1, implying an above-average systematic risk.
On average, post-issuance beta of firms in the sample is less than the pre-issuance
beta. The mean (median) value of the change in beta is −0.088 (−0.102). Assuming
each observation of change in beta to be independent and identically distributed, and
assuming that the change in beta is distributed normally, we can use the Fama and
Macbeth (1973) statistic to test if the change in beta is equal to zero. The Fama and
Macbeth test statistic value is −2.41, which has significance at the 5 per cent level
for rejecting the hypothesis that the change in beta is equal to zero.
To compare the characteristics of our sample with those of other researchers,
we calculate abnormal returns for a 2 day window surrounding announcement date.
We use the methodology used by Mehta and Khan (1995) to measure abnormal
returns. For a 2 day window (day −1 to day 0, where announcement is made on
day 0) abnormal returns for our sample are −2.18 per cent, with a t-statistic of −2.56.
This compares with results of other papers mentioned in the previous section, which
have also documented abnormal negative returns of similar magnitude. A negative
change in beta has the potential to exacerbate negative abnormal returns found at
the time of issuance: estimated expected returns are higher than the true expected
returns. However, the magnitude of the change in beta is not large enough to explain
a significant portion of the abnormal negative returns documented in prior research.
6 All the empirical analysis presented in the current paper was also conducted using the
equally weighted market index. Results were qualitatively similar to those presented in the
present paper.
7 Using
250 days instead of 150 days provided qualitatively similar results.
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Pre-beta
<0.200
0.201–0.400
0.401–0.600
0.601–0.800
0.801–1.000
1.001–1.200
1.201–1.400
1.401–1.600
1.601–1.800
1.801–2.000
2.001–2.200
>2.200
Total
Post-beta
<0.200
0.201–
0.400
2
2
2
4
2
1
3
1
9
0.401–
0.600
2
3
4
3
2
14
0.601–
0.800
2
1
8
4
2
2
2
1
22
0.801–
1.000
1
1
5
6
3
1
2
1
20
1.001–
1.200
1
6
4
8
1
2
22
1.201–
1.400
3
1
3
6
2
2
2
1
1
21
1.401–
1.600
1
0
1
0
1
6
2
0
1
12
1.601–
1.800
1
3
1
0
0
3
1
9
1.801–
2.000
1
0
0
0
0
1
2
0
1
5
2.001–
2.200
1
1
2
>2.200
Total
1
0
0
0
1
1
2
3
1
9
4
4
9
21
22
20
22
9
15
9
8
6
149
Pre-beta (B 1 i ) is the parameter estimate of firm i from the market model using stock return of the issuing firm and the value-weighted market return. Estimation
period begins 150 days before the date of issue of the convertible debt and ends 16 days before the issuance. Post-beta (B 2 i ) is the parameter estimate of firm i
from the market model using stock return of the issuing firm and the value-weighted market return. Estimation period begins 16 days after the date of issue of the
convertible debt and ends 151 days after issuance.
A. Rai / Accounting and Finance 45 (2005) 635–651
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Distribution of pre- and post-betas
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643
Table 2
Summary statistics of changes in beta of a firm after issuance of convertible debt
Pre-beta (B 1i )
Post-beta (B 2i )
Change in beta (B i )
t-statistics (t i )
n
n
Mean
Median
Minimum
First
quartile
Third
quartile
Maximum
149
149
149
149
1.196
1.108
−0.088
−0.285
1.120
1.025
−0.102
−0.356
−0.065
−0.099
−1.063
−3.148
0.793
0.666
−0.328
−1.156
1.619
1.399
0.110
0.349
2.660
2.915
1.853
3.516
n = sample size. Sample consists of 149 observations of convertible debt issuance from 1976 to 1988.
Pre-beta (B 1 i ) is the parameter estimate of firm i from the market model using stock return of the issuing
firm and the value-weighted market return. Estimation period begins 150 days before the date of issue of
the convertible debt and ends 16 days before the issuance date. Post-beta (B 2 i ) is the parameter estimate of
firm i from the market model using stock return of the issuing firm and the value-weighted market return.
Estimation period begins 16 days after the date of issue of the convertible debt and ends 151 days after the
2 + S 2 )1/2 .
issuance date. Change in beta (B i ) = B 2 i − B 1 i . t i = t-statistic for the ith firm = Bi /(S1i
2i
S 1 i = standard deviation of the estimate of pre-beta for firm i. S 2 i = standard deviation of the estimate of
post-beta for firm i.
We need not restrict ourselves to the assumption of identical distribution for each
observation; that is, the assumption that the variance of pre- and post-issuance beta is
the same for each observation is not necessary. We test whether change in beta for all
firms is from a stable distribution with mean equal to zero. Allowing heteroscedasticity in the sample requires that we calculate weighted mean of change in beta, where
weights are proportional to [1/(S12 + S22 )]1/2 . The weighted mean of the change in
beta is −0.0847 and the estimated standard error of the weighted mean is 0.0325.
The t-statistics for the test of hypothesis that the change in beta is zero is −2.602.
For 147 degrees of freedom, it is in excess of the critical value at the 1 per cent level.
A more comprehensive test can be constructed if one is willing to accept that
t(266) is approximately equal to N(0, 1). Under this approximation and the maintained
hypothesis, each of the t-statistics of change in beta in equation (4) has an independent
standard normal distribution. Squaring these statistics and summing up results in a
(approximate) test statistic:
χ 2 = ti2 ,
(5)
which has χ 2 (149) distribution. Table 3 reports the result of a χ 2 -test. The critical
value for one-tailed test at 1 per cent significance is 191, and the value of this statistic
is 253. Therefore, the data again reject the hypothesis of no change.
A much weaker test of the assumption of no change in beta might be obtained using
non-parametric methods. Specifically, if the changes in the estimated betas were only
because of random sampling errors, one would expect equal probability of positive
or negative changes; that is, the probability of a positive change would equal 0.5.
Again using the binomial distribution, we can establish a confidence interval for the
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Table 3
Test of Hypothesis 1: change in beta (B) is zero
Panel A: Binomial test of individual firm’s t-values
n
Confidence level (p)
|t i |∗
N∗
Na
σp
CL
149
149
149
10%
5%
1%
1.65
1.96
2.56
14.90
7.45
1.49
31.00
22.00
10.00
3.66
2.66
1.21
23.43
13.65
4.32
Panel B: χ 2 -test for the sample
Critical value of χ 2 with 149 degrees of freedom for 1% rejection level = χ 2 (149) 0.01 = 191
Observed value of χ 2 for the sample = 253
n = sample size. Sample consists of 149 observations of convertible debt issuance from 1976 to 1988.
|t i | = absolute value of t i . N ∗ = expected number of observations if null hypothesis of no change in beta
is true = n × confidence level (p). N a = actual number of firms whose t-statistic t i exceeds the critical
t-statistic value. σ p = standard deviation of N ∗ , using binomial distribution = v(np(1 − p)). CL = upper
bound on the number of rejections for a one-sided tail at 1 per cent level = N ∗ + 2.33 × σ p .
number of positive (or negative) changes in beta. At a 1 per cent level of confidence,
if the changes in beta are because of random sampling errors, the number of positive
changes should be within the interval:
(58.78 < n < 90.22).
In our sample, the number of firms with a positive change in beta is 55, which
lies outside of this interval. Therefore, the data reject the hypothesis that the observed changes in beta are the result of random sampling errors without making any
assumptions about the distribution of the individual ∼β i s.
H 2 : Changes in beta are determined by bond ratings of issued bonds.
As a preliminary test of the effects of bond ratings on the changes in beta, we
construct a cross-tabulation of bond ratings (investment grade or speculative grade)
versus the ‘standardized’ change in beta (<−1.0, between −1.0 and 0, between 0 and
1.0, and >1.0). We use Standard and Poor’s (S&P) ratings assigned to convertible
bonds in our sample at the time of issuance. In the bond market, a rating of BBB−
or better by S&P is considered ‘investment grade’, and any rating lower than this
is considered ‘below investment grade’. Ratings were obtained from Standard and
Poor’s Bond Guide. If data were not available from Standard and Poor’s Bond
Guide, then Moody’s Bond Guide was used to find the equivalent Moody rating of
an observation. Data were not available for 21 observations. Results are described
in Table 4. A χ 2 -test of differences in the distribution of changes in beta across the
different classes of bonds has a value of 1.13 with 3 degrees of freedom, well below
the critical value of 7.81 for a 5 per cent test. Therefore, we cannot reject the null
hypothesis that standardized changes in beta are not determined by bond ratings.
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645
Table 4
Test of Hypothesis 2: change in beta (B) is related to the convertible bond rating
S&P ratingsa of convertible bonds at
the time of issuance
Below investment
Investment
Z < −1
Frequency
12
23
Overall percentage
9.38%
17.97%
Row percentage
34.29%
65.71%
Column percentage
25.53%
28.40%
−1 ≤ Z < 0
Frequency
20
27
Overall percentage
15.63%
21.09%
Row percentage
42.55%
57.45%
Column percentage
42.55%
33.33%
0≤Z <1
Frequency
9
18
Overall percentage
7.03%
14.06%
Row percentage
33.33%
66.67%
Column percentage
19.15%
22.22%
Z ≥1
Frequency
6
13
Overall percentage
4.69%
10.16%
Row percentage
31.58%
68.42%
Column percentage
12.77%
16.05%
Total frequency
47
81
Total
36.72%
63.28%
χ 2 (change in beta is independent of the S&P rating of issued convertible bond) = 1.127c
Totalb
35
27.34%
47
36.72%
27
21.09%
19
14.84%
128
100.00%
a Standards
and Poor’s (S&P’s) rating of the convertible bond at the time of issuance. Investment grade is
a rating of BB− or higher; below investment grade is a rating of BB+ or worse.
b Total sample size is 149 convertible debts issued between1976 and 1988. Of these, S&P ratings were
available for 128 issuances only.
c Insignificant at conventional levels (degrees of freedom = 3).
H 3 : Changes in beta are determined by intended use of funds from issued bonds.
A preliminary test of the effects of reported fund usage on the standardized changes
in beta yields also shows no relation to the change in beta. Defining usage as retiring debt or all other (primarily working capital and/or expansion), we obtain the
cross-tabulation presented in Table 5. The χ 2 statistic for the independence of fund
usage and standardized change in beta is 3.18 with 3 degrees of freedom and is
clearly below the critical value of 7.81 for a 5 per cent test. Therefore, we cannot
reject the null hypothesis that standardized changes in beta are not determined by the
intended use of funds. This evidence suggests that changes in financial leverage might
not be an important determinant of the size or significance of the changes in beta.
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Table 5
Test of Hypothesis 3: change in beta (B) is related to the use of proceeds
Intended use of proceeds from issuance
of convertible bondsa
Debt retirement
General purpose
Totalb
Z < −1
Frequency
26
11
37
Overall %
20.16%
8.53%
28.68
Row %
70.27
29.73
Column %
29.55
26.83
−1 ≤ Z < 0
Frequency
26
18
44
Overall %
20.16
13.95
34.11
Row %
59.09
40.91
Column %
29.55
43.90
0≤Z <1
Frequency
22
6
28
Overall %
17.05
4.65
21.71
Row %
78.57
21.43
Column %
25.00
14.63
Z≥1
Frequency
14
6
20
Overall %
10.85
4.65
15.50
Row %
70.00
30.00
Column %
15.91
14.63
Total frequency
88
41
129
Total
68.22
31.78
100.00
χ 2 (change in beta is independent of the intended use of proceeds from issuance) = 1.127c
a Intended
use of funds from issuance of convertible bonds, as described in Wall Street Journal on the date
of announcement. Classified into two groups: debt retirement and general purpose.
b Total sample size is 149 convertible debts issued between 1976 and 1988. Of these, S&P ratings were
available for 128 issuances only.
c Insignificant at conventional levels (degrees of freedom = 3).
4.4. Cross-sectional determinants of change in beta
As a final test to determine factors that cause change in beta, we conduct a crosssectional regression of the change in beta upon certain financial variables that are
likely to affect beta of a firm. These variables are change in debt (as measured by
the debt-to-equity) and change in potential dilution of equity upon conversion of
convertible bonds (as measured by percentage change in outstanding common shares
if convertible bonds are converted). To test the mean-reversion hypothesis, we also
include pre-issuance beta as an explanatory variable. We use two control variables:
(i) intended use of funds; and (ii) rating of convertible bonds at the time of issuance.
C The Author
C AFAANZ
Journal compilation A. Rai / Accounting and Finance 45 (2005) 635–651
647
Equation (1) provides theoretical reasoning for including change in debt and potential
dilution as explanatory variables, as both variables directly impact leverage of a firm,
which in turn impacts the beta of a firm. Specifically, we predict that, ceteris paribus,
change in beta will be positively related to debt and negatively related to potential
dilution of equity upon issuance of convertible bond. Additionally, if the meanreversion hypothesis is true, then the predicted sign of pre-issuance beta should be
negative. Using available data, we estimate parameters for the following equation
using a cross-sectional OLS regression:
βk Xk + ε,
(6)
β = α + β1 DILUTE + β2 DE + β3 PREBETA +
k
where β is change in beta of a firm, post-issuance beta – pre-issuance beta, DE is
debt-to-equity ratio of a firm, DILUTE is percentage change in common shares
reserved for conversion, PREBETA is beta of the firm, before issuance of convertible
debt and X k is kth control variable.
Data for financial variables were from the COMPUSTAT database. Of the 149
observations in the sample for which change in beta was calculated using the CRSP
database, only 108 observations could be matched with the COMPUSTAT database.
To investigate whether the loss of observations has introduced a systematic bias in
our analysis, we calculated the mean and median of the change in beta (the dependent
variable in the regression) for the reduced sample of 108 firms with COMPUSTAT
data. The mean and the median of the reduced sample were almost the same as those
of the full sample. Results are not reported, for the sake of brevity. Therefore, we
believe that the loss of approximately 26 per cent of observations, when matching with
COMPUSTAT data, has not introduced any systematic bias in the reduced sample
as far as the change in beta is concerned. Nonetheless, our regression results must
be interpreted with caution, as our regression sample is likely to contain relatively
large firms.
The requirement of data for USE and RATING further reduces the sample. To
avoid influence of outliers, we eliminate the1 per cent highest and the lowest values
for the explanatory variables DE and DILUTE. We use dummy variables for intended
use (USE = 1 if the firm retires existing debt from funds; 0 otherwise) and S&P
rating (RATING = 1 if the bond is an investment grade; that is, has an S&P rating of
BBB− or higher; 0 otherwise). We also add interactive terms with these variables as
additional control variables as follows:
USE∗ DE = USE × DE,
USE∗ DILUTE = USE × DILUTE,
RATING∗ DE = RATING × DE,
RATING∗ DILUTE = RATING × DILUTE.
C The Author
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Journal compilation 648
A. Rai / Accounting and Finance 45 (2005) 635–651
If the data for USE or RATING were not available or if RATING was classified as
‘not rated’, then the observation was dropped from further analysis. For comparative
purposes, each model uses the same number of observations for which data for all
variables are available. The regression sample, with complete data for all variables,
consists of 98 observations.
Results from the estimation of equation (6) using an OLS regression are reported
in Table 6. We report the main model with additional control variables as well. We
also created interaction terms of PREBETA with USE and PREBETA with RATING.
Results with these variables did not provide additional insight and, therefore, were
not reported, for the sake of brevity. In general, the model shows explanatory power
for all versions. The F-value of the regression is significant at the 1 per cent level for
most models reported in the table.
We report t-statistics for DILUTE, DE and PREBETA variables using the onetailed test, because we make theoretical predictions about respective signs of these
variables: − for DILUTE, + for DE and − for PREBETA. Parameter estimates of
these variables are in the predicted directions for all regressions and are statistically
significant at conventional levels. DILUTE and PREBETA variables are significant
at the 5 per cent level or better for all models. This indicates that: (i) dilution potential
of a convertible bond plays a significant role in the change in beta of a firm; and
(ii) there is significant mean-reversion effect. The parameter estimate of DE is also
significant at the 5 per cent level or better for most models. Neither USE nor RATING
emerges as a significant variable in explaining changes in beta. The regression results
for these variables reconfirm conclusions drawn from χ 2 -tests in Tables 4 and 5
presented earlier.
5. Conclusion
The present paper presents evidence that shows that around the time of the issuance of convertible bonds: (i) the systematic risk (beta) of a firm changes; (ii) that,
on average, these changes are negative; but that (iii) there is significant heterogeneity
across firms and nearly 40 per cent have increases in beta. We also noted a significant reversion to the mean. A regression of change in beta on potential explanatory
variables indicates that, after controlling for mean-reversion, dilution from convertible bond and increase in debt-to-equity ratio are significant variables in explaining
cross-sectional differences in changes in beta, but bond ratings and the intended use
of fund do not.
Given that short window event studies have reported negative abnormal returns
at the time of issuance, the decline in beta documented in the present paper indicates that these results are somewhat overstated; but the magnitude of decline is not
sufficient to explain negative abnormal returns observed at the time of issuance. Implications of our results are more critical for long-duration windows that have studied
post-issuance performance. For these studies, negative abnormal returns would be
overstated by 10 per cent of the market return.
C The Author
C AFAANZ
Journal compilation β = α + β1 DILUTE + β2 DE + β3 PREBETA +
βk Xk + ε
k
Model
1
t-statistics
2
t-statistics
3
t-statistics
4
t-statistics
5
t-statistics
n
98
98
98
98
98
Intercept
−0.045
(−0.600)
0.141
(1.220)
0.160
(0.940)
0.122
(0.930)
0.224
(1.530)
DILUTE
(−)
DE
(+)
PREBETA
(−)
−0.751
(−2.57)a
−0.656
(−2.27)b
−0.711
(−2.33)b
−0.961
(−2.86)a
−0.792
(−2.53)a
0.828
(1.86)b
0.942
(2.15)b
0.956
(1.81)b
1.353
(2.71)a
0.887
(1.84)b
—
—
−0.183
(−2.10)b
−0.196
(−2.14)b
−0.188
(−2.17)b
−0.203
(−2.28)b
Control variables
F-value
USE
RATING
USE∗ DE
USE∗
DILUTE
RATING∗
DE
RATING∗
DILUTE
—
—
—
—
0.050
(0.460)
0.112
(0.480)
—
—
—
—
—
—
−0.061
(−0.523)
—
—
−0.167
(−0.960)
—
—
—
—
—
—
−0.702
(−1.100)
—
—
—
—
—
—
—
—
1.225
(1.800)c
—
—
—
—
—
—
—
—
—
—
−1.716
(−0.870)
—
—
—
—
—
—
—
—
−1.868
(1.250)
4.13d
4.28d
2.681e
2.85e
2.47e
n = sample size used in the regression.
DILUTE = percentage change in common shares if convertible bonds are converted into common shares = 100 × COMPUSTAT [item # 40]/[item # 25]. Top and bottom
1 per cent observations of DILUTE are deleted.
DE = change in long-term debt divided by equity = COMPUSTAT [item # 9]/[item # 25]. Top and bottom 1 per cent observations of DE are deleted.
USE = 1, if funds from convertible bonds issue were used to repay existing debt; 0 otherwise.
RATING = 1, if Standard and Poor’s rating (or equivalent Moody’s rating) is BBB− or better; 0 otherwise.
USE∗ DE = USE × DE; USE∗ DILUTE = USE × DILUTE; RATING∗ DE = RATING × DE; RATING∗ DILUTE = RATING × DILUTE.
a
One tailed significance at 1 per cent level.
b
One tailed significance at 5 per cent level.
c
Two tailed significance at 10 per cent level.
d
F-test significant at 1 per cent level.
e
F-test significant at 5 per cent level.
A. Rai / Accounting and Finance 45 (2005) 635–651
C The Author
C AFAANZ
Journal compilation Table 6
Ordinary least squares estimates of equation (6):
649
650
A. Rai / Accounting and Finance 45 (2005) 635–651
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