seungmook choi university of nevada, las vegas kookmin … the... · 2017. 1. 31. · jlt approach...
TRANSCRIPT
The Issuance of Callable, Defaultable Bonds under Information Asymmetry
by
Seungmook Choi
and
Mel Jameson
Department of Finance
University of Nevada, Las Vegas
and
Mookwon Jung
Department of Finance
Kookmin University
March 25, 2009
* This paper is prepared for the submission to a 2009 Joint symposium with KCMI in
Seoul Korea. Please correspond to Seungmook Choi at [email protected]
i
Abstract
In this paper we reconsider the evidence regarding the signaling theory of callable
bond issuance and the interpretation of that evidence. The data indicate that call spreads
are greater for speculative grade bonds than for investment grade bonds. For the
speculative grades, post-issue performance, as measured by rating changes and
cumulative stock returns, is better for callable than non-callable bonds. Among
investment grade bonds, such differences do not appear. All this might suggest that
callable bonds could serve a signaling function, at least for speculative grade bonds.
However, there is no evidence of a positive market reaction upon issuance of callable
debt.
To suggest a resolution of this apparent paradox, we simulate callable and non-
callable bonds yields for firms which do, or do not, have better than usual prospects, to
characterize the cost and benefits to issuing callable debt. The simulation results
illustrate that, although managers of firms with good prospects do have reason to prefer
to issue callable debt, there is enough noise in the system that this behavior does not
serve as a reliable signal to the market. It is asymmetric information, more than any
signaling effect, that characterizes this market.
1
1. Introduction
Despite the considerable literature analyzing callable bonds and why they are
issued, there is surprisingly little consensus regarding the empirical evidence on why call
features are employed.
Broadly speaking, theories of call usage fall into two categories: an interest rate
risk hedging tool and a tool to resolve conflicts between issuers and investors. The
interest rate hedging story is attributed to Pye (1966). Under this story use of call
features depends mainly on the properties of the stochastic process driving interest rates,
the availability of alternative instruments to hedge interest rate risk and factors affecting
an issuer’s desire to hedge.
A variety of theories in the second category have been proposed. Their common
feature is a relation between the presence of a call feature and the stochastic process
driving default behavior. Depending on the theory this relation results because presence
of the call option influences the post-issue decisions of management, or because
management’s initial decision to include the call feature results from information about
that process that is not ex ante available to the market.
These stories include: “resolving debt overhang” or “underinvestment” (Boddie
and Taggart 1978; Myers 1977) whereby straight debt would lead managers to neglect
positive NPV projects because part of their benefit would accrue to bondholders; “risk-
shifting” or “asset substitution” (Barnea et.al. 1980; Jensen and Meckling 1976) whereby
straight debt would incentivize stockholders to seek risk-increasing (even if expected
value-decreasing) changes in investment strategy; “removing restrictive covenants” (Vu
1986) whereby a call option limits the potential cost of removing a restrictive covenant
established to relieve some other agency cost of debt; “hedging investment uncertainty”
(Chen, Mao and Wang 2007) whereby the call allows an option to extend financing (or
not) at low transaction costs depending on investment prospects; and “signaling”
(Robbins and Schatzberg 1986, 1988) whereby the call option limits gains accruing to
bondholders when favorable information about the borrower is revealed to the market.
This latter implies managers will favor a call option when their information suggests the
2
firm’s prospects are better than indicated by publicly available information, potentially
signaling the existence of this information.
The empirical evidence is mixed, with each of the above theories having its
proponents. Each theory postulates a problem addressed by including the call feature.
An operational test selects variables arguably correlated with the presence of that
problem, and tests for their coincidence with use of the call feature. Larger issue size and
longer maturity or duration seem to be associated with call usage (Kish and Livingston
1992; Crabbe and Helweg 1994; Guntay et. al. 2004) as are high interest rates. This is
interpreted by these authors as consistent with the interest rate hedging theory. Chen et al
(2007) report similar results but support the hedging investment uncertainty story.
Smaller firms and first-time issuers are more likely to use calls: Guntay et.al.(2004) take
this to support interest rate hedging, while Chen et al (2007) to support hedging
investment uncertainty. Certain stylized facts seem clear: prior to the 1980s the
overwhelming majority of bonds were callable, since then call usage is lower. Since that
time call usage is more common in speculative grade bonds (Crabbe and Helweg 1994).
Alternatively, evidence of the problem may emerge through events observable
after bond issue. Crabbe and Helweg (1994) find callable bonds are downgraded more
often than straight bonds, which they interpret to contradict agency theory. Vu (1986)
and King and Mauer (2000) find many bonds are called far later than the apparent
optimum and argue the delay is due to transaction cost of exercise.
In this paper, we improve on extant tests in two ways. First, we treat investment
grade and speculative grade bonds separately using a matching sample technique. None
of the theories suggested in the literature are mutually exclusive, nor is there any
compelling a priori reason to believe only one motive would dominate in every case. On
the contrary, most of the stories suggest different impacts across the two classes of bonds
raising the possibility that different considerations govern the two market segments.
Even more significantly, the empirical literature indicates very different patterns in call
usage between the two. Our results confirm that behavior for the two segments of the
bond market is best understood separately.
Our second innovation is to apply a methodology that permits a more explicit link
between the callable bond issuer’s behavior and the market response under information
3
asymmetry. Jarrow, Lando, and Turnbull (JLT, 1997) develop a method for pricing
defaultable bonds in which there is explicit representation of both the interest rate process
and the default process. Specifically, the latter is represented by means of a transition
matrix describing the probability a bond will pass from one rating category to another
including, ultimately, default. In this paper we adapt the JLT method to include a call
option. This allows us to consider the impact of differences in the transition matrix on
the bond. Thus, it enables us to reflect either viewpoint in the transition matrix, and so to
derive the differing views of market and management regarding bond price as well as the
default premium and the call premium.
In the balance of the paper we use this approach to reconsider the evidence
regarding the signaling story of callable bond issuance. We look first at the available
direct empirical evidence, being careful to distinguish between investment grade and
speculative grade bonds. In order to help us understand these results, we then apply the
JLT approach to simulate the behavior of callable bonds given various assumptions about
the underlying default process. These simulations also yield values for the default
premium and call premium of the callable bonds. Thus we are able to identify the benefits
and costs explicitly associated with callable bond issuance. Consideration of how these
respond to information about the default process is, often vaguely defined in the literature,
central to determining the viability of the call feature as a signaling mechanism.
In our empirical study, we find that speculative grade callable bonds are more
likely to be upgraded subsequent to issuance than are speculative grade non-callable
bonds by using a matching sample technique. The long-term, post issue stock
performance of firms issuing speculative grade, callable bonds is also better than that of
firms issuing speculative grade non-callable bonds. However, there is no announcement
effect upon the issue of speculative grade callable bonds. This result seemingly
contradicts the empirical finding that the probability of an upgrade is higher after
issuance, suggesting existence of a market inefficiency. We show that this phenomenon
can be explained without violation of market efficiency through the numerical analysis.
In the following section, we describe the data and the empirical results. Section 3
briefly explains the JLT model and the basic set-up adopted for the numerical analysis to
4
be presented in Section 4, where we discuss how the observed empirical findings can be
explained. Section 5 concludes.
2. Data and empirical evidence
What observable consequences result when a callable bond serves a signaling
function? For signaling to occur, managers must first be asymmetrically better informed
than the market about the firm’s prospects. Those managers with favorable information
would conclude a call option is worth more than its market price and include it in their
debt issue. If market conditions were such that managers with unfavorable information
did not find it advantageous to “mimic” firms with good prospects by also issuing
callable debt, then using a call option would “signal” favorable information to the market.
If issuing a callable bond signals favorable information, the issue should be accompanied
by a favorable market reaction.1 Furthermore, after issuance, these theories imply
callable bonds should perform better than straight bonds.2
We first present empirical evidence on the magnitude of call premiums. While
this does not directly address the signaling hypothesis, it will be of value for purposes of
comparison with the simulation results to follow. We then consider post-issue
performance, as measured by rating changes and cumulative stock performance, and
finally the market response to bond issuance.
a) Data
We use primary market data on callable and non-callable bonds that come from
the New Issue Database of Security Data Corporation (SDC), covering 1981 through
2004. We exclude foreign companies, convertible bonds, Asset Backed Securities,
Gvernment/agency issues and non-fixed coupons, as well as all issues missing
information on the offering date, offering price, maturity, YTM, or initial bond rating.
Those observations for which CRSP data are unavailable were also eliminated, so that ex- 1 Firms that are particularly prone to information asymmetry should tend to favor callable bonds. Guntay et. al. (2004) and Chen, Mao and Wang (2007) report that smaller firms and first-time issuers are more likely to use callable debt. However these authors interpret this as support of interest rate hedging and hedging investment uncertainty, rather than of asymmetric information or signaling. 2 Nayar & Stock (2008) consider a sample of shelf-registered bond issues. They find that the market shows a significant negative reaction to the issue of straight bonds, but no significant reaction to callable bond issues. The difference between the callable and non-callable reaction is significant.
5
post long-term stock performance for the sample can be estimated. The resulting data are
summarized in Table 1.
(Insert Table 1 around here)
This yields a sample of 2,206 callable bonds and 6,071 straight bonds. We note that
during the early part of the sample period (1981-5) callable bonds predominated. This
was a period of high interest rates. Thereafter straight bonds have consistently been in
the majority. However, speculative grade bonds (BB+ and below) always show a
majority of callable bonds. Kish and Livingston (1992), Crabbe and Helweg (1994) and
Chen et.al. (2007) report similar results regarding speculative grade bonds. Bonds rated
CCC+ or lower are very rare in the sample.
To get an idea of the call premium, we construct a matched sample of callable and
straight bonds. The matching process is particularly critical in this application because
the transition matrix (describing the probability of movements between rating categories
or into default) can be expected to change over the business cycle. The criteria for
matching were: month of issue, industry, maturity (<4 yrs, 4 to 9 yrs, 9 to 14 yrs, 14 to 23
yrs, 23 to 36 yrs, >= 36 yrs), placement method and rating. Given a callable bond,
finding a match with regard to the first four criteria generally presented no difficulty.
Unfortunately, an exact rating match was not generally possible. In such cases we sought
an otherwise matched bond with a rating in the same bucket ( AAA to AA−, A+ to A−,
BBB+ to BBB−, BB+ to D ) This resulted in a total of 400 callable bonds and their
matched sample of 745 straight bonds as shown in Table 2. When a pair-wise
comparison between callable and non-callable bond is necessary, an average over the
values for all straight bonds matched with a given callable bond is used.
(Insert Table 2 around here)
The matches between callable and non-callable bonds are not perfect. However, on
average they are reasonably close. Since there can be more than one non-callable bond
matched to a callable bond, yields of non-callable bonds are averaged to get a
6
corresponding yield for the non-callable bond. From this table, we can take the
difference in yield at issue of each matched callable and non-callable pair as the measure
of the call premium. The results, segregated by investment/speculative grade appear in
Table 3.
(Insert Table 3 around here)
Note that the call premiums are larger for the speculative grade bonds. However, the
standard deviation of the premiums is also larger for this group.
b) Empirical tests
To compare the rating changes experienced after bond issue, we use the Mergent
FISD data base available through the Wharton Research Data Services (WRDS) to
identify rating changes for bonds in our sample during a five year period following issue.
The first rating change found during this period determined whether the observation was
classified as an upgrade or downgrade. It is highly unusual for the trend of rating
changes to reverse itself. If no further new rating was reported after issuance, the data
was considered a missing observation and was dropped from the sample. One possible
weakness of this approach is that defaults, which really should be counted as downgrades,
are not reported. However, our primary purpose is to compare rating changes of callable
and non-callable bonds within rating categories. If there is any bias in the distribution of
defaults across bond types, it is likely to follow the same pattern as that of downgrades.
Thus the most likely bias introduced by this problem would be against finding a
difference in the frequency of downgrades, particularly in speculative issues.
(Insert Table 4 about here)
Now let us consider the rating changes of the bonds after issuance. Define x=-1
for downgrade, x=0 for no change and x=1 for upgrade. And let F(x) and G(x) be the
cumulative probability distributions of rating change of a callable bond and a non-
callable bond respectively. A strictly better rating for callable bonds after issuance
7
relative to non-callable bonds implies F(x) < G(x) for all x. It is often stated in the
investment literature that F has first order stochastic dominance over G.
Table 4 reports the empirical rating change results for 5 years after issuance. We
observe there is little difference in the rating changes between callable and non-callable
bonds for investment grade issues. However, among the speculative grade issues the
probability of an upgrade is smaller, and that of a downgrade noticeably higher for a non-
callable, as opposed to a callable bond. This implies that the empirically observed F is
less than the empirically observed G in speculative category. We may argue that F has
first order stochastic dominance over G. However, they are empirical probability
distributions. There is a still chance that even under F(x) = G(x) for all x, empirically
observed F(x) can be less than empirically observed G(x) for all x Thus, it is necessary to
examine the statistical significance of this difference.
For the purpose of testing statistical significance, we use a bootstrapping
technique. Under the assumption that the empirically observed G(x) is the true G(x), the
same number of observations, x, as the non-callable bond observation are drawn from
G(x).3 Define N-1 , N0 and N1 are the number of chosen random numbers for x = -1, x = 0,
and x=1 respectively, where N = N-1 + N0 + N1 . Then we identify which cell in the
following 2-by-2 matrix this bootstrapping result belongs to.
1 0 (0)N N FN
− +≤ 1 0 ( 1)N N F
N− +
> −SUM
1 ( 1)N FN
− ≤ − C11 C12 C13
1 ( 1)N FN
− > − C21 C22 C23
SUM C31 C32 C33
We repeat this procedure 10,000 times so that C33 = 10,000. Note that Cell, for example,
C11 shows how many times the resulting experiments result in the smaller or equal to
3 We first generate a random number, y, from the standard normal distribution, Φ(y). Then we assign x=-1 for Φ(y) < G(-1), x = 0 for G(-1)< Φ(y) <G(0) and x = 1 for Φ(y) > G(1). Accordingly, the assigned x is equivalent to the random drawing from G(x).
8
empirically observed F(-1) and F(0). If C31/C33 and C13/C33 are less than a given
significance level, we may conclude that distribution F is significantly different from G.
Furthermore, the empirically observed F(-1) < G(-1) and F(0) < G(0), rejection of the
null that F = G implies that we can set the alternative hypothesis as F has first order
stochastic dominance over G. In addition, for this case, we may use C11 as the p-value
for the test of first-order stochastic dominance.
(Insert Table 5 around here)
Table 5 reports the bootstrapping results for the speculative grade case (Panel A),
Investment Grade case (Panel B) and total case (Panel C). For speculative grade case,
C11 shows only 0.24%. Thus we can reject the null that F=G and accept the alternative
that F has first order stochastic dominance over G at the 1% significance level. However,
the bootstrapping results for investment grade case and total grade case suggest that we
cannot reject the null that F=G.
These results are consistent with the story that managers possessing favorable
knowledge about their firm’s prospects that is not known to bond raters systematically
prefer callable bonds. This would be more prominent in a noisier market. Indeed,
speculative bond markets are very noisy as shown in Figure 1.
(Insert Figure 1 around here)
Fig. 1 shows yield curves for different grades on the last business day of
December 1998, available from the Fixed Income Securities Data (FISD), provided by
Mergent, Inc. The yields are a combination of trader quotes and matrix quotes. The
legend T stands for Treasury bonds, and other legends are S&P ratings. If there is a
signaling phenomenon, it is more likely to occur in the low rating bond markets, where
yields for bond of identical ratings vary widely for all maturities. More importantly, the
benefit of signaling (reduction of the market required yields on debts ) for speculative
rating firms would be substantially large relative to the investment grade firms.
9
We turn now to stock returns as evidence of post-issue performance. These
should be consistent with the bond ratings changes, since whatever information led to the
rating change, should also stimulate a market response. Table 6 reports the five-year
cumulative returns following bond issue.
(Insert Table 6 about here)
For issuers of investment grade bonds, there is little apparent difference in cumulative
returns or their standard deviation between callable and non-callable bonds. For the
speculative grade bonds returns appear to be better, although noisier (greater standard
deviation), for the callable than for the non-callable bonds, consistent with the rating-
change results. The bottom row of Table 6 shows results obtained looking at the
difference in return for the paired bonds. The results are similar. For investment grade
bonds the difference in return is small (actually negative) but statistically significant. For
the speculative grade bonds, the difference is larger, but not statistically significant. The
statistical insignificance may be due to the larger standard deviation. The large standard
deviation for callables relative to non-callables in the speculative group seems natural
even if both issuers face the same migration matrix because the option values change
after migrations are realized. At any rate, the pattern of post-issuance stock performance
is similar to that found for rating changes, and is consistent with the story that managers
with more favorable information than is available to the market tend to prefer callable
bonds.
If managers with favorable information prefer callable bonds, it is natural to
postulate that the announcement of a callable bond issue should convey favorable
information to the market. Table 7 reports the market response observed in a two-day
(0,+1) window at the time of the announcement of debt issuance.4 The table reports
results using both the market model of Brown-Warner (1985) and the market-adjusted
model.
(Insert Table 7 about here)
4 We use the offering date provided in SDC data as the announcement date.
10
The table reports results for the bonds used in the matching sample. In no case is
there a statistically significant announcement effect. This result is consistent with Nayer
and Stock (2005) who report an insignificant market response to the announcement of
callable debt issues, and of Eckbo (1986) and Lewis et al. (1999) who report an
insignificant response to straight debt issues.5
This is somewhat surprising since there would be a market reaction to callable
bond issuance announcements if callable bonds on average were expected to do better
than non-callable bonds. This would suggest an arbitrage trading strategy of buying a
diversified portfolio of speculative grade callable bond issuing firms’ stocks while
shorting a diversified portfolio of speculative grade non-callable bond issuing firms’
stocks. However, such an arbitrage may be difficult in practice due to transaction cost6
In the succeeding sections we provide theoretical justification for these empirical
results by numerically simulating the values of callable bonds.
3. The Simulation Model
These stories about the choice by asymmetrically informed managers to issue
callable or non-callable debt and why this choice seems to differ between investment
grade and speculative grade bonds depend on how the market values the call feature (and
the default prospects of the bond) given the available information set. In this section we
describe a model that permits us to calculate these values via numerical simulation given
a description of a stochastic process driving interest rates and of one driving bond
defaults. We then show that when the underlying stochastic processes are specified to
produce results that are qualitatively similar to those observed in the data, managers have
an incentive to use callable and non-callable bonds as observed.
Because the potential asymmetry of information mainly concerns the probability
of default, it is important to use a model in which this information enters explicitly. We 5As a check, we also test for the full (unmatched) sample. Again there is no significant announcement effect. 6 Kim, Klein and Rosenfeld (2008) consider the reverse stock split case where arbitrageurs are restricted in their ability to earn abnormal returns even if they correctly anticipated a price decline after reverse stock split, because of short sale restrictions on low-priced stocks.
11
use the bond valuation model developed by Jarrow, Lando and Turnbull (1997),
(hereafter JLT), in which a migration matrix describes the probability a bond will move
from one state (rating status) to another, with default being an absorbing state. The
model permits this default process to combine with almost any plausible interest rate
process. Adapting the boundary conditions of this model to allow for the exercise of a
call option permits the simulation to generate the desired outputs.
While the choice of a term structure and spot interest rate process may affect
predicted levels of bond prices, our primary interest is in call spreads. Thus the number
of factors in the interest rate process and the current term structure of spot rates are not
central to our objective. As we use discrete time model for our simulation, we briefly
explain the discrete time version of the JLT model. Let Vt be the K-dimensional column
vector of values for bonds in K rating classes, with the K-th element being the value for
the default status which is essentially recovery value. The i-th element, Vt(i), thus,
represents the value of a bond in state i (i-th highest rating) at time t. Then the values of
the bond at time t given information Ωt under the assumption that the migration matrix,
M, is homogeneous in time may be given by
( )~
1 1 |tr tt t t te E M−+ += ⋅ + Ω⎡ ⎤⎣ ⎦V V C (1)
where rt is the default-free spot rate over one period, ~
tE is the expectation operator under
risk-neutral world, and Ct is the vector of promised coupons. V0, can be calculated
recursively from maturity time T to time 0, given the terminal values, VT. The callable
bond values are also calculated by a given call decision rule. Since we are interested in
the comparison over different grade bonds, we may consider the callable bonds with the
same call prices, X, and the same call date, T1, for all bonds. Then equations (1) is
replaced by
( ) ~
1 1min , |tr tt t t tX e E M−+ += ⋅ + Ω⎡ ⎤⎣ ⎦V V C (2)
for all 1t T≥ .
Let G be a K-1 dimensional vector of recovery rates, g(i), for i=1,..K-1 differently
rated bonds. The recovery rates for each different grade bond may not necessarily be the
12
same.7 However, this is not important as will be discussed shortly. We assume that the
value of the bond in bankruptcy state, K, at time t depends on the state at time t-1. Thus,
the last element of Vt is assumed to be the recovery rate of the face value with no coupon
payment. However, the recovery rate may differ depending on the state at time t-1. Thus,
in the process of backward induction, the value of a bond, Vt-1(i) for i K≠ , is obtained by
setting the last element of Vt, Vt(K), equal to g(i).
In our simulations we choose a coupon “C” so that the bond in question is priced
at par according to equation (1) (straight bond) or (2) (callable bond). We report the
difference between the two coupon rates as the value of the call option in terms of
percentage point. We use a Ho-Lee interest rate process with a flat term structure at 10%
and a spot rate volatility of 2%. All bonds pay a semi-annual coupon and have a maturity
of seven years. Callable bonds offer three years of call protection, and may be redeemed
at 105% of par thereafter.
Note that the difference between a lower rate bond par yield and a higher rated
bond par yield is the difference in their default risk premiums. Note that because the
identical interest rate process drives all bonds in the simulation, any such difference
reflects differences in the default process, not in the spot rate volatility. Similarly, as
stated earlier, the specifics of the interest rate process and bond specification should not
materially affect our results because these are driven by differences in the default process.
Thus the heart of the model specification is the migration matrix describing the
probability of a rating change or of default. The most natural choice would seem to be to
use historical data describing default behavior over some appropriately chosen time span
for the migration matrix. However, many researchers, e.g., Hull et. al. (2005) and Tsuji
(2005), point out that this choice leads to a “credit spread puzzle” whereby the observed
risk premiums for lower grade bonds exceed values predicted using an historical or “real
world” migration matrix. This discrepancy is attributed to an additional liquidity
premium or non-diversifiable risk premium (associated with the default probability) that
is charged by the market for lower rated bonds. To incorporate this premium, a “risk
7 It is empirically observed that the lower the rating, the lower the recovery rate in the event of default. See Duffie and Singleton (1999) and Moody’s report.
13
neutral” migration matrix is used to generate the simulation data. The relation between
the two migration matrices is given by:
where:
Q = one-year real world migration matrix
Q = one-year risk-neutral world migration matrix
I = Identity matrix
Π = Diagonal matrix with the last diagonal element equal to 1
Under the assumption that the migration matrix is homogeneous in time, per-period
migration matrix in our simulation is obtained by first converting Q to its generator
matrix, ~
M = logm(Q) and then taking the matrix exponential, ~
1exp m ( )i iM M t t −⎛ ⎞= ⋅ −⎜ ⎟⎝ ⎠
for per-period risk-neutral world migration matrix. The matrix Π is interpreted as
reflecting the liquidity risk premium relative to the normalizing element set equal to 1.
To resolve the credit spread puzzle, these diagonal elements must increase as the
corresponding bond ratings become lower. Consistent with this, our simulations assume
the diagonal element of Π increases by .06 with each change of bond rating category.
The simulation also assumes a 50% recovery rate from all bonds entering default. This
assumption will not affect the results unless there is a higher recovery rate for lower rated
bonds.
It will turn out that understanding the relation between the call premium and bond
rating is important to understanding the use of call features. Thus, that relation is a
central object of our initial simulation. A priori, the nature of that relation is not clear. A
lower bond rating could mean more volatility in the future upward movements (upgrades)
of the bond. More volatility implies greater option value. Alternatively, a lower rating
increases probability of default, lowering option value. We have seen in Table 3 that the
data suggest that, in fact, call option value increases as bond rating decreases. An
important object of our initial simulation is to determine characteristics of the risk neutral
migration matrix such that this is the case.
~Q I Q I⎡ ⎤− = Π −⎢ ⎥⎣ ⎦
14
(Insert Table 8-a and 8-b about here.)
Table 8-a and Table 8-b show the associated one-year real world migration matrix
and its generator matrix respectively, based on (modified) data, from Moody’s Special
Report (2005).8 Using this real world migration matrix by setting Π = I generates the call
spreads (call option values of callable bonds ) illustrated in the upper figure of Figure 2.
In this figure, we omit the resulting yields for grade 17 that is, in fact, the sum of all
grades below 16 in the Table 1. This is done because our empirical data does not include
such low grades. Note that the call spreads decreases and then increases for lower rated
bonds. It is not immediately clear why this is so.
(Insert Figure 2 about here)
The difference between the Z-spread and OAS or “option adjusted spread” is often
understood as a call spread. The Z-spread is the additional yield of a callable, defaultable
bond over a comparable Treasury bond, and OAS is the additional yield of a callable,
defaultable bond over a hypothetical callable Treasury bond. We generate these spreads
for the par yields of a callable bond given by the model and that predicted for a callable
Treasury bonds having the same specification and calling decision, with the sole
exception of defaultability. We include it here for purposes of comparison. As shown in
all subsequent figures, the call spread thus obtained (Z-spread minus OAS) always
decreases as rating goes down. This implies that it always underestimates the true call
value. The OAS calculation ignores the default chance for a given par yield of a callable,
defaultable bond. Thus, the OAS value is inflated for the greater default chance, resulting
in lower call spread. For this reason, it is not relevant for comparisons with empirical call
spreads.
8 We modified the Moody’s one-year migration matrix as follows. We take the original one-year migration matrix and convert it to its generator matrix. Since the conditions to be a generator matrix must be met, where the sum of each row of the resulting generator matrix is equal to 0 and all off-diagonal elements must be non-negative, we modify the original one-year migration probabilities over each grade in a smoothing trend manner until the generator matrix satisfies the conditions.
15
To allow for the liquidity/non-diversifiable risk premium we also conduct the
simulation using the risk-neutral generator matrix. The resulting call spreads are shown in
the bottom figure of Figure 2. These are qualitatively similar to those generated by the
historical data, and the call spreads are smoothly increasing as rating goes down. Table 9
summarizes the results, comparing the call spread and also the default premiums for
investment grade and speculative grade bonds in the two cases. Using the real world
migration matrix produce a ten-fold difference in the default premium between the two
classes, but little difference in the call premium. By contrast, the risk neutral migration
matrix also produces larger call spreads for speculative grade bonds. This latter case
seems more in conformity with the data reported in Table 3. More generally, these
results show that the call spreads generated do depend on the assumptions about the
choice of Π. It should be noted in Table 9 that the spread between callable bond yield
and treasury yield results mainly from the default risk premium. Moody’s special report
documents that the default risk premium ranges historically from 300 to 800 basis points
for speculative bonds. This fact is important for our later simulation that examines the
signaling mechanism, because it tells us the magnitude of the effects of the default risk
premium and the call spread on migration. As a caveat we note that, because the
migration matrix used here includes all types of firms and all types of bonds issued at all
points in the business cycle, the results may not be completely comparable to those
reported in the data section.
4. Call option values and use of callable bonds
In this section we conduct simulations similar to those of the previous section.
Here the goal is to understand the empirical results by considering when a manager of a
speculative grade firm has an incentive to issue callable bonds, and when this issue
conveys information to the market. In these simulations we compare the behavior of a
“typical” or “normal” speculative grade firm, that is to say one whose true migration
matrix conforms to that expected by the market, with that of a “good” speculative grade
firm, whose true migration matrix reflects better prospects. However, these better
16
prospects are not apparent to the market. If this “good” information is realized, we
assume that this will be reflected in a manner of positive rating changes.
To examine the robustness of the results, we conduct two versions of the
simulation under very different assumptions about the default process driving the
“typical” firm. In both cases, the qualitative results are the same: managers of firms
whose prospects are better than typical prefer to issue callable bonds. However, this may
not convey information to the market, because of the noise resulting from the behavior of
the other firms.
We first consider the case in which the typical (normal) speculative grade firm
faces a migration matrix such that the value of a call option tends to decline as the bond
rating gets lower. Accordingly, the call value is relatively small for callable bonds issued
by such firms. A contrasting or “good” speculative grade firm has a more favorable
transition matrix, resulting in relatively large true option value. The situation of the
typical firm is in contrast to the situation indicated by the data and simulated in Section 3.
However, we consider this case because the strongly marked contrast between the two
kinds of firms would seem to offer the best chance for the market to discern the
difference between them. Subsequently we consider the arguably more realistic case in
which the “typical” speculative firm also faces a market-perceived migration matrix such
that its call value is increasing as bond rating declines. Here the “good” speculative firm
has an even better chance of an upgrade so that its call option value will be higher than
that of the typical firm.
The simulation approach is as described in Section 3. However the number of
bond rating categories has been consolidated to four, G1 (highest grade) through G4
(lowest grade) to streamline the procedure, while all other specifications remain the same.
Table 10-1 shows Case 1. The upper panel is the one-year migration matrix faced by the
“typical” firm that belongs to grade G4 initially, and the lower panel is the matrix faced
by a “good” firm that belongs to grade G4. These are the probabilities of the given
transition during the course of one year. The key observation is that the “good” firm has
a higher than typical probability of moving from a bad state to a better one.
(Table 10-1 about here)
17
The one year transition matrix is derived from a generator matrix that reflects transition
probability densities that are reported in Table 10-2. Here one sees clearly that transition
probabilities are the same for G1 through G3. They differ only for the G4 grade firms;
one with “typical” and one with “good” prospects.
(Table 10-2 about here)
Figure 3-1 reports the par yield and call spreads for the “typical” firm in this
scenario. We note that this is the case where the call premium does, indeed, decline as
the bond rating worsens.
(Insert figures 3-1 and 3-2 here)
Figure 3.2 provides the same information for the “good” firm. Here the call spread does
increase as bond rating declines.
Since we are examining two firms that belong to G4 under information
asymmetry, we summarize their corresponding yields associated with callable and
noncallable bonds in Figure 3-3. If the typical firm issues a non-callable bond, the market
yield on the bond is located at (). If the firm issues a callable bond, the market requires
the yield at (o), paying an extra yield, distance A, which could be viewed as the call
option cost. Note that the distance is very small as intended for Case 1. The manager of a
good firm knows the prospects better than the market, and if he successfully conveys the
information to the market, a non-callable bond can be issued at (*), which is much lower
than the typical firm’s yield (). If the issuance of the callable bond is necessary in order
to signal to the market, then the firm must pay the higher yield (x). Of course in this case
the true option cost(distance B) is now much larger than that of the typical firm (distance
A).
(Insert Figure 3-3 here)
18
Because only managers, not potential equity or bond investors, know which firms
are good, the market requires the typical yield () for non-callable debt. If issuing
callable debt works as a signal to distinguish a good firm, the market would require the
higher yield (x) for callable debt. In that case a manager of a “typical” firm would not
wish to issue callable debt, because the market would want to charge more than its fair
price. The manager of a good firm, however, would indeed wish to issue callable debt.
Even though the total cost of the debt is higher, the price of the call option is fair,
meaning that the firm will recoup it, on average, when the call is exercised. Thus C is
also the resulting benefit to the firm. This is just the value of having the market truly
assess default risk. If these were the only two kinds of firms in the system and there were
no other sources of noise to confuse the market, then a separating equilibrium would be
sustainable in which “good” firms issued callable debt and “typical” firms did not. In this
case, issuance of callable debt signals to the market that the issuer is a “good” firm
conferring a benefit of C to the firm. Therefore, the issuance announcement of a callable
bond will have a positive effect on the issuing firm’s stock price. However, this might
not be immediately apparent, since one could observe only that non-callable bonds offer
the typical yield () while callable debt yields (x). The difference between the two is not
the call spread for either type of firm, although it might erroneously be interpreted as
such.
It should be noted that the migration matrix that the market perceives is assumed
to be the one faced by the “typical” firm. If the market did not take callable debt to be a
signal of a good firm, managers of “good” firms would still prefer to issue callable debt
because now it is underpriced to them by the market. Managers of typical firms would be
indifferent between the two. Would “good” firm like to pay (x) which is more than
market requires to signal? The choice would depend on the size of immediate under-
valued benefit (distance D-A) with no signal and the size of immediate stock market
reaction benefit with signal at the additional cost, distance D-A. The empirically
observed absence of stock market reaction to callable bond issuance announcement
supports the former choice. Also, the data suggest that this is the less realistic of the two
cases we are considering. Allowing a multiplicity of firm types could also confound the
market’s ability to sort cleanly into a separating equilibrium. We take the key lesson of
19
this exercise to be that, even in this case in which they are most strongly differentiated
from typical firms, good firms prefer to issue callable bonds.
In Case 2, prospects of the “good” firm remain the same as in the previous case.
However, those of the “typical” firm are now somewhat more favorable, as can be seen in
the one-year migration and generator matrices reported in Tables 11-1 and 11-2.
(Insert Tables 11-1 and 11-2 about here.)
Now the call spread generated from the migration matrix faced by the “typical” firm
show the more usual pattern of increasing as bond rating declines.
(Insert Figure 4.1 about here)
As in the previous case, being identified as a “good” firm results in a reduced default risk
premium. However now, the difference in magnitude of the two call spreads is smaller.
As illustrated in Figure 4-2, this may lead to a situation in which the callable yield for a
“good” firm lies below that of a “typical” firm.
(Insert Figure 4-2 about here)
Unlike the previous case, the simple act of issuing callable debt does not immediately
result in the penalty of higher borrowing costs for the typical firm. However, even if
issuing callable debt does not work as a signal, meaning the market treats all debt issues
as “typical”, managers of “good” firms will prefer callable debt when the situation is as
illustrated. If the firm issues non-callable debt, the market overcharges by C, the
difference in the default premium. Issuing callable debt adds a cost equal to the call
spread for a “typical” firm, but ultimately confers a benefit equal to the call spread for a
“good” firm. Although the good firm can not prevent itself from being overcharged by
the market, it can reduce the amount of this overcharge from C to D. Since the market
always charges the price appropriate to typical firms, these are indifferent between
callable and non-callable debt. If, for some reason, the market did treat callable debt as a
20
signal of a “good” firm, the good firms would be all the more eager to issue callable debt.
Of course in the situation illustrated, the typical firms would also issue callable debt and
investors would lose money to them. In this case, “good” firms all prefer to issue callable
bonds, but the value of this act as a signal is lost, because nothing prevents “typical”
firms from issuing callable bonds as well.
Two key points emerge from these illustrations. The first is that “good” firms
generally have an incentive to issue callable bonds whether or not there is any signaling
effect. This is because their assessment of the benefit of the call feature derives from
their (asymmetrically favorable) knowledge of the firm’s prospects, which may not be
fully reflected in market pricing. The managers of “good” firms systematically prefer
callable debt is consistent with the empirical evidence that firms issuing callable debt
perform better post issue with respect to ratings upgrades and cumulative stock
performance. However, the illustrations also show that it is easy to devise circumstances
under which managers of typical firms are also happy to issue callable debt. This, in
combination with the general level of noise found in the data for speculative grade bonds,
suggests that it should not be all that surprising if the market is unwilling to draw a strong
conclusion from the fact of callable bond issuance. For these reasons, the absence of a
market response to the issuance of callable debt need not be considered surprising.
5. Conclusion
In looking at the data, we find that call spreads are greater for speculative grade
bonds than for investment grade bonds. In addition, for the speculative grades, callable
bonds are more likely to be upgraded and less likely to be downgraded following issue
than non-callable bonds, and they show better post-issue cumulative stock return
performance. Among investment grade bonds, evidence of such differences generally
does not appear. One might expect that these differences in post issue performance
would lead to a positive market reaction upon announcement of issue of callable debt.
However, this is not the case. We explain this puzzling effect by simulation. This
simulation approach plays an important role in identifying any benefits and costs
explicitly.
21
The results of the simulation examples point toward a resolution of this apparent
paradox. They illustrate that, although managers of “good” firms do have reason to
systematically prefer to issue callable debt, there is enough noise in the system that this
behavior does not serve as a reliable signal to the market. It is asymmetric information,
more than any signaling effect that seems to drive this behavior.
22
Table 1: Initial sample of bonds for callable and non-callable bonds Primary market data on callable and non-callable bonds come from the New Issue Database of Security Data Company (SDC). The data covers the period from 1981 to 2004. We exclude foreign companies, convertible bonds, ABS, Government/agency issues and non-fixed coupons, as well as all issues missing information on the offering date, offering price, maturity, YTM, or initial bond rating. The reported rating categories are from S&P and ratings in the parentheses are from Moody’s. AAA through BBB- are considered to be investment grades and BB+ and below speculative grades.
Ratings
(S&P)
Total
1981-
1985
1986-
1990
1991-
1995
1996-
2000
2001-
2004
Callable 428 124 114 58 86 46 AAA to AA-
(Aaa to Aa3) Non-
callable 1,144 51 188 269 422 214
Callable 692 172 181 67 130 142 A+ to A-
(A1-A3) Non-
callable 2,951 62 283 999 1,252 355
Callable 299 40 73 54 49 83 BBB+ to BBB-
(Baa1-Baa3) Non-
callable 1,612 19 93 514 775 211
Callable 787 17 41 133 315 281 BB+ and below-
(Ba1 and blow) Non-
callable 364 6 15 109 169 65
Callable 2,206 353 409 312 580 552 Total
Non-
callable 6,071 138 579 1,891 2,618 845
1 2 3 4 5 6 7 8 9 10Investment Grades AAA
(Aaa) AA+
(Aa1) AA
(Aa2)AA-
(Aa3)A+
(A1)A
(A2)A-
(A3)BBB+ (Baa1)
BBB (Baa2)
BBB-(Baa3)
11 12 13 14 15 16 17 18 19 20BB+
(Ba1) BB
(Ba2) BB-
(Ba3)B+
(B1)B
(B2)B-
(B3)CCC+(Caa1)
CCC (Caa2)
CCC- (Caa3)
CC(Ca)
21 22 23 24
Speculative Grades
C (C)
DDD (D) DD D
23
Table 2: Matched sample
Descriptive statistics for 400 callable bonds are grouped according to their initial bond ratings. Maturity is the time to maturity of the callable bond. Industry groups are the industries to which the issuer belongs. Private bonds are the bonds offered privately to selected individuals and institutions. Public bonds are the bonds offered to the public. The data for 745 non-callable bonds matched for each rating category are in parenthesis.
Maturity Industry group Private/Public Rating category
No obs (Yr) Industrial Finance Utility Private Public
75 13.4 37 36 2 0 75AAA to AA-(131) (9.81) (68) (60) (3) 0 (131)
201 14.7 132 59 10 0 201A+ to A-(432) (13.70) (287) (124) (21) 0 (432)
53 17.7 42 7 4 3 50BBB+ to BBB-(96) (18.30) (84) (8) (4) (4) (92)
BB+ to B- 71 8.9 67 1 3 49 22 (86) (9.00) (82) (1) (3) (61) (25)
400 13.8 278 103 19 52 347Total(745) (13.10) (521) (193) (31) (65) (680)
* No data below B- Table 3: Yield differences between callable and non-callable bonds This table is obtained from the matched sample: 400 obs of callables and 745 obs of noncallables. In the case that there is more than one non-callable bond matched for a callable bond, yields of non-callable bonds are averaged to get the yield difference.
Ratings Nobs Min Median (%)
Mean (%)
SD (%) Max (%)
Investment 329 -2.540 0.145 0.179 0.644 3.973
Speculative 71 -1.875 0.626 0.991 1.423 5.944
Total 400 -2.540 0.194 0.323 0.891 5.944
24
Table 4: Rating changes of the matched sample after issuance The number of observations is further reduced due to the lack of rating change information. If we drop the observations from the sample when any one of the matched pair is not known for rating changes after issuance, we get 224 pairs for investment grades and 46 pairs for speculative grades. However, no qualitative difference is found.
Migration in 5 years (%) Samples Type Initial Grade Up Grade No Change Down Grade Nobs
Investment Grade 22.34 37.11 40.55 291 Speculative Grade 28.00 36.00 36.00 50
Non Callable Total 23.17 36.95 39.88
341
Investment Grade 18.65 35.32 46.03
252 Speculative Grade 33.85 45.15 20.00 65
Matched Callable Total 21.77 37.54 40.69
317
25
26
Table 5: Bootstrapping results Panel A: Speculative Grades
CumP(No
Change)<65.15% CumP(No
Change)>65.15% SUM CumP(Down)<20.00% 24 0.24% 14 0.14% 38 0.38%CumP(Down)>20.00% 1,324 13.24% 8,638 86.38% 9,962 99.62%SUM 1,344 13.44% 8,652 86,52% 10,000 100.00% Panel B: Investment grade
CumP(No
Change)<81.35% CumP(No
Change)>81.35% SUM CumP(Down)<46.03% 9,005 90,05% 570 5.70% 9,575 95.75%CumP(Down)>46.03% 305 3.05% 120 1.20% 425 4.25%SUM 9,310 93.10% 690 6.90% 10,000 100.00% Panel C: Total
CumP(No Change)<78.23%
CumP(No Change)>78.23%
SUM
CumP(Down)<40.69% 4,858 48.58% 1,134 11.34% 5,992 59.92%CumP(Down)>40.69% 2,164 21.64% 1,844 18.44% 4,008 40.08%SUM 7,022 70.22% 2,978 29.78% 10,000 100.00%
27
Table 6 : Five-year cumulative stock returns ( ) is the difference between medians of callable and non-callable groups. The standard deviation for the row of “pairwise difference in returns” is the standard deviation of the mean.
Investment Grade (224) Speculative Grade (46) Total (270) Median Mean STD Median Mean STD Median Mean STD
Callables 0.685 0.664 0.492 0.707 0.557 1.242 0.689 0.646 0.678Non-callables 0.745 0.747 0.475 0.395 0.238 1.075 0.664 0.661 0.646
-0.033 0.391 0.003Pairwise Difference (-0.060)
-0.083 0.046(0.312)
0.319 0.242(0.025)
-0.015 0.057
28
Table 7: Bond Issuance Announcement effect on abnormal stock returns The table reports results using both the market model (carmm) of Brown-Warner (1985) and the market-adjusted model (carmar). For callable bond firms, 400 observations are used, and for non-callable bond firms, 745 observations are used.
Total(%) Investment Grade(%) Speculative Grade(%)
Median Mean t-value Median Mean t-value Median Mean t-value carmm -0.044 -0.088 -0.57 -0.046 -0.093 -0.65 -0.009 -0.062 -0.11
Callables carmar -0.186 -0.108 -0.7 -0.18 -0.149 -1.02 -0.349 0.082 0.15
carmm -0.259 0.011 0.11 -0.26 -0.046 -0.51 0.12 0.446 0.83 Non- callables carmar -0.252 0.028 0.27 -0.256 -0.028 -0.31 0.022 0.458 0.87
29
Table 8-a : Modified Moody’s one-year transition matrix The Moody’s one-year transition matrix based on 1983-2004 rating changes is modified so that the generator matrix obtained by taking matrix-logarithm on one-year transition matrix satisfies the condition for generator matrix. Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 D Aaa 0.8961 0.0615 0.0290 0.0043 0.0060 0.0022 0.0008 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa1 0.0206 0.8082 0.0852 0.0663 0.0152 0.0027 0.0005 0.0010 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa2 0.0067 0.0332 0.8160 0.0917 0.0326 0.0129 0.0050 0.0010 0.0006 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa3 0.0010 0.0062 0.0385 0.8184 0.0930 0.0312 0.0070 0.0023 0.0010 0.0008 0.0002 0.0001 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000A1 0.0005 0.0010 0.0048 0.0581 0.8073 0.0821 0.0301 0.0073 0.0021 0.0007 0.0026 0.0016 0.0003 0.0007 0.0005 0.0001 0.0001 0.0001A2 0.0004 0.0004 0.0035 0.0079 0.0546 0.8019 0.0789 0.0306 0.0091 0.0049 0.0029 0.0007 0.0015 0.0008 0.0007 0.0002 0.0006 0.0003A3 0.0005 0.0013 0.0008 0.0019 0.0191 0.0712 0.7738 0.0719 0.0352 0.0131 0.0047 0.0014 0.0016 0.0018 0.0003 0.0005 0.0007 0.0003Baa1 0.0004 0.0004 0.0014 0.0018 0.0024 0.0220 0.0692 0.7590 0.0813 0.0326 0.0099 0.0046 0.0022 0.0068 0.0009 0.0009 0.0026 0.0018Baa2 0.0006 0.0011 0.0004 0.0017 0.0023 0.0065 0.0363 0.0602 0.7708 0.0742 0.0180 0.0057 0.0071 0.0055 0.0034 0.0013 0.0038 0.0013Baa3 0.0005 0.0001 0.0003 0.0008 0.0019 0.0042 0.0071 0.0323 0.0862 0.7300 0.0646 0.0281 0.0182 0.0068 0.0047 0.0024 0.0073 0.0042Ba1 0.0003 0.0000 0.0001 0.0003 0.0026 0.0023 0.0058 0.0103 0.0336 0.0928 0.6923 0.0553 0.0497 0.0171 0.0123 0.0087 0.0097 0.0068Ba2 0.0000 0.0000 0.0004 0.0004 0.0004 0.0021 0.0012 0.0040 0.0088 0.0271 0.0978 0.6777 0.0845 0.0287 0.0340 0.0117 0.0145 0.0064Ba3 0.0000 0.0002 0.0002 0.0001 0.0005 0.0015 0.0015 0.0022 0.0022 0.0071 0.0276 0.0615 0.6922 0.0714 0.0547 0.0302 0.0241 0.0228B1 0.0002 0.0000 0.0002 0.0002 0.0006 0.0012 0.0008 0.0006 0.0024 0.0022 0.0051 0.0316 0.0641 0.6689 0.0907 0.0520 0.0484 0.0307B2 0.0000 0.0000 0.0003 0.0003 0.0003 0.0003 0.0012 0.0023 0.0009 0.0026 0.0035 0.0077 0.0190 0.0749 0.6308 0.0893 0.1073 0.0591B3 0.0000 0.0000 0.0008 0.0000 0.0004 0.0008 0.0008 0.0012 0.0012 0.0015 0.0012 0.0039 0.0065 0.0348 0.0580 0.6056 0.1798 0.1033Caa1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0001 0.0005 0.0005 0.0024 0.0005 0.0043 0.0076 0.0105 0.0465 0.7193 0.2071D 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
30
Table 8-b : Modified Moody’s Generator matrix This generator matrix is obtained from the modified Moody’s one-year transition matrix of Table 7-a. Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1 D Aaa -0.1107 0.0717 0.0302 0.0003 0.0058 0.0019 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa1 0.0238 -0.2163 0.1030 0.0755 0.0125 0.0005 -0.0002 0.0011 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa2 0.0073 0.0403 -0.2082 0.1097 0.0332 0.0120 0.0046 0.0006 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Aa3 0.0009 0.0065 0.0466 -0.2074 0.1129 0.0324 0.0049 0.0015 0.0008 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000A1 0.0005 0.0009 0.0040 0.0711 -0.2220 0.0997 0.0327 0.0058 0.0010 0.0000 0.0030 0.0019 0.0000 0.0008 0.0006 0.0000 0.0000 0.0000A2 0.0004 0.0003 0.0039 0.0070 0.0666 -0.2292 0.0978 0.0343 0.0074 0.0043 0.0030 0.0004 0.0016 0.0006 0.0008 0.0000 0.0006 0.0002A3 0.0005 0.0015 0.0006 0.0010 0.0210 0.0884 -0.2663 0.0908 0.0398 0.0132 0.0045 0.0009 0.0013 0.0017 0.0000 0.0005 0.0005 0.0001Baa1 0.0004 0.0003 0.0015 0.0018 0.0009 0.0239 0.0870 -0.2851 0.1025 0.0375 0.0102 0.0046 0.0010 0.0087 0.0000 0.0006 0.0027 0.0014Baa2 0.0007 0.0012 0.0003 0.0018 0.0019 0.0050 0.0432 0.0750 -0.2710 0.0964 0.0194 0.0045 0.0073 0.0059 0.0035 0.0007 0.0037 0.0004Baa3 0.0006 0.0000 0.0003 0.0008 0.0019 0.0041 0.0047 0.0384 0.1117 -0.3274 0.0872 0.0353 0.0197 0.0063 0.0038 0.0015 0.0081 0.0030Ba1 0.0004 0.0000 0.0000 0.0002 0.0031 0.0019 0.0059 0.0096 0.0379 0.1278 -0.3808 0.0754 0.0651 0.0188 0.0120 0.0094 0.0088 0.0047Ba2 0.0000 0.0000 0.0005 0.0005 0.0001 0.0023 0.0004 0.0036 0.0073 0.0287 0.1402 -0.4015 0.1170 0.0324 0.0436 0.0101 0.0127 0.0021Ba3 0.0000 0.0003 0.0002 0.0000 0.0005 0.0016 0.0015 0.0022 0.0012 0.0061 0.0333 0.0864 -0.3800 0.0986 0.0724 0.0364 0.0203 0.0191B1 0.0003 0.0000 0.0002 0.0002 0.0007 0.0013 0.0007 0.0002 0.0028 0.0015 0.0022 0.0423 0.0902 -0.4172 0.1328 0.0690 0.0499 0.0229B2 0.0000 0.0000 0.0003 0.0004 0.0003 0.0001 0.0014 0.0030 0.0005 0.0030 0.0036 0.0078 0.0223 0.1108 -0.4770 0.1359 0.1390 0.0485B3 0.0000 0.0000 0.0011 -0.0001 0.0005 0.0010 0.0008 0.0015 0.0013 0.0017 0.0006 0.0042 0.0056 0.0484 0.0892 -0.5199 0.2665 0.0976Caa1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0000 0.0005 0.0003 0.0032 0.0000 0.0052 0.0084 0.0118 0.0697 -0.3396 0.2400D 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
31
Table 9: Simulated Call Spreads This summarizes Figure 2.
Real world Transition Risk-neutral world Transition
Grades Default premium Call spread
Default Premium Call spread
Investment 39 56 (53) 56 56 (54)
Speculative 342 55 (44) 693 92 (49)
32
Table 10-1: One-year migration matrix for simulation Typical G 1 G 2 G 3 G 4 DG 1 0.8179 0.1589 0.0163 0.0012 0.0057G 2 0.0349 0.7534 0.1759 0.0205 0.0153G 3 0.0004 0.0183 0.7003 0.2172 0.0638G 4 0 0.0001 0.0053 0.871 0.1236D 0 0 0 0 1 Good G 1 G 2 G 3 G 4 DG 1 0.8179 0.1589 0.0164 0.0012 0.0057G 2 0.0353 0.754 0.1765 0.0186 0.0156G 3 0.0064 0.0274 0.71 0.1879 0.0683G 4 0.0598 0.0915 0.1019 0.5821 0.1647D 0 0 0 0 1 Table 10-2: Generator matrix for simulation
Typical G1 G2 G3 G4 D
G1 -0.205 0.2 0.0000 0 0.005G2 0.04 -0.26 0.21 0 0.01G3 0 0.02 -0.29 0.22 0.05G4 0 0 0.005 -0.105 0.1D 0 0 0 0 0
Good G1 G2 G3 G4 D
G1 -0.205 0.2 0.0000 0 0.005G2 0.04 -0.26 0.21 0 0.01G3 0 0.02 -0.29 0.22 0.05G4 0.06 0.09 0.1 -0.4 0.15D 0 0 0 0 0
33
Table 11-1: One-year migration matrix for simulation
Typical G1 G2 G3 G4 D
G1 0.8179 0.1589 0.0164 0.0012 0.0057G2 0.0349 0.7534 0.1765 0.0197 0.0155G3 0.0004 0.0194 0.71 0.2045 0.0658G4 0.0002 0.0112 0.1017 0.7441 0.1427D 0 0 0 0 1
Good G 1 G 2 G 3 G 4 D
G 1 0.8179 0.1589 0.0164 0.0012 0.0057G 2 0.0353 0.754 0.1765 0.0186 0.0156G 3 0.0064 0.0274 0.71 0.1879 0.0683G 4 0.0598 0.0915 0.1019 0.5821 0.1647D 0 0 0 0 1
Table 11-2: Generator matrix for simulation
Typical G1 G2 G3 G4 D
G1 -0.205 0.2 0 0 0.005G2 0.04 -0.26 0.21 0 0.01G3 0 0.02 -0.29 0.22 0.05G4 0 0.01 0.1 -0.23 0.12D 0 0 0 0 0
Good G1 G2 G3 G4 D
G1 -0.205 0.2 0 0 0.005G2 0.04 -0.26 0.21 0 0.01G3 0 0.02 -0.29 0.22 0.05G4 0.06 0.09 0.1 -0.4 0.15D 0 0 0 0 0
34
Fig 1: Yield curves This plots yields vs maturities of bonds as of the last business day of December 1998, available from the Fixed Income Securities Data (FISD), provided by Mergent, Inc. The yields are a combination of trader quotes and matrix quotes (predominantly trader quotes). The legend T stands for Treasury bonds, and other legends are moody’s ratings.
Rating OBS Mean STD
Treasury T 66 5.7759 0.1191
Aaa 48 6.2531 0.1499
Aa 196 6.2581 0.2465
A 666 6.4097 0.1936
Investment Grades Baa 522 6.6603 0.2635
Ba 297 8.0283 0.8683
B 833 9.3677 1.2148
Speculative Grades C 86 11.6089 2.2503
Figure 1 is summarized in the table.
35
Fig 2: Simulated Call spreads The call spreads in the top figure are generated by using the Table7-b one-year generator matrix associated with Π = Ι. In the bottom figure the diagonal elements in Π increases by 0.06 for each lowering bond grade. Bond grade 0 means default-free grade and the numbers for grades are associated with the grade numbering in Table 1.
0 2 4 6 8 10 12 14 1640
45
50
55
60
65
70Par Yields
Bond Grades
Bas
is points
Call spreadZ spread-OAS
0 2 4 6 8 10 12 14 1620
40
60
80
100
120
140
160
180Par Yields
Bond Grades
Bas
is points
Call spreadZ spread-OAS
36
Fig 3-1: Call spreads with migration matrix faced by “typical” firm (Case 1)
0 1 2 3 410
11
12
13
14
15
16
17
18Par Yields
Bond Grade
Par
Yie
lds
(%)
Non callableCallable
0 1 2 3 48.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5Call Spreads
Bond Grade
Spr
eads
(bas
is p
oint
)
Call - NoncallableZ spread - OAS
Fig 3-2: Call spreads with migration matrix faced by “Good” firm (Case 1)
0 1 2 3 410
12
14
16
18
20Par Yields
Bond Grade
Par
Yie
lds
(%)
Non callableCallable
0 1 2 3 40
20
40
60
80
100
120Call Spreads
Bond Grade
Spr
eads
(bas
is p
oint
)
Call - Non-callZ spread - OAS
37
Fig 3-3: Signaling benefits and costs (Case 1)
Grade 3 Grade 416
16.5
17
17.5
18
18.5
19
Callable Yield (Typical)Noncallable Yield (Typical)Non-callable Yield (Good)Callable Yield (Good)
CB
AD
38
Fig 4-1: Call spreads with migration matrix faced by “typical” firm (Case 2)
0 1 2 3 410
11
12
13
14
15
16
17
18
19Par Yields
Bond Grade
Par
Yie
lds
(%)
Non callableCallable
0 1 2 3 45
10
15
20
25
30
35
40Call Spreads
Bond Grade
Spr
eads
(bas
is p
oint
)
Call - NoncallableZ spread - OAS
Figure 4-2: Signaling benefits and costs (Case 2)
Grade 416
16.5
17
17.5
18
18.5
19
Bond Grade
Par
Yie
ld (%
)
Callable Yield (Typical)Noncallable Yield (Typical)Noncallable Yield (Good)Callable Yield (Good)
DA
C
B
39
Reference Altman, Brady, Resti and Sironi, 2005, “The link between Default and Recovery Rates: Theory, Empirical evidence, and Implications,” Journal of Business, vol. 78 no. 6 2203-2227 Asquith, P. and D. Mullins, 1986, Equity issues and offering dilution, Journal of
Financial Economics 15, 61-89. Barnea, A., Haugen, R., Senbet, L., 1980, “A rationale for debt maturity structure and call
provisions in the agency theoretic framework,” Journal of Finance 35, 1223-1234. Bodie, Z., Taggart, R., Jr., 1978, “Future investment opportunities and the value of the
call provision on a bond,” Journal of Finance 33, 1187-1200. Brown, S. and J. Warner, 1985, Using daily stock returns, Journal of Financial Economics 14, 3-31. Chen, Z., C. Mao and Y. Wang, 2007, “Why Firms Issue Callable Bonds: Hedging Investment Uncertainty,” Temple University, Working paper. Crabbe, L., Helwege, J., 1994. Alternative tests of agency theories of callable corporate bonds. Financial Management 23, 3-20. Duffie, Darrell and Kenneth J. Singleton, 1999 “Modeling Term Structures of
Defaultable Bonds” The Review of Financial Studies 12, 687-720 Eckbo, B. E., 1986, Valuation effects of corporate debt offerings, Journal of Financial
Economics 15, 119-151. Guntay, L., Prabhala, N., Unal, H., 2004 “Callable bonds, interest-rate risk, and the
supply side of hedging,” University of Maryland Finance Working Paper, July 2004.
Hull, J., M. Predescu, and A. White, 2005 “The Relationship Between Credit Default
Swap Spreads, Bond Yields, and Credit Rating Announcements” Journal of Banking and Finance.
Jarrow, Robert A. and S. M. Turnbull, 1995,”Pricing Derivatives on Financial Securities
Subject to Credit Risk,” Journal of Finance, Vol L, No. 1, 53-85 Jarrow, Roberet A., David Lando, and Stuart M. Turnbull, 1997, “A Markov Model for
the Term Structure of Credit Risk Spreads”, The Review of Financial Studies 10, 481- 523
40
Jarrow, Robert A., Haitao Li, Sheen Liu, and Chunch Wu, 2006 ,”Reduced-form Valuation of Callable Corporate bonds: Theory and Evidence,” Journal of Financial Economics, forthcoming . Jensen, M., Meckling, W., 1976. Theory of the firm: managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3, 305-360. Kim, Seoyoung, April Klein and James Rosenfeld, 2008, “Return Performance Surrounding Reverse Stock Splits: Can Investors Profit?”, Financial management, Summer, 173-192 King, T.-H., Mauer, D., 2000. Corporate call policy for nonconvertible bonds. Journal of Business 73,403-444. Kish, R. and Livington, M., 1992. Determinants of the call option on corporate bonds. Journal of Banking & Finance 16, 687-703. Lando and Skodeberg, 2002, “Analyzing Rating Transitions and rating Drift with Continuous Observations,” Journal of Banking and Finance, 26, 423-444 Lewis, C.M., R.J. Rogalski, and J.K. Seward, 1999, Is convertible debt a substitute for
straight debt or for common equity? Financial Management 28(3), 5-27. Longstaff, Mithal and Neis, 2005, “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit-Default Swap Market,” Journal of Finance, Vol. 60, No. 5, 2213-2254 Mikkelson, W. H. and M. M. Partch, 1986, Valuation effects of security offerings and the
issuance process, Journal of Financial Economics 15, 31-60. Myer, S. and N. Majluf, 1984, Corporate financing and investment decisions when firms
have information that investors do not have, Journal of Financial Economics 13, 187-221.
Moody’s Investors Service, 2005, “Default and Recovery rates of Corporate Bond Issuers,
1920-2004, Speacil Comment, Global Credit Research Myers, S., 1977. Determinants of corporate borrowing. Journal of Financial Economics 5,
147-175. Nayer, Nandu and Duane Stock, 2008, “Make-whole Call Provisions: A Case of much ado about nothing?” Journal of Corporate Finance 14, 387-404 Pye, G., 1966. The value of the call option on a bond. Journal of Political Economy 74,
200-205.
41
Robbins, E., Schatzberg, J., 1986, “Callable bonds: a risk-reducing signaling
mechanism,” Journal of Finance 41, 935-949. Robbins, E., Schatzberg, J., 1988, “Callable bonds: a risk-reducing signaling mechanism-
-a reply,” Journal of Finance 43, 1067-1073. Tsuji, Chikashi, 2005, “The Credit Spread Puzzle,”, Journal of International Money and
Finance, 24, 1073-1089 Vu, J., 1986. “An empirical investigation of calls of non-convertible bonds,” Journal of
Financial Economics, 16, 235-265.