Discussion Paper No. 553

AN EMPIRICAL ANALYSIS OF
THE FINANCING STRATEGY OFCALLABLE BONDS

Keunkwan Ryu
andJung Bum Wee

August 2001

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

An Empirical Analysis of the Financing Strategy of Callable Bonds

by

Keunkwan Ryu
Department of Economics
Seoul National University, andISER, Osaka University
ryu02@prome.snu.ac.kr

andJung Bum Wee
School of Business
Kyung Hee University
jbw@khu.ac.kr

July 27, 2001

Abstract
This paper empirically analyzes the call timing of callable bonds to see how refunding
opportunity, cost of financial distress, agency cost of debt, and private information affectthe call decision. The empirical results show that firms issue callable bonds, convertible ornot, to enjoy future refunding options; that the cost of financial distress weakly expedites
calling convertible bonds but not non-convertibles; that firms which are in debt delay
calling non-convertibles but not convertibles; that callable bonds, convertible or not, areissued to mitigate adverse selection under information asymmetry; and that after the end ofcall protection periods the call intensity monotonically decreases for the non-convertible
bonds but not for the convertible bonds.

1. Introduction

This paper explores the motivations for designing and calling callable nonconvertible bonds and callable convertible bonds. It investigates whether callable debt hasa relative advantage over non-callable bonds or straight equity; how a firm determines toexercise an embedded call option; and how calling is different between callable nonconvertible bonds and callable convertible bonds.
Having issued a callable bond, a firm makes a decision to call the bond based on
its own characteristics and the outside environment. The factors predicted to affect callingare classified into two categories. One is a set of firm characteristics including the cost offinancial distress, the agency cost of debt, the information released after issuance, and thetransaction cost of refunding. The other category includes the movements of the market
interest rate and the stock value. We estimate the hazard rate of calling a bond at each point
in time as a function of the set of predicted factors observed by that time.
In this paper, we analyze both callable non-convertible bonds and callable
convertible bonds. A call option provides the issuing firm with an optional right to redeem
the bond at a pre-determined call price before maturity. In the case of a callable non-1

convertible bond, once the firm exercises the call option, the bondholder has no otherchoice but to exchange the bond for cash.
A conversion option provides the bondholder with an optional right to convert thebond into equity according to a pre-determined conversion ratio. In the case of a callable
convertible bond, once the firm exercises the call option, the bondholder chooses either toconvert it into equity or to exchange it for cash. The choice depends on the relative
magnitude of the call price and the conversion value. The conversion value is the value ofthe shares a bondholder receives upon conversion of a unit of bond. If the call price werehigher than the conversion value, the bondholder would not exercise the conversion option
and receive cash (non-conversion forcing call). If the conversion value were higher thanthe call price, the bondholder would choose to exercise the conversion option and receive
shares (conversion forcing call).
A callable bond might be issued primarily to utilize favorable refunding
opportunities in the future. Firms face an incentive to issue a callable non-convertible bondwhen they expect the market interest rate to fall after issuance, and an incentive to issue acallable convertible bond when they expect stock prices to go up. By calling outstanding
bonds, firms refund at a lower interest rate (callable non-convertible bonds and nonconversion forcing calls), or force bond-equity swap (conversion forcing calls).
2However, future refunding may not be the only reason why firms issue callable
bonds. In the United States, firms relied on callable bonds more heavily during the late1970s and early 1980s, when the market interest rate kept rising, than during the late 1980s
and early 1990s, when the market interest rate kept falling. The one-year Treasury bill ratein the secondary market showed a uniform increase from 4.64% in December 1976 to
14.7% in August 1981. Thereafter, the market interest rate fluctuated, generally going
down, but remained above 10% until September 1984. The one-year Treasury bill rateuniformly decreased from 9.93% in October 1984 to 3.33% in July 1993. According to
Moody’s Industrial Manuals, about 90% of the listed bonds issued from the late 1970s to1982 were callable, whereas only about 60% of all bonds issued since 1983 have beencallable.
This paper empirically analyzes the call decision of firms to see how
recapitalization opportunities, cost of financial distress, agency cost of debt, and private
information affect the call decision. This paper differs from previous studies and, indeed,
has several advantages over them. Harris and Raviv (1985) analyzed the calling of acallable convertible bond but ignored the actual call structure. In their model, a firm isassumed to have a callable convertible bond with a call price of zero so that the firm canalways force a conversion. Unlike Harris and Raviv, this paper takes into account the3actual call structures in analyzing the call timing. Vu (1986) examined the stock pricereaction to calling a non-convertible bond. Unlike Vu, this paper directly analyzes thedecision to call using survival analysis techniques, and thus better addresses the call designand call timing issues.
The rest of the paper is organized as follows. Section 2 reviews the existing
literature. Section 3 sketches the theoretical predictions and draws testable hypotheses
regarding the effect on call timing of the cost of financial distress, the agency cost of debt,
information asymmetry, and refunding opportunity.

Section 4 discusses various

measurement issues and describes the empirical model.

Section 5 identifies the data

sources and presents selective summary statistics. Section 6 shows the estimation resultsfor each of the non-convertible bonds and convertible bonds. Section 7 concludes the paper.
Other details relating to measurement issues, summary statistics, and empirical results canbe found in the Appendix.

2. Literature review

To explain the prevalence of callable debt, previous studies have investigatedwhether a callable bond has a relative advantage over a non-callable bond or straight equity.
4

These studies have identified several advantages of a callable bond including its ability tofacilitate recapitalization, mitigate default cost, provide tax subsidy, and signal private
information.

2.1 Literature related to callable non-convertible debt

The literature suggests that the most prominent function of a callable bond is tofacilitate recapitalization in the future.

For a non-convertible bond, a call provision

facilitates the issuing of a new security. For instance, Pye (1966) views a call provision asa pure option to facilitate refunding when the market interest rate falls. Vu (1986) suggeststhat a call provision is included to facilitate removing restrictive financing covenants andthus to facilitate recapitalization. He finds that firms are willing to pay a higher callpremium if calling removes a restrictive covenant. Narayanan and Lim (1989) also findevidences supporting Vu’s findings. Many callable zero-coupon bonds have restrictive
covenants compared with non-callable counterparts because they can be removed by calling.
Smith and Warner (1979) postulate that a call provision mitigates the agency costof debt. When a firm is in debt, the manager who acts in the interests of the shareholders
may attempt to extract bondholder wealth in favor of the shareholders.
5This action

typically entails increasing the firm’s risk, which does not necessarily lead to firm value
maximization. Bondholders rationally expect this kind of managerial incentive distortion
when evaluating the value of a bond at the time of purchase, which results in firm value
reduction ultimately damaging the shareholder interests. A call provision mitigates thistype of agency cost because it facilitates refunding before maturity. This is because themanager’s action to reduce firm value is penalized later at the time of refunding.
Fischer, Heinkel, and Zechner (1989) postulate that firms have the incentive to callbonds as soon as the recapitalization benefits the shareholders. The call time that serves
shareholders’ interests comes earlier than the call time that maximizes firm value, creating
a potential agency cost of recapitalization. Bondholders demand a higher coupon rate tocompensate for an early redemption. The resulting higher coupon rate becomes a burden to
the firm. Since a firm eventually bears this kind of agency cost, it attempts to pre-commit
to calling no earlier than the firm-value maximizing time. This explains why many callable
bonds have so-called call protection periods, whether absolute or conditional, immediately
after issuance.
Under a condition of information asymmetry, the call option benefits firms,
especially good ones, by providing them with recapitalization opportunities. A good firm
can easily refund by calling outstanding debts after favorable information is released.
6

2.2 Literature related to callable convertible debt

Callable convertible bonds are equity-like as well as debt-like issues. They canreplicate the cash flows of issuing callable non-convertible bonds followed by those of
issuing straight equity.
Several studies have examined whether the types of bonds issued signal private
information. Stein (1992) suggests that good firms issue long-term debts to signal their
good type while bad firms issue callable convertible debts to reduce default risk. Goodfirms can manage risks arising from the issuing of a long-term bond, whereas bad firms
cannot. According to Stein, when callable convertible bonds are issued for deferred equity
financing under information asymmetry, a good firm forces a conversion by calling thebonds after favorable information is released.
Smith and Warner (1979) and Green (1984) postulate that a callable convertible
debt mitigates the aforementioned agency cost of debt more efficiently than a callable nonconvertible bond does. As discussed earlier, the call option mitigates the agency cost ofdebt because it offers a refunding opportunity before maturity. The conversion option
further mitigates the agency cost of debt because it offers bondholders the right toeventually be shareholders. In equity-financed firms, shareholder wealth maximization
7

complies with firm value maximization, thus avoiding the agency cost of debt. According
to this view, callable convertible bonds are a debt-like issue.
Dann and Mikkelson (1984) find that common shareholders earn significantly
negative abnormal returns both at the announcement of a convertible bond offering and at
issuance. In contrast, the effect of a non-convertible bond offering is only marginallynegative at the initial announcement and almost zero at issuance. They conclude thatconvertible bonds are an equity-like issue.
The optimal timing of call and conversion has also been studied in the literature.
Brennan and Schwartz (1977) claim that it is optimal for firms to call a convertible bond assoon as the conversion value exceeds the call price. Ingersoll (1977) finds that in practice
calling is deferred long after the optimal timing predicted by Brennan and Schwartz (1977).
Harris and Raviv (1985) attempt to resolve this apparent discrepancy using a signalingargument under a condition of information asymmetry. According to them, good firms
voluntarily choose to defer calling to signal their good type, whereas poor firms are lesslikely to defer calling because they have higher probabilities of being unable to force a
conversion in a later stage. Further, Wee (1995) suggests that a callable convertible bond isdesigned to be converted if the realized return of the issuing firm is relatively low.

8

Empirical studies support that calling a convertible bond is related with low
performance of a firm. Lin and Chen (1991) find that stock prices show a negative reaction
to the announcement of calling a convertible bond. Ofer and Natarajan (1987) document a
drop in profitability upon calling a convertible bond.

3. The determinants of call timing: a theoretical overview

This paper studies how calling a callable bond is influenced by firm characteristics
and market conditions. Using survival analysis techniques, this paper empirically analyzes
the impact on call decisions of movements in the market interest rate, the transaction cost ofrefunding, the cost of financial distress, the agency cost of debt, revealed information afterissuance, the structure of the call clause, the change in stock price, and the elapsed timesince issuance. The theoretical predictions are briefly outlined below.

93.1 Refunding opportunity

Refunding opportunity affects the decision to call. Market interest rate movements
and the transaction cost of refunding influence the call timing. Stock price movements also
matter in the case of callable convertible bonds.

(1) Non-convertible bonds

The decision to call a non-convertible bond depends crucially on the availability ofrefunding opportunity and the transaction cost of refunding. A firm is more likely to
exercise the call option when the spread between the bond’s interest rate and the market
interest rate gets larger, and less likely to call when the transaction cost of refunding
becomes larger.
This paper proxies the market interest rate with the one-year Treasury bill rate in
the secondary market. The secondary market rate is preferred to the auction rate because
the secondary market is deeper. The interest rate spread is measured by the bond’s interest
rate minus the one-year Treasury bill rate.

10

We postulate that there are economies of scale in refunding transactions, and thatthe unit refunding cost decreases with the size of refunding amount. This amount is
expected to expedite the calling. We use the authorized amount of bond issue as a proxy
for the refunding amount. We postulate that the unit refunding cost decreases as the natural
logarithm of the authorized amount of bond issue gets larger.

(2) Convertible bonds

Refunding opportunity has a different impact on calling a convertible bond,depending on whether a call is conversion forcing or not. In the case of a non-conversion
forcing call, calling is more likely when the market interest rate falls below the bond’sinterest rate and when the transaction cost of refunding is low. A conversion forcing call ismore likely when the conversion value is higher than the conversion price (value of thebond submitted for conversion).

The interest rate difference is less important indetermining the time to exercise the conversion forcing call.

The conversion value of a convertible bond increases in the stock price. We use
the stock price as a proxy of the conversion value.

For each issue of the callable

convertible bonds, we have normalized the corresponding stock price as one at the time of11

issuance, and then have constructed its price path using the monthly rates of return.
Monthly rates of return are adjusted for stock split, dividend payment, etc.

To sum up, we expect that calling a convertible bond is more likely as the interest
rate spread widens, as the unit refunding transaction cost decreases, and as the conversion
value rises.

3.2 The cost of financial distress

A firm is in financial distress when the value of total liabilities exceeds the valueof total assets including future business opportunities. Under a condition of financial
distress, a firm is likely to go through financial restructuring or liquidation.
Financial distress is costly. First, restructuring or liquidation normally incurs aconsiderable amount of administrative cost, including legal expenses. The resale value of
assets during restructuring or liquidation is likely to be lower than the value under theoriginal firm.

Second, bondholders are in general different from managers andshareholders.

After restructuring, the former bondholders usually emerge as newshareholders.

They tend to be less efficient at managing the firm or at monitoring

professional managers compared with the original shareholders.
12Rationally expecting the possibility of financial distress, creditors properly
incorporate the expected cost of such distress when evaluating the value of a bond issue.
This way, a default risk eventually costs the shareholders. In response, firms issue callable
convertible bonds to reduce the chance of financial distress. By exercising call option
embedded in callable convertible bonds, firms forces debt-equity swap without having toraise new funds. They tend to have a stronger incentive to exercise the call option and thus
to avoid financial distress as the cost of financial distress becomes larger. Calling a
convertible bond will be expedited as the cost of financial distress gets larger.
Non-convertible bonds do not quite serve this purpose.

Calling entails

recapitalization. To retire existing debts by calling non-convertible bonds, firms have toraise new funds. The cost of financial distress is not expected to have any significant effecton calling a callable non-convertible bond.
In the case of callable convertible bonds, firms face an incentive to exercise thecall option either to redeem the bond or to induce a conversion when the cost of financial
distress is high. Firms become equity- financed and thus free from additional borrowing
once their convertible debts are converted into shares.

Thus, faced with financing

difficulties, managers are more willing to call the callable convertibles than the nonconvertibles.
13

This paper proxies the cost of financial distress with the size of firm-specific assets.
Firm-specific assets have a relatively low resale value at restructuring or liquidationcompared with assets for general use. The paper measures the size of firm-specific assets
by the proportion of fixed assets to total assets. Fixed assets include both tangibles andintangibles, whereas current assets are mostly cash, securities, and inventories. Intangibles
are regarded as more fixed in nature than tangibles. Fixed assets, like intangibles, lose
more of their value through resale.

3.3 The agency cost of debt

When a firm is in debt, a manager’s action to maximize shareholder wealth does
not necessarily comply with firm value maximization (see, for example, Barnea et al. 1980).
This incentive distortion tends to be severe for firms that are highly in debt.
This cost is mitigated if the manager expects to recapitalize in the future. Thus,
calling is delayed when the potential agency cost of debt, as measured by the amount of thedebt, is large. The presence of an unexercised call option mitigates a manager’s incentive
distortion.

This is because the manager’s commitment to firm-value maximization isrewarded when the firm recapitalizes. As a result, firms that are in debt tend to defer14

calling and leave call options unexercised. This effect is expected to be stronger for the
non-convertible bonds than for the convertible bonds since the possibility of forced
refunding is higher in the case of calling the non-convertible bonds.
We proxy this agency cost of debt with the indebtedness, measured by the ratio of
total liability to total asset.

3.4 Information asymmetry

Suppose that firms are classified as either good type or bad type depending on
their profitability. Suppose also that there is information asymmetry in that firms knowwhat type they are but the investors do not. In this situation, a good firm suffers fromadverse selection. It will try to mitigate this problem by issuing callable bonds, expectingthat its type will hopefully be revealed after bond issuance.
A good firm exercises the call option to recapitalize in a more favorable term after
the information is released. We expect that a firm is more likely to call a bond whenfavorable information is released. We proxy this information release with the profitabilityof firms after the issuance, measured by the ratio of net income to total assets. This15

variable is expected to expedite the calling of a callable bond, whether convertible or nonconvertible.

4. Measurement issues and the empirical modelThis paper analyzes the time to call, measured by the interval from the time whencalling becomes possible to the time when calling is in fact made. This paper uses the term
“time to call” instead of the usual term “duration.” This is to avoid a possible confusion
because “duration” is a term reserved to represent the weighted average maturity of a bondin finance.
By using survival analysis techniques, this paper estimates the hazard rate of calltiming. The hazard rate shows the call intensity at each moment in time as a function of theavailable information at that time.

4.1 The measurement of the time to call

In practice, measuring the time to call of a callable bond is not straightforward
because of the different structures that appear across different callable bonds.
16

Time

horizons are different for different bonds. Protection periods exist for some but not forothers. The absolute call protection periods that prohibit calling under any circumstance,
range from several months to several years when they exist. The conditional call protection
periods that prohibit calling unless a certain pre-specified condition is met, may or may notexist. When they exist, they range from several months to several years. Also, the timeintervals from the end of the absolute call protection period to call expiration are alldifferent.
Figure 1 illustrates a hypothetical life path of a callable bond. There are four
possible time points: t 0 , t1 , t 2 , and t 3 in increasing order. A firm issues a callable bond attime t 0 . The bond matures at time t 3 . The bond is not callable until t1 in any circumstance.
In some cases, a bond is not callable further until t 2 elapses under a certain set of
conditions. After t 2 , the bond is callable without restriction.
We call the time interval from t 0 to t1 an absolute call protection period, and thetime interval from t1 to t 2 a conditional call protection period. When there is no absolute
call protection period, we have t 0 = t1 . When there is no conditional call protection period,
we have t1 = t 2 .
The conditional call protection clause takes a different form depending on whether
the bond is convertible or not. In the case of a non-convertible bond, the bond is not17

callable before t 2 when refunding is made at a lower interest rate than the bond’s interest
rate. This is to protect the bondholder from a forced reinvestment as a result of the call, forwhich the return is likely to be lower than the retiring bond’s interest rate. In the case of acallable convertible bond, the bond is not callable until t 2 elapses unless the corresponding
stock price exceeds a certain level for a specified length of time. This is to guarantee thebondholder a minimum conversion value at an earlier stage.

<Figure 1> The hypothetical life path of callable bonds: from issuance to maturity

timebond issued (t0)strict call protection ends (t1)conditional call protection ends (t2)bond expires (t3)Now, let us consider how to define the time to call in a meaningful way. The time
to call is the time interval from the end of the absolute call protection period to the actual
call time. It measures how long the bond issuer waits until he exercises the call option after18

calling becomes possible. The absolute length of calendar time, however, is not a goodmeasure. Calling a callable bond after one year of call eligibility has different implication
depending on whether the bond has a longer life span or a shorter one.
To illustrate, let us take two callable bonds differing in their callable life spans.
Suppose that one bond has a 10-year life span and the other bond has just a 5-year life span.
If both bonds were called after one year of call eligibility, the call would have been
exercised earlier in relative terms for the first bond than for the second. The first bond iscalled at 10% location in its life span, whereas the second bond is called at 20%.
We adopt percentage life as a measure of normalized time to call. The percentage
life is defined as the ratio (t c − t1 ) /(t 3 − t1 ) , where t c is the observed call time if a call ismade and is equal to t 3 if no call is made until maturity. The use of percentage life allows
us to compare the time to call across different bonds.
Call observations are classified into three categories. First, there are bonds that are
called during the sample period. These are complete observations because a call is actuallyobserved. These bonds have a value of normalized time to call of less than one. Second,
there are bonds that are neither called nor matured by the end of the sample period. Thesebonds are incomplete in spell and have a value of normalized time to call of less than one.

19

Finally, there are bonds that are not called until maturity. We say these observations are
maturity censored. For these observations, the normalized time to call takes a value of one.

4.2 Controlling for heterogeneity in the structure of the call protection period

A callable bond may or may not have a conditional call protection clause.
However, we measure the time to call from the end of the absolute call protection period
whether there is a conditional call protection clause or not. Thus, the time to call variable
may suffer from heterogeneity arising from whether a bond has a conditional call protection
period or not.
Even though there is a conditional call protection clause, a manager may choose to
avoid it and thus exercise the call before the expiration of the conditional call protection.
This choice could be costly. For example, in the case of non-convertibles, the manager has
to bypass opportunities of refunding at a lower interest rate to avoid the protection clause
and thus be able to call early. Bypassing these opportunities is costly. Thus, the manager isless likely to make such a choice faced with a conditional call protection clause. We want
to see whether this kind of effect in fact exists.

20

To capture differences in call patterns depending on whether there exists a
conditional call protection clause or not, we first define a dummy variable (say, a call
protection dummy) that takes a value of one if there is a conditional call protection clause
and if this clause is currently binding, and zero otherwise.

For callable bonds withconditional call protection clauses, this dummy variable becomes time varying. It takes avalue of one during the conditional call protection period and zero thereafter. Of course,
for callable bonds without a conditional call protection clause, this dummy variable takes avalue of zero throughout.
The hazard rate should then be estimated separately for convertible bonds and nonconvertible bonds, with the dummy variable included in each specification. Through thedummy, we want to see whether a conditional call protection clause in fact has a delaying
effect on the time to call.

4.3 The empirical model

The empirical model we use is a hazard rate model specified as follows:h(t | xt ) = h0 (t ) exp( xt ' β ) ,21

where h(t | xt ) is the call hazard rate at time t given xt , h0 (t ) is the so-called baseline
hazard function, xt is a collection of the explanatory variables available at time t , and β isa vector of unknown parameters. To make it always positive, let us represent h0 (t ) as
h0 (t ) = exp( g 0 (t )) so that the resulting hazard function becomes:h(t | xt ) = exp( g 0 (t ) + xt ' β ) .

To complete the model, we need to specify g 0 (t ) . We use a step function forg 0 (t ) by introducing a set of time dummy variables to partition the unit interval. To design
the partition to be used, we consider a trade-off between flexibility and reliability. If more
steps are estimated, the resulting function is more flexible but less reliable, and vice versa.
The chosen intervals in the step function are progressively wider over time to avoid the
problem of thin data at later times. We end up partitioning the unit interval into five subintervals, {[0,0.1], (0.1, 0.2], (0.2, 0.3], (0.3, 0.5], (0.5, 1]}, by introducing four time
dummy variables indicating the first four intervals together with an overall constant term.
The coefficient of the first dummy variable shows whether the call hazard rate is higher (+)
or lower (-) in the first sub-interval (birth to 10% of age) relative to the second half of thecallable life span, and similarly for other dummies.
22

To test the theoretical implications using the time to call data, we let xt include
those variables discussed and defined in previous sections. Many explanatory variables aretime varying in nature. Since a firm’s financial situation and other environments keepchanging, it is a better idea to use these time varying explanatory variables to explain amanager’s decision to call at each moment in time. To control for the presence/absence ofthe conditional call protection, we also let xt include the call protection dummy.
To sum, the set of variables used in the model specification are as follows.

Baseline hazard function: D[0,0.1], D(0.1,0.2], D(0.2,0.3] and D(0.3,0.5] are time-dummy
variables defined on the intervals [0,0.1], (0.1,0.2], (0.2,0.3] and (0.3,0.5] respectively.
These four dummy variables together with an overall constant term model the baseline
hazard function as a step function with five steps.

Time varying covariates: FASS is the ratio, (fixed asset)/(total asset). DEBT is the ratio,[(total liability)/(total asset)]. PRO is the ratio, (net income)/(total asset). DFREE is thedummy variable measuring freedom from conditional call protection periods. It takes thevalue 0 if the callable bond is prohibited from being called by a conditional protection

23

clause, and 1 otherwise. DINT is the difference, the bond’s interest rate (%) minus the oneyear Treasury bill rate (%).

Time constant covariates: Ln(Amount) is the natural logarithm of the authorized amount of
the bond issue measured in 1 million dollars. Callable life span is the length of time fromthe end of the absolute call protection period to maturity measured in 100 thousand days.
The above variables are commonly used for the hazard rate specification of the
non-convertible bonds and the convertible bonds. In the case of the convertible bonds,
VCONV is additionally used. VCONV is the normalized stock price so that the price at thetime of issuance is one. VCONV is time-varying.

4.4 The baseline hazard

Existing literature provides implications for the shape of the baseline hazard
function. Fischer, Heinkel and Zechner (1989) show that a manager has incentive to call abond as soon as it is in the interest of the shareholders. They further show that thisshareholder-wealth maximizing time of calling is earlier than the firm-value maximizing
time, i.e., there is a potential incentive problem of recapitalization. To mitigate this agency
24

cost, a firm can set the expiration of a call protection period matching the firm-value
maximizing time. Thus, a firm has incentive to call a bond immediately after the expirationof a call protection period because the total gain from recapitalization decreases as callingis further deferred. This is illustrated in Figure 2.

<Figure 2> Call protection as a device to curb incentive distortion of recapitalization

intensity to call0

shareholder-wealthfirm-value

maximizing time

time

(end

maximizing
of

call

protection period)

We expect that this incentive be reflected in the shape of the baseline hazard
function.

Recall that we measure the time to call from the end of the absolute call

protection period. Thus, the time origin coincides with the end of any call protection
periods for bonds without a conditional call protection clause. For these bonds, we expect
the baseline hazard function to exhibit a monotonically decreasing pattern.

25

Time zero is not necessarily the end of call protection period for bonds with aconditional call protection clause. For these bonds, the effective ending of call protection
varies a lot depending on the structure of the conditional call clauses and also on whether
the condition is met or not. Figures 6 and 7 in the appendix show that there is lots ofvariation in the normalized length of conditional call protection periods. We do not expect
any visible baseline hazard pattern for these bonds with conditional call protection.
The above pattern is expected to emerge from curbing the agency cost of debt. We
expect this pattern is stronger for bonds of a debt nature and weaker for bonds sharing anequity nature. Non-convertible bonds are more like a debt than convertible bonds. We
expect the monotone decreasing baseline pattern most visible in calling non-convertible
bonds without a conditional call protection clause. For other bonds, the baseline pattern is
expected to be weak or invisible.

4.5 The construction of the likelihood function

To construct the likelihood function, we need to compute the probabilities of thefollowing two forms:26

f (T = t ) or P (T > t ) , 0 ≤ t ≤ 1 ,where the first denotes the density of the event T = t (a complete observation) and thesecond denotes the probability of the event T > t (right-censored, whether incomplete or
maturity censored).
To illustrate, let us assign a likelihood value to both the complete event T = 0.35
and the right-censored event T > 0.35 .

First, in the case of a complete observation,

T = 0.35 means that a callable bond survives 35% of its callable life and then is called
immediately at 35% location of its callable life span. By using a relationship between thehazardratefunction

andthedensity

0.35
f (T = 0.35) = h0 (0.35) exp( x 0.35 ' β ) exp − ∫ 0function,

we

end

up

with

h0 (u ) exp( x u ' β ) du .
 Second, in thecase of a right-censored observation, T > 0.35 means that a callable bond is only known tohavesurvived35%

0.35
P(T > 0.35) = exp − ∫
 0

of

its

callablelife.

Similarly,

we

find

h0 (u ) exp( xu ' β ) du .
Here arise several issues that need to be addressed in order to compute the above
likelihood values from the available data. First, the time varying explanatory variables arerecorded according to the calendar time (either monthly or yearly), not the normalized time.
Therefore, we need to rearrange the data on time varying explanatory variables according to27

the normalized time. Since the time horizons are all different across different callable
bonds, this has to be done on an individual basis (the details of this are in the Appendix).
Once this has been done, assigning the above likelihood values is trivial. This is because
the integration reduces to summation due to the discrete nature of the time varying
explanatory variables as well as the baseline hazard function.

5. DataIn this section, we explain the data sources and present basic descriptive statistics
before carrying out the survival analyses in the next section (additional summary statistics
can be found in the Appendix).

5.1 Data sources

The sample of callable bonds is taken from those listed in Moody’s Industrial
Manuals. The sample bonds were issued between September 1, 1980 and December 31,
1991. Moody’s Manuals provide important features of bonds, specifically, issuance date,call protection period, maturity, face value, coupon rate, and call date. Data needed to28

construct explanatory variables are collected from Compustat files, the Citibank database,
CRSP (Center for Research in Security Prices) files, and the International Financial
Statistics. Compustat files provide firm characteristics such as net income, liabilities, net
fixed assets, and total assets. The market interest rates are taken from the Citibank database.
CRSP files provide rates of return data. As a relevant price index, we use the industrial
price index available from the International Financial Statistics.
The sample excludes callable bonds that are retired or suspected to have retired
before or after a major merger or acquisition. Specifically, the sample excludes the bonds
called by either an acquiring or an acquired firm within 12 months before and 6 months
after a major merger or acquisition. The sample also excludes bonds wherein the issuing
firm goes bankrupt after issuance. This is to preclude observations that are likely to show
different call patterns. Also, we exclude data points that lack some relevant informationsuch as financial ratios or the coupon rate. In the end, we have 586 usable observations forcallable non-convertible bonds and 166 usable observations for callable convertible bonds.

5.2 statistics

Tables 1 and 2 show selected sample data used in this paper.
29

<Table 1> Selected sample data: callable non-convertible bonds1

Company name

Issuance

Acquisition

Date

Date

End of

End ofabsoluteconditional

Call

Expiration

date

date

call

call

protection

protection

Abbott Industries

19830201.

.

19930201

19870101

20130201

Abbott Industries

19830201.

19900201.

19900201

19930201

Allied Siganl Inc (Allied Corp)

19831001

19850919.

19941101

19870227

20091101

American Medical Holdings Inc

19840115.

19910115.

19911108

19940115

American Medical Holdings Inc

19840115.

.

19940115

19870819

20140115

American Medical Holdings Inc

19850601.

19920601.

19920610

19950601

American Medical Holdings Inc

19850601.

.

19950601

19930701

20150601

American Medical Holdings Inc

19860115.

19900115.

19910115

19910115

American Medical Holdings Inc

19860201.

19910201.

19930201

19930201

Armco Inc

19811201.

19851201.

19860101

19861201

Atlantic Richfield Co

19811201.

.

.

19911201

19911201

Atlantic Richfield Co

19820915.

.

19920915

19870430

20120915

Atlantic Richfield Co

19830415.

.

19930415

19900301

20130415

Atlantic Richfield Co

19850601.

.

19950601

19900301

20150601

Atlantic Richfield Co

19851015.

19921015.

19930101

19951015

Atlantic Richfield Co

19860101.

19930101.

19930101

19960101

Baxter Int'l Inc

19870615.

19880615.

19930701

20180615

Baxter Int'l Inc (American Hosp. Supply)

19820815

19851125

19890901.

19890901

19920901

Cabot Corp

19820801.

.

.

19860930

19920801

Cabot Corp

19841101.

.

19911101

19870427

19941101

Cabot Corp

19850901.

.

19920901

19880427

19950901

Chevron Corp

19841101.

19911101.

19920101

19941101

Chevron Corp

19860301.

19930301.

19930516

19960301

Chevron Corp

19860415.

19930415.

19930416

19960415

Chevron Corp

19850201.

19890201.

19900201

19900201

Chevron Corp

19850601.

19920601.

19920616

19950601

Comdisco Inc

19860515.

19920515.

19920629

19940515

Data General Corp

19850515.

.

19950515

19870518

20150515

Digital Equipment Corp

19840401.

19910415.

19910415

19940415

Digital Equipment Corp

19840415.

.

19940415

19860619

20140415

1
In the case of acquisition, the firm within parentheses is acquired by the firm outside. If a firm which has issued a callable
bond is acquired by another firm during the life of the callable bond, we use the acquisition date instead of the original30

<Table 2> Selected sample data: callable convertible bonds

Company name

End of

End ofIssuance

Acquisition

absoluteconditional

Call

Expiration

date

date

call

call

date

date

protection

protection
19930701

19980401

19930701

20020115

19870507

19950701

Action Industries Inc

19830401

19850401

Anacomp Inc

19820115

19840115

Anacomp Inc

19840701

Automatic Data Processing Inc

19850215

19870215

19870216

20100215

Automatic Data Processing Inc

19860301

19890101

19891116

20110301

Black & Decker Corp

19870715

19900715

19900101

20020715

Boise Cascade Corp

19860501

19890301

19930701

20160501

Bowater Inc

19841215

19870224

20091215

Browning-Ferris Industries Inc

19870801

19930701

20120815

Caesars World Inc

19860401

19880401

19870701

20060401

Champion Int'l Corp

19860415

19890422

19930701

20110415

Comdisco Inc

19830501

19841101

19860701

20030501

Crane Co

19851001

19871001

19870331

20051001

Deere & Company

19830315

19850315

19871016

20080315

Diagnostic/Retrieval Systems Inc

19830801

19930801

19930801

Digital Equipment Corp

19840901

19860417

20090901

Dole Food Co Inc

19830615

19870101

20130615

Eaton Corp

19831216

19870116

20081215

EDO Corp

19861215

19891215

19930701

20111215

Emerson Electric Co (Liebert Corp)

19851115

19871201

19930701

20101115

Flowers Industries Inc

19850301

19870301

19920819

20050301

General Dynamics Corp (Cessna Aircraft Co)

19830701

19850701

19900101

20080701

Gillette Co

19821112

19830301

19860701

20130301

Grow Group Inc

19860201

19930625

20060201

Grumman Corp

19840815

19930707

20090815

H.J.Heinz Co

19850215

19900101

20150215

Harcourt Brace Jovanovich Inc

19860315

19880101

20110315

Hercules Inc

19850815

19930701

20100815

Int'l Paper Co

19870923

19900923

19930701

20020923

Int'l Paper Co

19870315

19890315

19911121

20120315

Int'l Rectifier Corp

19850615

19910614

20100615

19870115

19900815

19850801
19860916

19851215

19860316

19870815
19880215
19890315
19880815

19870615

issuance date as the birth date of the bond.

31

Table3

cross-tabulates

thesamplecallable

bonds

by

convertibility,

presence/absence of an absolute call protection clause, and presence/absence of aconditional call protection clause. As can be seen, most callable bonds have either anabsolute call protection clause or a conditional call protection clause, but seldom both. We
infer that the two types of call protection clause function as substitutes rather than ascomplements in protecting investors.

<Table 3> Joint distribution of absolute and conditional call protection clauses
Conditional call protection period
Non-convertible bonds

Absolute call
protection period

Exist

Not exist

Exist

0.04

0.48

Not exist

0.36

0.12

Conditional call protection period
Convertible bonds

Absolute call
protection period

Exist

Not exist

Exist

0.03

0.26

Not exist

0.50

0.21

For call protection, non-convertible bonds prefer an absolute call protection to aconditional counterpart. It is opposite for the convertible bonds. This difference seems to32

reflect that investors in non-convertible bonds care for a safe long-term investment whereas
investors in convertible bonds care for possibility of conversion before maturity.
Figures 3 and 4 show the distribution of the length of the absolute call protection
period (t1 − t 0 ) when it exists for the sub-sample of callable non-convertible bonds and thesub-sample of callable convertible bonds. The mean length of the absolute call protection
period is 5.14 years for the non-convertibles, and it is 2.28 years for the convertibles. On
the average, the absolute call protection period is longer for the non-convertible bonds thanfor the convertibles, lending another support to the fact that non-convertible bonds are moreof a debt compared with convertible bonds.

<Figure 3> Histogram showing length of absolute call protection period:
callable non-convertible bonds with an absolute call protection period33

<Figure 4> Histogram showing length of absolute call protection period:
callable convertible bonds with an absolute call protection period

Table 4 shows a classification of the sample data by convertibility and censoring
status. An observation is said to be complete when its call time is observed within thesampling horizon (T = t ,0 < t < 1) . An observation is said to be incomplete when its call
option has not been exercised by the end of the sample observation period, which comes
before maturity (T > t ,0 < t < 1) . Finally, an observation is said to be maturity censoredwhen its call option has not been exercised by the maturity (T > 1) .

34

<Table 4> Classification of sample data by convertibility and censoring status
Non-convertible bonds

Convertible bonds

Total
Number

Proportion
(%)

Total
Number

Proportion(%)

Complete

367

62.6

88

53.0

Incomplete

173

29.5

77

46.4

Maturity censored

46

7.8

1

0.6

Total

586

100.0

166

100.0

Table 5 shows mean and standard deviation of the covariates used in our empiricalmodel for each sub-sample of the non-convertible bonds and the convertible bonds.

<Table 5> Mean and standard deviation of covariates used for estimation
Non-convertible bonds

Convertible bonds

Mean

SD

Mean

SD

FASS

0.41220.21210.3277

0.1954DEBT

0.36640.20050.36350.1727PRO

0.03020.08830.01840.0982DFREE

0.41990.49350.72310.4475

DINT(%)

4.33662.8072

1.63212.3813

Ln(Amount)

4.75500.8401

3.97840.9452.

.

0.96780.548913.7034

11.500321.2006

4.9861VCONV
Callable life span(year)

35

Figures 5 and 6 show the distribution of the callable life span (t 3 − t1 ) for the subsample of callable non-convertible bonds and the sub-sample of callable convertible bonds.
Here we are using an absolute time scale, not a relative one. By looking at these figures,
we can see how the callable life span has different lengths across different callable bonds.

<Figure 5> Histogram showing callable life span: callable non-convertible bonds

36

<Figure 6> Histogram showing callable life span: callable convertible bonds

6. Results

In this section, we present the estimation results for the call hazard rate function
for each of the non-convertible bonds and the convertible bonds. Tables 6 and 7 show theseresults. In the Appendix, we also present other call hazard function estimates. For thispurpose, each sub-sample of the non-convertible bonds and the convertible bonds arefurther classified according to the presence or absence of the conditional call protection
period. Tables 9-12 in the Appendix show these results. Findings are basically the same as37

those reported in Tables 6 and 7 other than that the statistical significance in general drops
due to sample split.

<Table 6> Call hazard function estimates: non-convertible bonds

Variable

Estimate

Expected
Sign

Standard
error

t-valuep-valueConstant

-2.62

0.38

-6.97

0.00

D[0,0.1]

1.57

0.22

7.15

0.00

D(0.1,0.2)

0.77

0.23

3.36

0.00

D(0.2,0.3)

0.83

0.24

3.46

0.00

D(0.3,0.5)

0.78

0.23

3.45

0.00

FASS

0.39

0.34

1.15

0.25

DEBT

-2.23

0.40

-5.59

0.00

PRO

4.98

1.21

4.10

0.00

DFREE

0.66

0.18

3.61

0.00

DINT

0.12

0.06

1.95

0.05

DINT•Ln(Amount)

0.06

0.01

5.35

0.00

Callable life span

5.75

2.36

2.44

0.01

D[0,0.1], D(0.1,0.2], D(0.2,0.3] and D(0.3,0.5] are time-dummy variables defined on the intervals [0,0.1], (0.1,0.2], (0.2,0.3]
and (0.3,0.5] respectively.
FASS is the ratio, (fixed asset)/(total asset).
DEBT is the ratio, [(total liability)/(total asset)].
PRO is the ratio, (net income)/(total asset).
DFREE is the dummy variable measuring freedom from conditional call protection periods. It is time varying and takes thevalue 0 if the callable bond is prohibited from being called by a conditional protection clause, and 1 otherwise.
DINT is the difference, the bond’s interest rate minus the one-year Treasury bill rate.
Ln(Amount) is the natural logarithm of the authorized amount of the bond issue measured in 1 million dollars.
Callable life span is the length of time from t1 to t3 measured in 100 thousand days.

38

<Table 7> Call hazard function estimates: convertible bonds

Variable

Estimate

Expected
Sign

Standard
error

t-valuep-valueConstant

-4.78

1.24

-3.84

0.00

D[0,0.1]

0.87

0.76

1.15

0.25

D(0.1,0.2]

1.30

0.69

1.87

0.06

D(0.2,0.3]

0.36

0.77

0.47

0.64

D(0.3,0.5]

0.74

0.71

1.04

0.30

FASS

0.90

0.52

1.72

0.09

DEBT

1.39

0.93

1.49

0.14

PRO

6.48

2.32

2.80

0.01

DFREE

0.67

0.37

1.82

0.07

DINT

-0.13

0.12

-1.07

0.29

DINT•Ln(Amount)

0.09

0.04

2.28

0.02

VCONV

1.11

0.20

5.69

0.00

Callable life span

20.49

9.82

2.09

0.04

VCONV is the normalized stock price so that the price at the time of issuance is one.

The findings can be summarized as follows. First, calling a non-convertible bondis not expedited as the cost of financial distress increases. This effect is not statisticallysignificant for the callable non-convertible bonds, whereas this effect is marginallysignificant at 10% level for the callable convertible bonds. Calling a convertible bond is
weakly expedited as the cost of financial distress increases. Comparing Tables 9-12 in the39

Appendix, this effect is only statistically significant for the convertible bonds without aconditional call protection clause.
Second, calling tends to be deferred in the case of callable non-convertible bonds
if the potential agency cost of debt is large. This effect cannot be found for the callable
convertible bonds (wrong in sign, though insignificant). This supports the postulation thatthe distortion of manager incentive in a levied firm can be mitigated if a callable nonconvertible bond is outstanding. Results in Tables 9-12 in the Appendix are basically thesame.
Third, a firm tends to speed up calling if favorable information is released afterissuance. Excepting one case, this effect is found significant regardless of convertibility
and whether or not each sub-sample is further split based on presence/absence of aconditional call protection clause. In the case of convertible bonds with a conditional callclause, the profitability variable turns out insignificant. This is potentially due to the factthat a call is possible only when stock value satisfies a certain condition under which
profitability measure (PRO) and the stock value (VCONV) would be highly collinear.
Fourth, freedom from conditional call protection clauses speeds up calling asshould be the case. Callable bonds of a longer life span tend to live a shorter percentage
life. These two effects are commonly found regardless of whether a callable bond is40

convertible or not.

Calling a convertible bond is expedited as the conversion value

increases, possibly due to conversion forcing call.
Fifth, to compare the effect on calling of the interest rate spread across nonconvertible and convertible bonds and to see how this effect interacts with the transaction
cost, we plot the estimated effects separately as a function of transaction cost. Specifically,
ht x
Figure 7 shows the estimated values of ∂ log ( | t ) / ∂DINT against ln(Amount)separately for each sub-sample.
As you see, the effect on calling of the interest rate spread is stronger for the nonconvertible bonds than for the convertible bonds. For both types of bonds, this effectincreases in ln(Amount) suggesting that the interest effect gets stronger as the unit
refunding transaction cost drops.

41

<Figure 7> Estimated effect of DINT in each sub-sample

The following table numerically summarizes the above graph by showing theestimated effects together with their standard errors as computed at three levels of thetransaction cost for each sub-sample.

<Table 8> Estimated effect of DINT in each sub-sample
Non-convertible bonds
Transactionln(Amount)
Cost

Convertible bonds

Estimated effect

S.E.

Estimated effect

S.E.

High

2.5

0.266

0.050

0.084

0.042

Medium

4.0

0.353

0.057

0.214

0.036

Low

5.5

0.441

0.103

0.344

0.036

42

Sixth, the baseline hazard function shows a monotonically decreasing pattern for
the non-convertibles bonds, but not for the convertible bonds. Tables 9-12 in the Appendix
show that this monotonic pattern is in fact only significant for the non-convertible bonds
without a conditional call protection clause, which is consistent with our prior expectation.
Lastly, in other model specifications not reported here (available upon request), we
have included return volatility as an additional determinant of the call hazard rate. We have
tried two different measures. One is the standard deviation of the stock rates of returnusing the most recent 12-month data, and the other using the most recent 24-month data.
These volatility measures are time-varying in that they measure the volatility using themost recent data at each point in time. Option theory predicts that the higher the rate of
return volatility, the higher the value of the conversion option. Return volatility would givefirms an incentive to exercise the call option early to preempt the conversion option of thebond holders. In our estimation, none of the volatility measures turns out statisticallysignificant, convertibles or non-convertibles.

43

7. Concluding remarks

The empirical results are consistent with the theoretical predictions that the cost offinancial distress expedites calling, of which the effect is only marginally significant for theconvertible bonds but not significant for the callable non-convertible bonds; and that acallable non-convertible bond mitigates the agency cost of debt because firms that arehighly in debt delay calling a callable non-convertible bond.
This paper shows that a callable bond, convertible or not, is called to issue a new
security if the market interest rate falls; that the interest effect becomes stronger as thetransaction cost of refunding is low; that calling a callable convertible bond is significantly
expedited by a rise in the conversion value, which suggests that firms often call callable
convertible bonds to force a conversion; and that calling a callable bond, convertible or not,is significantly expedited if favorable information is released after issuance, which supports
the view that callable bonds mitigate the problem of adverse selection under information
asymmetry.
Additionally, this paper shows that callable bonds of a longer life span tend to live
a shorter percentage life; and that after the end of call protection periods the call intensity
monotonically decreases for the non-convertible bonds but not for the convertible bonds.
44

The empirical results in this paper lend a support to the view that a convertible bondis partly an equity-like issue (Stein 1992) and partly a debt-like issue (Smith and Warner
1979; Green 1984). On one hand, callable convertible bonds are often called to force a
conversion, suggesting that a callable convertible bond is an instrument of deferred equity
financing. On the other hand, callable convertible bonds are not a perfect equity-equivalent
security. Calling a callable convertible bond is also heavily affected by the refunding
opportunity measured by the coupon rate minus the market interest rate, which is a property
of debts.

45

Appendix: Measurement issues, descriptive statistics, and other results

The measurement of time

Let us explain the various time concepts, the time intervals, and normalized time
to call by using an example. Consider a convertible bond in Table 2 that was issued by
Action Industries Inc. on April 1, 1983. The absolute call protection period ended on April
1, 1985. The company called the bond on July 1, 1993 before it matures on April 1, 1998.
There is no conditional call protection period. Using the notation defined in the text, wehave t 0 = 1983 / 04 / 01 (April 1, 1983), t1 = t 2 = 1985 / 04 / 01 , t c = 1993 / 07 / 01 , andt 3 = 1998 / 04 / 01 . The callable life span is computed as follows (using one year as themeasurement unit):t 3 − t1 = (1998 − 1985) + (4 − 4) / 12 + (1 − 1) / 365 = 13.

Thet c − t1 = (1993 − 1985) + (7 − 4) / 12 + (1 − 1) / 365 = 8.25 .

Finally, the normalized time is

time

to

call

is

computed as t = (t c − t1 ) /(t 3 − t1 ) = 8.25 / 13 = 0.6346 . The callable bond is called ataround 63% location of its callable life.
For some observations, various calendar times are available up to a specific date; for others,
they are only up to months or years. In the latter case, we need approximations. We adopt
46

mid-point approximation within an interval. For example, when a date is known only up toa year, say 1999, then 1999/07/01 is assigned. When a date is known up to a month, say
May 1999, 1999/05/16 is assigned.

Normalization and time varying explanatory variables

At each moment in time, the decision to exercise a call or not is made based onwhatever information is then available. In our data set, some explanatory variables aremeasured annually and others monthly. Suppose it is July 10, 1986. To the corporate
manager, yearly data is available for the years up to and including 1985 (up to the previousyear) and monthly data is available for the months up to and including June 1986 (up to theprevious month). We assume that data for the current year is not available for the yearlydata and similarly that data for the current month is not available for the monthly data.
In our data set, variables such as FASS, DEBT and PRO are recorded annually,and variables such as DINT and VCONV are recorded monthly. These variables form timevarying explanatory variables in our estimation. For these time varying variables, we
assume that the most recently available data affect the decision to call and thus appear in
the call hazard rate function. For example, in specifying the hazard rate for July 10, 1986,47

year 1985 values are used for the yearly recorded explanatory variables, whereas June 1986
values are used for the monthly recorded explanatory variables.
Let us try to understand the way the time varying explanatory variables are
rearranged according to the normalized time. This understanding is very important for
properly assigning a likelihood value to each individual observation. Note that our hazard
rate model uses the normalized time scale, whereas the data are recorded according tocalendar time. We have to reconcile this discrepancy. Since our explanatory variables arerecorded discretely, we assume that each explanatory variable only varies across different
observation intervals and stays the same within each observation interval.
For each callable bond, we observe a realized sample path of each explanatory
variable from birth to death, where a death is defined as the earliest time point among calltime, right-censoring time, and maturity time. At a point in time between birth and death,the relevant explanatory variable value affecting a manager’s call decision is the mostrecent one. For each time-varying explanatory variable, collection of the relevant values
over the course of a call life will form a sample path. Once a realization of an explanatory
variable path is thus constructed, we map it on to the normalized time scale. The resulting
sample path in the unit time interval will be a step function covering the time horizon from48

birth to the percentage death point. The number of steps will be larger for the monthly
recorded data and smaller for the yearly recorded data.
Once the sample paths are constructed over the unit interval for the time varying
explanatory variables, we can easily compute individual likelihood values. This is because
the integration appearing in the likelihood function (see subsection 4.4 of the text) reduces
to summation due to the step function nature of the time varying explanatory variables aswell as of the baseline hazard function.
Note that we have already modeled the baseline hazard function as a step function
with five steps partitioning the unit interval. The partition points can be represented as aset: A={0, 0.1, 0.2, 0.3, 0.5, 1}. Given a callable bond, the sample path of a monthly
recorded explanatory variable will be a step function over the unit interval. This step
function will partition the unit interval. Let us refer to the resulting set of partition points as
B, which is common to all monthly data. Similarly, let us refer to the set of partition points
for the yearly recorded data as C. Of course, C will be a subset of B. Let D be the union of
the above three sets, A, B, and C.
Then, the hazard rate function h(t | xt ) = h0 (t ) exp( xt ' β ) itself will become a step
function in the unit interval with steps shifting only at points in set D. Using this hazard
rate path, we can easily assign individual likelihood values. Note that sets B and C (and49

thus D) will be different depending on individual call structures. Therefore, we have toassign individual likelihood values on an individual basis.

Other descriptive statistics

Figures 8 and 9 show the distribution of the normalized time to the end of theconditional call protection periods for those bonds with a conditional call protection clause
for the sub-sample of non-convertible bonds and the sub-sample of convertible bonds. The
convertible bonds have shorter percentage life covered by a conditional call clause than the
non-convertible bonds.

50

<Figure 8> Histogram showing normalized time to the end of the conditional call protection period:
callable non-convertible bonds<Figure 9> Histogram showing normalized time to the end of the conditional call protection period:
callable convertible bonds

51

To account for right-censoring, we compute Kaplan-Meier survival function
estimates. Figures 10 and 11 show the Kaplan-Meier survival function estimates for the
sub-sample of non-convertible bonds and the sub-sample of convertible bonds. From
Figures 10 and 11, we observe that about two thirds of calls are made before 50% locationof its callable life span for the callable non-convertible bonds, whereas about three fourthsof calls are exercised before 50% location of its life span for the callable convertible bonds.

<Figure 10> Survival function estimate for normalized time to call: callable non-convertible bonds

52

<Figure 11> Survival function estimate for normalized time to call: callable convertible bonds

Figures 12 and 13 show the distribution of the normalized time to call for the subsample of non-convertible bonds and the sub-sample of convertible bonds.

These

histograms are constructed using the information contained in Figures 10 and 11. Theyshow the relative frequency of time to call for each decile of callable life span (10 bars
in the middle), proportion of calls made exactly at absolute call ending point (thick line on
the left), and the proportion of calls not exercised until maturity (thick line on the right).
By comparing Figures 12 and 13, we observe that the time to call is more spreadthroughout its life for the non-convertible bonds than for the convertible bonds. As you see,53

11.7 % of calls are made right after the absolute call protection period ends whereas 19.7%
of calls are left unexercised until maturity for callable non-convertible bonds. These figuresare 2.4% and 13.9% for the callable convertible bonds.

<Figure 12> Histogram showing normalized time to call: callable non-convertible bonds

3 0 .0 0

relatve frequency(%)

2 5 .0 0

2 0 .0 0

1 5 .0 0

1 0 .0 0

5 .0 00 .0 00

0 .0 0 .1 0 .1 0 .2 0 .2 0 .3 0 .3 0 .4 0 .4 0 .5 0 .5 0 .6 0 .6 0 .7 0 .7 0 .8 0 .8 0 .9 0 .9 1 .0

no rm a lized tim e to ca ll

541

<Figure 13> Histogram showing normalized time to call: callable convertible bonds

3 0 .0 0

relatve frequency(%)

2 5 .0 0

2 0 .0 0

1 5 .0 0

1 0 .0 0

5 .0 00 .0 00

0 .0 0 .1 0 .1 0 .2 0 .2 0 .3 0 .3 0 .4 0 .4 0 .5 0 .5 0 .6 0 .6 0 .7 0 .7 0 .8 0 .8 0 .9 0 .9 1 .0

1

no rm a lized tim e to call

To see whether the normalized time to call differs systematically across callable
bonds of different life spans, we draw scatterplots of the normalized time to call against thecallable life span for the sub-sample of non-convertible bonds and the sub-sample ofconvertible bonds. Figures 14 and 15 show these scatterplots. We also include simple
linear regression lines with correlation coefficients.

55

<Figure 14> Scatterplot showing normalized call time vs. callable life span: non-convertible bonds

1 .2

normalized time to cal

1 .0

y = ‑ 0.00 41x + 0 .3 433
r = ‑ 0.16 19 6

0 .8

0 .6

0 .4

0 .2

0 .0
0

5

10

15

20

25

30

35

40

ca lla b le life sp a n(yea r)<Figure 15> Scatterplot showing normalized time to call vs. callable life span: convertible bonds

1 .2

normalized time to cal

1 .0

y = ‑ 0.01 19x + 0 .4 753
r = ‑ 0 .3 87 79

0 .8

0 .6

0 .4

0 .2

0 .0
0

5

10

15

20

ca lla b le life sp a n(yea r)

56

25

30

35

These scatterplots show that a callable bond with a longer life span is called earlier
in terms of percentage of life. This is true for callable non-convertible bonds as well as forcallable convertible bonds. We naturally expect that the call hazard rate would be higher
for a callable bond with a longer life span than for a similar bond with a shorter life span ateach percentage point in callable life.

Other estimation results

Tables 9-12 show the call hazard function estimates for each of four sub-samples
classified by convertibility and presence/absence of conditional call protection periods.

57

<Table 9> Call hazard function estimates: non-convertible bonds with conditional call clause
Variable

Estimate

Standard error

t-valuep-valueConstant

-2.75

0.81

-3.37

0.00

D[0,0.1]

-0.56

0.65

-0.87

0.38

D(0.1,0.2)

0.00

0.59

0.00

1.00

D(0.2,0.3)

-0.09

0.57

-0.16

0.88

D(0.3,0.5)

0.28

0.46

0.62

0.54

FASS

-0.03

0.47

-0.07

0.94

DEBT

-2.08

0.60

-3.47

0.00

PRO

4.92

1.64

3.00

0.00

DFREE

0.48

0.37

1.30

0.19

DINT

0.15

0.12

1.22

0.22

DINT•Ln(Amount)

0.08

0.02

3.70

0.00

Callable life span

14.33

4.00

3.58

0.00

58

<Table 10> Call hazard function estimates: nonconvertible bonds without conditional call clause
Variable

Estimate

Standard error

t-valuep-valueConstant

-1.70

0.39

-4.30

0.00

D[0,0.1]

2.18

0.25

8.65

0.00

D(0.1,0.2)

0.57

0.31

1.82

0.07

D(0.2,0.3)

0.86

0.31

2.79

0.01

D(0.3,0.5)

0.81

0.29

2.83

0.00

FASS

0.40

0.41

0.97

0.33

DEBT

-2.21

0.55

-4.05

0.00

PRO

5.18

1.68

3.08

0.00

DINT

0.07

0.07

0.99

0.32

DINT•Ln(Amount)

0.05

0.01

4.32

0.00

Callable life span

-0.32

3.12

-0.10

0.92

59

<Table 11> Call hazard function estimates: convertible bonds with conditional call clause
Variable

Estimate

Standard error

t-valuep-valueConstant

-4.13

1.09

-3.78

0.00

D[0,0.1]

0.10

1.21

0.08

0.94

D(0.1,0.2)

0.49

0.86

0.57

0.57

D(0.2,0.3)

-1.28

0.88

-1.45

0.15

D(0.3,0.5)

-0.36

0.64

-0.57

0.57

FASS

-0.29

0.80

-0.37

0.72

DEBT

2.93

1.49

1.97

0.05

PRO

0.78

3.67

0.21

0.83

DFREE

0.92

0.78

1.18

0.24

DINT

-0.90

0.28

-3.24

0.00

DINT•Ln(Amount)

0.27

0.08

3.65

0.00

VCONV

2.60

0.29

8.92

0.00

Callable life span

-0.14

13.00

-0.01

0.99

60

<Table 12> Call hazard function estimates: convertible bonds without conditional call clause

Variable

Estimate

Standard error

t-valuep-valueConstant

-3.89

1.67

-2.33

0.02

D[0,0.1]

0.75

1.01

0.75

0.45

D(0.1,0.2)

0.96

0.88

1.09

0.28

D(0.2,0.3)

0.25

0.99

0.26

0.80

D(0.3,0.5)

-0.34

1.06

-0.32

0.75

FASS

1.54

0.68

2.27

0.02

DEBT

0.30

1.43

0.21

0.84

PRO

7.03

2.57

2.73

0.01

DINT

0.07

0.14

0.49

0.63

DINT•Ln(Amount)

0.02

0.05

0.52

0.61

VCONV

1.00

0.21

4.75

0.00

Callable life span

23.80

14.53

1.64

0.10

61

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66