1

Managerial Decisions and Credit Ratings – New

Evidence

Abstract

Survival analysis of the timing of in-the-money bond calls reveals that managerial decisions to call such

bonds are strongly linked to bond rating changes. Specifically, firms delay calls after downgrades, or

hasten them following upgrades. Our results demonstrate that managers react to ratings in a timelier

manner than shown in prior studies relating ratings to managerial decision making.

1. Introduction

In theory, the optimal time for an issuer to redeem a callable bond is generally the first

time that the market price exceeds the call price, i.e., when the call option goes in-the-money

(Brennan and Schwartz, 1977; Ingersoll, 1977). However, in our sample of called bonds, we

find that there are significant deviations from this theoretical prescription. We hypothesize that

one of the main drivers for this deviation is the link between managerial decisions and the time

varying nature of the issuing firm’s credit rating. Our view is motivated by recent empirical work

of Kisgen (2006), Kisgen (2009), and Hovakimian, Kayhan, and Titman (2009) which shows

that managerial decision-making is associated with their firms’ credit ratings. In addition to these

empirical papers, Graham and Harvey’s (2001) survey of chief financial officers identified credit

ratings as important to managers. However, none of these aforementioned papers (i.e., Kisgen

(2006), Kisgen (2009) and Hovakimian, Kayhan and Titman (2009)) examine the relationship

between credit ratings and bond calls.

We predict that managers use asymmetric information about their firm including

impending rating changes to delay or hasten a call. Testing for this effect of rating changes on

calls is complicated by the time-varying nature of firm fundamentals, including the ratings

2

themselves. We use survival analysis to address credit ratings and other variables that trigger a

call. Employing survival analysis is an important contribution to the literature examining call

timing because unlike previous research, which uses conventional regression analysis, the former

incorporates the dynamic effects of variables that are related to the call decision. Specifically, the

proportional hazard model, which accounts for how factors affect an “at risk” population over

time, can be employed to model the call decision over the life of the bond. Survival analysis

supports the examination of time variation in interest rates, firm value, and importantly, credit

ratings, which can jointly trigger the call decision (Sarkar, 2001; Acharya and Carpenter, 2002).

This methodology enables us to provide unique insights into the call decision.

Our paper not only buttresses prior evidence, but also persuasively demonstrates the link

between credit ratings and bond calls due to the granularity associated with the month by month

ratings data that we employ on every bond. We are able to pin down a more timely connection

between ratings and managerial decisions than has been achieved in Kisgen, 2006; Kisgen, 2009;

Hovakimian, Kayhan, and Titman, 2009.1 It adds another dimension to the findings on the

relevance of bond ratings in managerial decision making, and provides empirical validation for

the survey evidence in Graham and Harvey (2001).

Theory suggests that it would be inefficient to call a bond that is out-of-the-money. To

rationalize such calls, Vu (1986), Kish and Livingston (1992), Mann and Powers (2003), Nayar

and Stock (2008), and Powers and Tsyplakov (2008) have suggested explanations that are based

on market frictions such as agency costs and asymmetric information – eliminating covenants or

increasing flexibility to enable restructuring, even though such transactions may not decrease the

firm’s interest expense burden. We find that issuers who call when the call option implicit in

1 Note that Kisgen (2006), Kisgen (2009) and Hovakimian, Kayhan, and Titman (2009) reach their conclusions using static

techniques and coarser data on ratings.

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their bonds is out-of-the-money are structurally different from those who wait until the bonds go

in-the-money or delay beyond that point. Therefore, we separate in-the-money and out-of-the-

money bonds, unlike prior work on bond calls.

For in-the-money bond calls, our results using survival analysis indicate that firms delay

calls when they have received a downgrade or accelerate calls following an upgrade. Using the

path of ratings over time, we can see whether ratings are related to the call decision. The

dynamic analysis relates managerial decisions and rating changes, as opposed to just rating level,

in a more persuasive manner than prior studies based on Ordinary Least Squares (OLS)

methodologies. We also show that firm profitability, the persistence with which a bond stays in-

the-money, opportunity cost and yield curve steepness can all hasten calls. By (i) using survival

analysis to examine time-varying data, (ii) employing a comprehensive dataset of bond calls with

transaction bond prices, and (iii) separating bond calls by moneyness, we are able to provide new

insights into the timing decision behind bond calls.

The rest of this paper is organized as follows. We review the literature and develop our

hypotheses in Section 2. In Section 3, we discuss our data, the timing convention used in creating

our dependent variable measuring call delay, and empirical methods. In Section 4, we present the

results of our analyses, and we conclude in Section 5 with a summary of the results.

2. Literature and Hypothesis Development

2.1 Relationship between the call decision and credit ratings

Since one of our main research questions is the link between the call decision and credit

ratings, we first discuss how these two concepts are connected. A call feature on a bond enables

the issuing firm to retire the bond issue prior to its stated maturity at a pre-specified price. The

firm can thus reduce borrowing costs if interest rates decline by refinancing the previously issued

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higher rate debt with newly issued lower cost debt. There are two possibilities underlying this

logic of including the call feature in a bond issue to take advantage of cheaper future interest

rates.

Given that the rate payable on corporate borrowings is the sum of two components – a

maturity-based risk-free rate, and a credit spread based on the default risk of the firm – cheaper

future interest rates may come about because of a decrease in the risk-free rate, a decline in the

credit spread because of reduced default risk, or both. Managers may include a call option

because they either believe that they are better forecasters of the future risk-free rate, or will face

smaller credit spreads in the future. The former is rather implausible, while the latter seems to be

more reasonable given that managers have asymmetric information about their firm’s prospects

(e.g., Myers and Majluf, 1984). In fact, asymmetric information is frequently the basis for

theoretical explanations rationalizing the existence of the call option as an optimal security

design feature. In this respect, the call feature may (i) address agency costs (Smith and Warner,

1979; Myers, 1977), (ii) serve as a signal of positive information (Robbins and Schatzberg,

1986), and (iii) serve to provide financial flexibility if future restructuring is necessary (Mann

and Powers, 2003; Nayar and Stock, 2008).

Including such a call feature is not costless, since the issuer of bonds typically has to pay

a premium for its inclusion over an otherwise noncallable bond. While the inclusion of call

options in the context of agency and adverse selection costs has been explored in prior literature

(e.g., see Myers, 1977; Robbins and Schatzberg, 1986; Mann and Powers, 2003; Nayar and

Stock, 2008), we discuss the call option with respect to its relationship to the manager’s decision

to call the bond when ratings change.

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The premium the issuer pays to include the call feature is a costly signal that is justified

only if the firm’s credit spread declines in the future, and the firm is able to refinance at cheaper

future rates. Sarkar (2001) shows the link between the probability of a call and its inclusion in a

bond issue. If this logic is valid, then managers who include a call option in their bond issue must

be anticipating a reduction in their future default risk. When this reduction in default risk occurs,

it is “recognized” by the market when the firm’s credit rating is upgraded. A manager then

rationally calls the bond and is able to refinance at lower rates commensurate with the new

superior credit rating. Thus, the exercise of the call option in response to a credit rating upgrade

is an outcome of the inclusion of the call feature to address asymmetric information related

costs.2 Analogously, a manager may delay an in-the-money call in anticipation of an upgrade in

the near future.

Several studies have shown that credit ratings are important for debt policy. In Graham

and Harvey’s (2001) survey of Chief Financial Officers (CFOs), 57% of respondents stated that

credit ratings were important or very important in determining their firm’s debt policy. On the

empirical front, Kisgen (2006) shows that firms adjust the mix of their debt and equity issuance

in anticipation of a rating change, and Kisgen (2009) presents evidence that firms target

minimum rating levels. Hovakimian, Kayhan and Titman (2009), in a comprehensive study of

several transactions and controlling for the endogeneity between target debt levels and ratings,

demonstrate that managers target ratings when they make decisions about securities issuances,

repurchases, acquisitions, and dividend changes. This evidence is to be expected, since rating

changes convey information to investors, and can have valuation implications for the affected

firms. This is primarily because ratings are used as metrics in investment management and in

2 For example, a firm’s bonds may not be on the candidate list of certain mutual funds because the credit rating does not satisfy

minimum rating requirements of the fund. A credit rating upgrade may open up that barrier, adding to the demand for the firm’s

bonds, which further reduces the yield on the bonds.

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regulation (Cantor and Packer, 1994). Given this importance of credit ratings to both managers

and investors, it is surprising that the literature establishing the link between ratings and the call

decision is sparse. Consequently, our study, which provides the first conclusive evidence of this

link, makes a key contribution to the literature on managerial decision making related to bond

calls.

2.2 Optimal call policy and timing

While several studies have explored an issuer’s decision to include a call option in an

issue (e.g., Kish and Livingston, 1992; Ederington and Stock, 2002; Mann and Powers, 2003;

Nayar and Stock, 2008), relatively few have analyzed the issuer’s propensity to call a bond.

Early theoretical studies (Brennan and Schwartz, 1977; Ingersoll, 1977) concluded that, under

perfect capital markets, the optimal policy would be to call the bond the first time its market

price reaches the call price (the first hitting time). Based on agency theory, once a bond is issued

by a firm, the objective of the issuer is to maximize the value of the equity of the levered firm, as

opposed to maximizing overall firm value. If the bond’s market price equals or exceeds the call

price (i.e., the call option of the bond is in-the-money3) and the issuer does not call the bond, the

equity holders are not minimizing the value of debt.4 Given this view, a delay in calling is

unexpected since it is actually a loss to shareholders.

Sarkar (2001) and Acharya and Carpenter (2002) model the optimal points at which a

bond will be called or will default as jointly determined to maximize the equity value of the firm.

Sarkar (2001) asserts that the optimal call premium, and therefore, the probability of the call

3 We include bonds that are at-the-money (full market price equals the effective call price) when referring to bonds that are in-

the-money.

4 Out-of-the-money exercise would not be consistent with either option theory or agency theory. If the bond’s market price is

below the call price (i.e., the bond is out-of-the-money), and the issuer calls the bond, a gain is being conferred on the

bondholders (Brennan and Schwartz, 1977). Consequently, there must be other explanations for such calls.

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being exercised, is influenced by the value of the firm. He predicts that the probability of a call

decreases with the volatility of firm value and bankruptcy costs.

King and Mauer (2000) investigate call delay using an OLS regression equation for a

sample of calls of nonconvertible bonds over the period January 1973-March 1994. They group

together bonds called out-of-the-money, bonds called immediately after going in-the-money, and

in-the-money bonds called after a delay.5 We compare in-the-money (immediate and delayed

callers) with out-of-the money callers to see if the issuers or bonds are structurally different. If

this is the case, then analysis of the two groups’ call behavior should be performed separately.

King and Mauer’s (2000) use of OLS does not allow for dynamic examination of the

decision to call a bond. Our use of survival analysis is thus a methodological improvement over

their OLS-based study. Since a hazard function dynamically evaluates the characteristics of firms

that call with those who can possibly call, survival analysis can better compare the rating status

of those who do call with those who are eligible to call in each period. This is particularly useful

in understanding call behavior, where the decision of whether or not to redeem is constantly

being reevaluated depending on ratings and other variables that are evolving over time. OLS can

only capture the average relation between call decisions and firm, bond, or economic

characteristics in a static framework.

Two other studies have used survival analysis to examine calls of bonds. McDonald and

Van de Gucht (1999) estimate hazard rate functions for calls and defaults of high yield bonds

issued during the 1977-1989 period. They find that the likelihood of a bond being called during

its call period (given that it has not defaulted) increases with initial maturity, issue size, and bond

age, and leading interest rates, but decreases with lagging interest rates. The aging aspect

5 King and Mauer (2000) assign a delay of zero months to the out-of-the-money callers and the immediate in-the-money callers,

and compute the delay in months from the first hitting time for the third group. They form two cohorts for their study – a cohort

consisting of all three groups (immediate, out-of-the-money, and delayed), and a delayed cohort consisting of just the third group.

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dominates the cross-sectional factors, however. They attribute 92% of the time variation in call

hazard to the pure aging of a bond. However, a drawback of their study is that they do not

explore individual issuer-firm characteristics, and therefore cannot exploit the richness of

explanations based on firm-specific factors for the timing of the call decision. Ryu and Wee

(2001) include firm characteristics in their survival analysis models but they do not examine the

possibility of the call decision being predicated on credit ratings. Given our discussion in section

2.1, ignoring ratings would indicate an omitted variable in their models. Thus, our study is a

richer and more comprehensive examination of bond calls compared to prior studies employing

survival analysis.

3. Data and Methods

3.1 Data

Bond characteristics (e.g., ratings, coupon rate, maturity, etc) and pricing information are

from the Warga Fixed Income Securities Database. Only public, senior, refundable corporate

notes and debentures are included in the study. Bonds in the initial sample are callable without

exception, and are not putable, convertible, nor have any other redemption features. Sinking fund

and first mortgage bonds are included. Foreign, Yankee, Canadian, REIT, Original Issue

Discount bonds, and bonds with less than one year to maturity are excluded.

All of the bonds in the study have call protection ending on or after January 1, 1973 and

are called before December 31, 1997. Our sample ends in 1997 since this is the last date of

coverage on the Warga Database.6 We used observations with quoted month-end prices, and

6 We are subject to this constraint because we need a time series sequence of month-end prices for the called bonds and the

Warga database is the only one with that data available to us at our universities. Further, while there are other sources of data that

are available (NAIC data from FISD, TRACE, etc), none of these databases provides a consistent data series which spans as long

a time period as the Warga database. Our usage of the Warga data therefore ensures data consistency and also a direct

comparison with earlier work.

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excluded any observations with matrix prices. A bond also had to have a quoted price (not a

matrix price) on its call announcement date to be included. For in-the-money bonds, the first

month-end observation where the bond’s full market price (market price plus accrued interest)

equaled to or exceeded the effective call price (call price plus accrued interest) also had to be a

quoted price for the bond to be included.

This leaves 595 bonds of 211 issuers, with a total of 41,134 quoted month-end prices for

the period of 1973-1997.7 Four hundred ninety-one bonds are called in-the-money, and 104 are

called out-of-the-money. The majority of both in- and out-of-the-money calls (91% and 71%,

respectively) took place in the 1990s, consistent with the lower interest rate environment during

the period.

None of our bonds are right-censored, because all of the bonds have been called by the

end date of December 31, 1997. We do, however, have right truncation, since experiencing the

event of interest (the call announcement) is the determining criteria for entry into the sample

(Hosmer and Lemeshow, 1999).8 While right truncation may inhibit us from accurately

estimating the median delay, it should not be an obstacle in drawing inferences about linkages

between the path of ratings and the eventual managerial decision to call the bond.9

Quarterly issuer and firm accounting data are from Compustat. The data matched to each

month is the data for the quarter in which that month is contained (for example, the financial

statement data for the first quarter of 1995 is matched to the January, February and March 1995

7 King and Mauer (2000) who also use the Warga database have a final sample of 1,642 called bonds by 530 issuers over the

period 1973-1994. Our sample is smaller than theirs despite a longer sample period because of our restriction involving quoted

month-end prices for the called bond. Thus, our sample is not directly comparable to theirs. Insomuch as our restriction causes a

bias due to the most liquid bonds being selected, the King and Mauer sample would include illiquid bonds and the attendant

effects of illiquidity. 8 An analogy would be in a medical study where the effect of a treatment is being studied. A death from the disease may occur

before the end of the study period, or the patient may still be alive at the end of the study period. The patients alive at the end of

the study are right-censored. We examine only the bonds that are called, which is comparable to including only the patients who

have died by the end of the study period.

9 Also see Lagakos, 1988; Kalbfleisch and Lawless, 1989 for issues related to right truncation.

10

pricing observations for a December fiscal year-end firm). Changes in financial data are

computed quarter-to-quarter and matched to the appropriate months for each quarter. In cases

where the issuer is a subsidiary which files its own financials, those data are used; otherwise, the

parent’s financials are used. The financial data covers 204 underlying filers (85 parent firms and

119 subsidiaries filing their own data). The observations that were not matched are either from

firms that did not file public financial statements, began their record in Compustat in a quarter

after bond pricing started, or were missing data (18 bonds).

Market capitalization data are from CRSP. Five hundred eighty-seven bonds have market

capitalization data from 175 underlying parent firms (some firms contain multiple issuers; some

issuers issue multiple bonds10

) matched to their monthly bond prices. The firms from the eight

bonds that were not matched were either private or had foreign parent companies. Treasury yield

data is from the Federal Reserve’s H15 publication. For time-varying covariates, such as

accounting data, market capitalization, and the risk-free rate, we use the observation as of each

month-end.11

The list of called bonds for the 1973-1994 period was obtained from King and Mauer

(2000).12

CUSIPs for bonds called during the 1995-1997 period were identified from Moody’s

Annual Bond Record. Call announcement dates for these bonds were obtained through Dow

Jones Factiva and Lexis-Nexis. Consistent with the mandated 30-day call notice period in most

bond indentures, we assumed a call announcement 30 days prior to the call for issues where no

10 For example, Southern Company is a holding company that includes Alabama Power Company, Georgia Power Company,

Gulf Power Company, and Mississippi Power Company, all of which file separate financial statements, and Savannah Electric &

Power Company, which does not. Alabama and Georgia Power are issuers of multiple callable bonds in the sample.

11 Since accounting data is only available on a quarterly basis, we assume that the month-end value is the same as the value that

existed at the preceding quarter-end for that month. This accounts for the earliest date that information is revealed.

12 The authors are extremely grateful to Professor Dolly King for providing the CUSIP numbers and call announcement dates for

these bonds, which were used in her study (King and Mauer, 2000).

11

call announcement was found in the press (120 bonds from the sample of 595).13

As in King and

Mauer (2000), we use the call announcement date instead of the actual date the bonds are

tendered since a bond’s market price will reflect the call price beginning on the day of the

announcement.

3.2 Measuring call timing

The event of interest is the call announcement. In order to separate the in-the-money

callers from the out-of-the-money callers, we need two metrics for the length of time that the

bond remains outstanding (i.e., is not called) while it is at risk of being called. Figure 1 illustrates

the timing convention.

< Insert Figure 1 here >

The call announcement date is time T. The time at which a bond first becomes at risk of

being called, in indexed time, is t0. As illustrated in Figure 1, t0 is the first time that two

conditions are satisfied – (1) the bond’s contractual call protection ends as specified in the

indenture (the first call date); and (2) the bond goes in-the-money (where its full market price at

least equals its effective call price (Brennan and Schwartz, 1977; Ingersoll, 1977). From a

“perfect markets” perspective, the bond would be called optimally the first time the bond

satisfies both these conditions, so the bond becomes “at-risk” for in-the-money callers. We

measure Delay as the time, in months, from t0 to the date of the call announcement (T – t0). The

natural logarithm of the hazard rate, which itself is an inverse function of Delay, is the dependent

variable in our survival analysis of the in-the-money sample of 491 bonds.

13 Ninety-nine bonds without cited call announcement dates were in-the-money bonds, and 21 were out-of-the-money bonds.

12

In our full sample, 104 bonds have been called, despite their market prices never equaling

or exceeding their call prices. Since there is no first hitting time, the first call date as specified in

the indenture is the first date the bond is at risk of call (t0΄ in Figure 1). We compute Time to call,

as the time, in months, from t0΄ to the date of the call announcement (T – t0΄). Time to call can be

computed for bonds that are called in-the-money as well, since we know the first call date t0΄ for

all callable bonds.

King and Mauer (2000) compute the delay in months from the first month-end for those

called after having gone in-the-money. They assign a delay of zero months to out-of-the-money

bonds that have been called. In our study, a Delay of zero is only assigned to in-the-money bonds

that were called immediately (in the same month that the call option went into the money). Delay

cannot apply to out-of-the-money bonds in our framework. We use Time to call for the direct

comparison of in-the-money and out-of-the-money callers. For the in-the-money call sample, the

values of the two variables, Delay and Time to call, are not equal unless the bond is already in-

the-money before call protection ends, and the bond is called optimally immediately upon

becoming contractually callable.

3.3 Hazard rate and survival functions

We use the Cox (1972) semi-parametric proportional hazard function to model the hazard

rate, which is the conditional probability that a callable bond will be called at time t. It is

conditional because if a bond is called, then it can no longer be part of the “at-risk” set for the

next interval.14

Since the hazard rate is always positive, Cox (1972) expresses the hazard

function for bond i in exponential form as:

14 Continuing the medical analogy, once a patient has died (i.e., experienced the event), he is no longer at risk for the event.

13

)(

0 )()(tx

iiett

(1)

where 0 (t) = the baseline hazard function, representing the rate at which a bond is called at each

time, t, depending solely on the passage of time, = vector of coefficients, and xi(t) = vector of

covariates for bond i measured at time t.

3.4 Separating in-the-money and out-of-the-money callers

Table 1 provides the mean and median values for our sample of 595 bonds called

between 1973 and 1997, along with results of Kruskal-Wallis tests of the hypothesis that there

are no differences in the distributions of the characteristics of in- and out-of-the money bonds.

< Insert Table 1 here >

For in-the-money callers, the median Time to call is 99 months and is negatively skewed;

for out-of-the-money callers it is 70 months. Based on a Kruskal-Wallis test, the distributions of

Time to call are significantly different for in-the-money and out-of-the-money callers. Time to

call for the in-the-money callers is longer than that for the out-of-the-money callers because the

in-the-money callers are waiting for the bond’s market price to reach its call price, while the out-

of-the-money callers are calling before this, presumably motivated by other factors. The mean

Delay is 11 months, and the median delay is eight months. Forty bonds are called immediately

upon going in-the-money, and therefore have a Delay of zero.

Table 1 shows that out-of-the-money callers are in a worse rating position than the in-the-

money callers at the time of the announcement.15

Although the median rating for both groups is

A2, the out-of-the-money cohort is skewed towards inferior ratings and vice-versa for the in-the-

15 The alphabetical rating is transformed into an ordinal rating index as it appears in the Warga database, and we employ that

measure for our rating variable. A larger value for this index implies a more inferior rating.

14

money cohort. The hypothesis that the distributions of ratings for the two groups are equal is

rejected at a significance level of 0.05.16

As measured by Leverage change, leverage falls after the call for the out-of-money group

and rises after the call for the in-the-money group. Leverage change is the percentage change in

the ratio of book value of debt to book value of debt plus market value of equity between the call

announcement date and one year later. We use Leverage change to assess the importance of

financial flexibility. Campbell and Harvey (2001) find that CFOs believe that financial flexibility

(59%) and credit rating (57%) are important or very important factors in choosing the amount of

debt for the firm. The difference in Leverage change between the in- and out-of-the-money

groups is statistically different from zero, and is seven percentage points in economic terms,

which represents an approximate change in Total Long-Term Debt of $81 million on average for

the out-of-the-money callers.17

Finally, out-of-the-money callers are on average more profitable than in-the-money

callers in the year prior to the call, although profitability is not statistically significantly different

between the two groups. We measure Profitability as the percentage change in earnings before

interest and taxes (EBIT) for the year leading up to the call announcement.

Taken together, the more inferior rating, the reduction in leverage, and the increased

profitability of out-of-the-money callers suggests that these firms may be taking advantage of

their profitability to reduce leverage, and thereby trying to improve their ratings. These results

16 This difference can be material: for example, Damodaran (http://pages.stern.nyu.edu/~adamodar/) suggests that a difference in

credit rating from A to A- could translate into a yield spread differential of 20 basis points for a large manufacturing company, as

of January 2008.

17 King and Mauer (2000) find that leveraging-increasing calls (measured over the year around and after the call announcement)

have a positive effect on stock prices, while leverage-decreasing calls have a negative effect on stock prices. They combine in-

and out-of-the-money bonds in their event sample. It is not clear how this might have affected the announcement effects. We

found that marginal tax rates were not significant in our hazard analysis (not shown). Further, only 10% of CFOs surveyed by

Campbell and Harvey (2001) said the signaling effect of debt had an important or very important influence on debt policy.

http://pages.stern.nyu.edu/~adamodar/

15

are consistent with the view that managers are targeting their debt ratings when they make

capital structure decisions.

The in-the-money callers are calling in a lower interest rate environment (median ten-

year Treasury yield at time of call of 6.26% for the in-the-money group versus 6.95% for the out-

of-the-money group). The Yield curve slope in the month of the call announcement, as measured

by the yield differential between the ten-year Treasury and the one-year Treasury as a percentage

of the ten-year Treasury yield, is steeper at the time of the call announcement for the in-the-

money callers (median of 0.41% versus 0.37%). The combination of differences in yield curve

level and slope effects (each of which is significant at the 1% level) suggest that refinancing at

lower rates may not be the motivation underlying out-of-the-money calls.

In Figure 2, we use the Kaplan-Meier estimator (Cox, 1972) to depict the survival

functions for the in-the-money and out-of-the-money groups. Ŝ(t) is the estimate of the

cumulative probability of bond i not being called at the kth

time, conditional on the bond having

been contractually callable, but having not been called up to the (k-1)th

time:

)(ˆ

)( )(

)()(

tt t

tt

k k

kk

r

mrtS (2)

where r is the number of bonds at risk at time t(k), and m is the actual number of bonds called at

time t(k). The index k indicates the rank-ordered survival times. For example, t(1) is the first time

at which any bond(s) are called; t(2) is the second time at which any bond(s) are called; t(k) is the

kth

time at which any bond(s) are called.

< Insert Figure 2 here >

The survival functions illustrate the probability that a bond will remaining outstanding in

month t, given that it was not called in month t-1. In the first five months after call protection

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ends, the two groups experience very similar survival. After that, the increasing rate of calls for

the out-of-the-money sample causes the survival function for this group to lie below the in-the-

money group. The log-rank, Wilcoxon and likelihood ratio test (not shown) all reject the null

hypothesis of no difference between the survival functions of the two cohorts at the one percent

significance level.

The results of the Kruskal-Wallis tests on the covariates from Table 1, the graph of the

survival function in Figure 2, and the results of the homogeneity tests of the survival functions

all support significant structural differences between bonds that are called having been in-the-

money and those that are called never having been in-the-money. Given this heterogeneity,

separating in-the-money and out-of-the-money callers is important because it allows for a clearer

analysis of the factors that relate to call timing. The rest of the paper focuses on analyzing the in-

the-money group.18

3.5. Estimating the hazard function

We estimate the hazard rate function using a semi-parametric partial likelihood function

(Cox, 1972). The partial log-likelihood function is:

lnln1 )( )(

)(

K

k tRr

x

p

k

rexL

(3)

where x(r) is the vector of covariates for the bond called at time t(k); is the vector of coefficients;

K is the total number of bonds and ordered survival times; and R(t(k)) is the set of bonds at risk at

time t(k). This is a proportional hazards model, where we are estimating the hazard function of

bond i called at time t(k) relative to the hazard functions of all the bonds at risk at time t(k). The

18 We focus on the in-the-money group since the puzzle of calling beyond the theoretically optimal call point only applies to

these calls. Further, the calls that occur out-of-the-money are apparently motivated by restructuring reasons (e.g., as in Mann and

Powers (2003)). We leave it to future research to expand on these types of calls.

17

model assumes that while the hazard function for each bond may change over time, the ratio of

the hazards is time invariant (Hosmer and Lemeshow, 1999).

The proportional hazards model has two advantages: the baseline hazard function as

shown in Equation (1), λ0(t), divides out of the numerator and denominator, so we do not need to

specify a distribution for the baseline hazard; and the model can accept time-dependent

covariates (Allison, 1995). Time-dependent covariates are of particular use in our study, where

the path of variables over time factors into the call decision. Our proportional hazards model

estimates the risk of a bond being called at time t given that it has not been called up to that

point, based on the relationship between Delay and the covariates. We do this by estimating the

natural logarithm of the hazard function, which is a function of Delay. Therefore, the parameter

estimate for the hazard has a negative relationship to the effect on Delay. Forty-four bonds were

eliminated from the sample for the hazard analysis because they did not have enough consecutive

monthly accounting data, so 447 firms are included in the survival model.

3.6. Definition of variables

Our first hypothesis is that issuers’ call behavior relates to credit rating changes. To test

this hypothesis, we use rating changes over the month prior to the call announcement. Rating

change is the one-month change in rating index from the Warga Database19

for each bond.

Specifically, for any month, t, the variable, Rating change, is the change in rating from month t-2

to t-1. In other words, the manager is looking back at whether a change occurred in the past

month at each decision point. In this way, Rating change assesses the extent to which a rating

19 The index assigns a 1 for a Moody’s rating of Aaa1, 2 for Aaa, 3 for Aa1, 4 for Aa2, et cetera, down to 23 for D and 24 for Not

Rated. Thus, a higher number for the index implies a more inferior rating, and consequently, a higher positive number for the

Rating change variable implies a more severe downgrade.

18

transition observed by management might subsequently prompt or defer exercise.20

In the

survival model, we can implicitly compare the ratings transition of the called bond versus those

bonds that are yet to be called in the “at-risk” set each month. This is clearly an advantage over

using only the rating or rating-change immediately before the call in a static model (or as an

average over time) in OLS models. A favorable change in rating in any month would suggest a

lower cost of interest and therefore a greater likelihood of refinancing in that month (King,

2002). In our model, since an increase in the rating index indicates a downgrade, Rating change

should relate negatively to the hazard of call.21

Leverage change should have a negative relationship to the hazard of a call. If reducing

leverage improves the credit rating, and managers target ratings (see Kisgen, 2006; Kisgen,

2009), then a manager seeking leverage reduction would hasten a call. Therefore, a shorter delay

and higher hazard rate would be consistent with decreased post-call leverage.

To account for the impact of agency cost, we include Book-to-market, the ratio of book

value of equity to market value of equity. A low book-to-market ratio is indicative of positive

future growth opportunities for the firm. If future growth prospects are good, equity-holders will

not want to share the wealth with debt-holders, and will thus be more eager to call the bonds

(Ryu and Wee, 2001; Guntay, Prabhala, and Unal, 2002). Given this view, we anticipate a

negative relationship between Book-to-market and the hazard rate. Higher book-to-market

implies lower growth, which implies lower hazard rate, which implies longer delay to call.

Profitability measures the past year-on-year percent change in earnings before interest

and taxes (EBIT). Based on the agency rationale, rising profitability makes the bond less risky,

20 Given the timing convention employed here wherein managers observe the rating change before deciding to call the bond, we

believe that the direction of causality runs from rating changes to managerial decisions.

21 We do not separate upgrades and downgrades because there are too few rating changes in either direction (41 upgrades and 49

downgrades).

19

so leaving the bond outstanding confers a gain to the bondholders at the expense of the

stockholders. Ederington and Stock (2002) find a significant difference in profitability between

issuers who include a call feature and those who do not. They also find that the increase in

EBIT/Total Assets measured two years after the issuance of a bond with a call provision is

significantly positive. Their results suggest that rising profits are compatible with inclusion of a

call option. Under this explanation, the sign for Profitability should be positive.

Yield curve slope, Interest rate volatility, and Default premium control for market

conditions that would relate to the propensity to call a bond at each time interval. Yield curve

slope equals the difference between the ten-year Treasury note yield and the one-year Treasury

bill yield, divided by the ten-year Treasury note yield at each month end.22

A steeper slope would

indicate an expectation of rising rates and would increase the hazard rate (i.e., hasten a call) as

suggested in King and Mauer (2000), and McDonald and Van de Gucht (1999). Interest rate

volatility is the standard deviation of daily observations of the ten-year Treasury yield for the

trailing twelve months (King and Mauer, 2000). Since an increase in interest rate volatility

increases the value of the call, there is a benefit to delaying a call in higher volatility

environments. Therefore, the coefficient on Interest rate volatility should be negatively related to

the hazard rate (King, 2002; Sarkar, 2001). Default premium equals the spread between the yield

to worst for the Lehman Long Corporate Bond Index and a Treasury security, as a percentage of

the Treasury yield.23

If corporate bond default spreads are generally wide despite reduced

Treasury rates, refinancing cost will be greater, and calls will be delayed, indicating a negative

relationship to hazard.

22 The one-year Treasury bill data series was available for the length of the study.

23 For the Lehman Long Corporate Bond Index, we match the appropriate industry sector (Utility, Finance, or Industrial) to each

bond. For the Treasury yield, we use the ten-year Treasury note for the period January 1, 1973 – December 31, 1976, and the 30-

year Treasury note for the period January 1, 1977 – December 31, 1997 (since January 31, 1977 is the first available date for the

30-year Treasury).

20

In-the-money percentage is the number of monthly pricing observations where the bond

is in-the-money (number of hitting times), divided by the total number of monthly pricing

observations between the first time the bond is in-the-money and the observation preceding the

call announcement. The in-the-money observations may or may not be consecutive months.

Rather than counting the absolute number of hitting times (Vu, 1986), we choose this

formulation to capture the intensity of moneyness after the first time in-the-money. The

percentage of months in-the-money, consecutive or not, may better reveal the company’s

threshold for refinancing relating to price. The median In-the-money percentage is 60%, meaning

that for the median firm, the bond’s price exceeded the call price about two-thirds of the time

between the first hitting time and the call announcement. We expect the sign of In-the-money

percentage to be positively related to the hazard rate, since the greater the percentage of passing

time that the firm has to initiate redemption, the more likely it will be called.

Opportunity cost is the difference between the current yield on the bond and the

replacement yield, in basis points.24

Current yield is the coupon rate on the bond divided by the

effective call price. The replacement yield is the weighted average yield to worst (yield to

maturity for noncallable bonds or yield to call for callable bonds) from the Lehman Brothers US

Domestic Credit Index.25

We use an index with similar characteristics as the called bond to

better represent the overall credit conditions and debt choices that a manager faces at the time of

the refinancing decision. For the period January 1, 1973-November 30, 1989, we match the

appropriate industry sector (Utility, Finance, or Industrial) of the Long Corporate Bond Index to

each bond. For the period December 1, 1989-December 31, 1997, when the index became

24 Results using the dollar cost (amount outstanding × opportunity cost) were not materially different.

25 The authors thank Seth Weber and Gary Sutton of the former Lehman Brothers for providing an extract from the Lehman

Brothers US Domestic Credit Index database.

21

available by rating cells, we match the appropriate industry sector and rating class

(Moody’s/Standard and Poor’s ratings of Aaa/AAA, Aa/AA, A/A, or Baa/BBB) of the Corporate

Bond Index to each bond. For issues with ratings below investment grade, we match to the

appropriate industry sector of the Long Corporate Bond Index. Matching this way allows us to

maintain the size of our sample, with 486 of the 491 in-the-money bonds matched to an index.

As shown in Table 1, Opportunity cost is 120 basis points per annum for the median bond,

slightly less than the mean of 128 basis points. For bonds that are in-the-money, we expect a

positive relationship to the hazard of call: the greater the economic cost of forgoing exercise, the

shorter the delay (Vu, 1986; King and Mauer, 2000).26

Remaining maturity is the remaining life, in months, of the bond at the time of the call.

The firm will incur higher interest cost for a longer time if the call option is not exercised,

implying the longer the remaining maturity, the greater the likelihood of the call in order to

generate the greatest cost savings (McDonald and Van de Gucht, 1999; King and Mauer, 2000;

Ryu and Wee, 2001).

At the firm level, we control for industry and liquidity. Utility equals one for bonds

issued in the telecommunications or power industries (408 bonds), and zero otherwise (66

industrials; 17 financials). Because utilities can pass on interest cost to consumers through rate

increases, and do not have the same competitive pressures as other types of firms, we expect a

positive relationship between Utility and Delay (King and Mauer, 2000; Kish and Livingston,

1992), so a negative relationship to the hazard of call. Liquidity is the natural logarithm of cash

and marketable securities. The more liquid the firm is, the more quickly it can act to redeem

26 Since Opportunity cost incorporates coupon (directly) and prevailing interest rates (via the replacement yield), we eliminated

the coupon, risk free rate, and default premium, retaining Opportunity cost to address multicollinearity issues arising from the

interrelationships between bonds, options, and firm values.

22

bonds should conditions permit, indicating a negative relationship (King and Mauer, 2000) to

Delay and positive relationship to the likelihood of call.

Announcement year is the year of the call announcement, standardized to a mean of zero

and a standard deviation of one.27

Its purpose is to capture unobserved heterogeneity across

years (Gross and Souleles, 2002).

< Insert Table 2 here >

A summary of the variables we employ and their definitions is provided in Table 2. The

model includes dynamic covariates for Rating change, Book-to-market, Profitability, Leverage

change, Yield curve slope, Interest rate volatility, Credit default premium, Opportunity cost, and

Liquidity. The remaining variables, In-the-money percentage, Utility, Remaining maturity, and

Announcement year, are observations from the last month-end before the call announcement.

4. Results

Table 3 presents the results from the survival analysis using the time-varying proportional

hazard model. In Table 3, we present two models – the first, which we call the Full model,

includes all variables of interest and controls, while the our Final model employs only those

variables that have significant coefficients in the Full model’s estimation. Table provides results

from our Final model that aid in interpreting the economic significance of our parameter

estimates.

Table 3 displays maximum likelihood parameter estimates for covariates with their robust

standard errors (Lin and Wei, 1989). The hazard rate is e, where is the parameter estimate.

27 We use a continuous variable instead of year dummies representing each year of 1973 – 1997 because the data set is too small

to accommodate so many degrees of freedom. This formulation implies that the relationship between Delay and Announcement

year is linear.

23

Since hazard is an inverse function of Delay, a negative parameter estimate implies an inverse

relationship to the likelihood of a call, and a positive relationship to Delay.

Taken together, the covariates have a significant effect on the hazard and therefore the

manager’s propensity to delay calling the bonds. The score test of the global null hypothesis

using the robust standard errors is a chi-squared of 154 and 148 for the Full and Final models,

respectively, implying that the parameter estimates are jointly different from zero at a

significance of at least the 0.01 level.28

In Table 3, Rating change is negatively related to the hazard of a call in both models at a

significance level of 0.01. The sign on the covariate is negative since a downgrade causes an

increase in the rating index. An in-the-money bond that has been downgraded in the past month

is less likely to be called than one that has not, and one that has been upgraded is more likely to

be called than one that has not.29

The survival analysis shows that the manager’s decision

whether or not to call each month is highly related to rating actions the previous month. This

result supports the asymmetric information hypothesis. Specifically, managers possess

asymmetric information about their future bond rating and use that information in their call

decision. Since we use a time series of monthly rating change data for every bond, we are able to

link the manager’s call decision to changes in ratings at the monthly level. This evidence is

important because it shows that managers have a more timely reaction to ratings changes than

indicated in prior studies.30

< Insert Tables 3 and 4 here >

28 The Wald and likelihood ratio tests yield similar conclusions.

29 In a separate model with three-month rating changes but all the other covariates the same, three-month rating changes were

significant at the 5% level. Results for the other covariates were largely the same as for the model with the one-month rating

change. Six- and twelve month ratings changes were not significant in similar models (not shown).

30 Kisgen (2006), and Hovakimian , Kayhan, and Titman (2009) relate decisions to annual ratings obtained from Compustat (i.e.,

ratings data are on an annual basis), whereas we show that managers react to monthly ratings.

24

A rating change in the preceding month has a considerable economic influence in the

decision to call an in-the-money bond, as illustrated in Table 4. Assuming a one-notch

downgrade on a bond with the median rating of the sample (1/7, where an index value of seven

represents the median Moody’s rating of A2), the economic result is a seven percent decrease in

the hazard rate, corresponding to an increase in Delay. This result has not been quantified before

in the callable bond literature. Further, it supports the literature that bond ratings are important in

shaping managerial decisions.

Agency does not appear to be a major motivating factor in delaying calls. While

Profitability is significant and positively related to call hazard in Table 3, Table 4 shows that

even the large median EBIT change of 34% corresponds to only a one percent change in the

hazard rate, which is not economically meaningful. In the Full model, Book-to-market is

negatively related to hazard, but not significant. Also, Leverage change is not significantly

related to hazard, suggesting that for in-the-money callers, neither increasing nor decreasing

leverage has a significant relationship to the dynamic call decision.

As expected, in Table 3, the control variables Yield curve slope, In-the-money percent,

and Opportunity cost are positively related to the likelihood of a call, with significance at the

level of 0.01, consistent with option theory and the literature (King and Mauer, 2000; Sarkar,

2001). These three effects are all economically significant as well. Table 4 shows that a five

percentage point increase in the average slope of the yield curve, which would be consistent with

a 50 basis point increase in the average yield on the ten-year Treasury note, would increase the

likelihood of a call by 13%. One additional month in-the-money, on an average Delay of 11

months, increases the risk of the bond being called by 12%. A 50 basis point increase in relative

25

opportunity cost would increase the likelihood of a call by 10%. The market control variables

Interest rate volatility and Default premium are not significant.

Utility is significant and negative, with utility firms 61.8% as likely to call their bonds as

industrial or financial firms, suggesting they are passing on higher interest costs to rate-payers.31

Firm Liquidity is not significant. Remaining maturity at the time of call is not significantly

related to the likelihood of the bond being called.32

Announcement year is negative and significant, indicating that there is some unmeasured

effect related to time period where the hazard rate appears to be decreasing over time. We

suspect that in the later years of the sample period, the better developed interest rate derivatives

market may have made hedging a cheaper alternative to calling outstanding debt (see Guntay,

Prabhala, and Unal, 2002, for similar arguments). Thus, changes in the structure of the market, if

any, are captured in the Announcement year variable. Nonetheless, the rating change variable is

significant even after controlling for these structural changes.

5. Conclusions

While the theoretical prediction of call timing is derived under the assumption of perfect

capital markets and the absence of market frictions, managers actually make the call decision

under conditions which do not satisfy these assumptions. Firms that choose to call despite their

bonds being out-of-the-money face higher leverage than those who choose to defer calling after

going in-the-money. Firms that delay calling after their bonds are in-the-money are possibly

maintaining interest cost savings after downgrades. Segregating in- and out-of-the-money callers

paints a clearer picture of call decisions.

31 For categorical variables, the hazard rate indicates the likelihood of a call for those assigned a value of one (in this case, utility

firms), relative to those assigned a value of zero (industrial or financial firms).

32 A non-linear formulation of remaining maturity produced similar results.

26

Our study shows a robust relationship between the call timing decision and credit rating

changes. Because the survival model captures information that changes through time, it is ideally

suited to understanding the call exercise decision where, at each point in time, that decision

depends on the path of prior information. Our results support the asymmetric information

hypothesis: firms delay calls after downgrades and hasten calls in response to upgrades. Call

delays are not strongly related to agency costs of debt, although there is some weak evidence that

less profitable companies may keep bonds outstanding longer, shifting risk to bondholders.

Our main contribution is to the literature linking managerial decision-making and ratings

by showing that managers react in a much timelier manner than has been established in prior

studies. Specifically, survival analysis enables us to examine the decision making on a monthly

basis as opposed to prior studies, which have shown the link between ratings and managerial

decisions using an annual data based framework. This timeliness is an important dimension that

persuasively demonstrates the link between credit ratings and managerial decisions. Our dynamic

analysis shows that managers time bond calls incorporating their knowledge and expectations of

their creditworthiness. This adds to the body of knowledge establishing an undeniable link

between managerial decision-making and credit ratings.

27

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30

Table 1

Descriptive statistics Means and medians for variables calculated for the in-the-money (N = 491) and out-of-the-money (N = 104) groups.

As illustrated in Figure 1, Delay is the time in months from the first time the bond is in-the-money until the call

announcement date; Time to Call is the time in months from the end of call protection until the call announcement

date. Coupon is the coupon rate on the bond. Remaining maturity is the remaining maturity in months at time of call.

Premium equals the difference between the full market price and the effective call price at time of call, as a

percentage of the effective call price. Rating index is based on the Warga rating index, which assigns a 1 for a

Moody’s rating of Aaa1, 2 for Aaa, 3 for Aa1, et cetera, down to 23 for D and 24 for Not Rated, so a rating index of

seven on the Warga scale corresponds to a Moody’s rating of A2. Ten-year Treasury yield is the yield on the

constant maturity ten-year US Treasury note. Other variable definitions are in Table 2. The asterisks indicate the

level of significance with which we can reject the null hypothesis that the distributions for each variable are the

same for in- and out-of-the-money callers based on a Kruskal-Wallis test.

Mean Median

In-the-

money

Out-of-

the-money

In-the-

money

Out-of-

the-money

Delay 11 N/A 8 N/A

Time to call 95 70 99 70 ***

Coupon 9.21% 9.33% 8.88% 9.13%

Remaining maturity 181 173 166 162 **

Premium 0.07% -2.58% 0.01% -1.13% ***

Opportunity cost 128 43 120 65 ***

Liquidity 4.48 4.39 4.58 4.34

Book-to-market 0.63 0.97 0.61 0.64

Leverage change 0% -2% 1% -6% ***

Profitability 34% 46% -2% 1%

Rating index 6.9 (A2) 8.0 (A3) 7.0 (A2) 7.0 (A2) **

Ten-year Treasury yield 6.43% 7.12% 6.26% 6.95% ***

Yield curve slope 0.38% 0.33% 0.41% 0.37% ***

Interest rate volatility 0.42 0.47 0.40 0.41

Default premium 0.10 0.12 0.10 0.11 ***

*** and ** indicate statistical significance at the 0.01and 0.05 levels, respectively.

31

Table 2

Variable definitions for survival analysis

Variable Definition

Rating change Moody's rating change over prior month, based on the

Warga rating numeric scale where Aaa1=1, Aaa=2,

Aa1=3, Aa2=4, etc.

Book-to-market Book value of equity divided by market value of

equity

Profitability Percent change in earnings before interest and taxes

(EBIT) from one year prior to call until call date

Leverage change Percent change in book value of debt divided by book

value of long-term debt plus market value of equity

from date of call to one year later

Yield curve slope Difference between the yield on the ten-year Treasury

note and the one-year Treasury note, divided by the

yield on the ten-year Treasury note

Interest rate volatility Standard deviation of daily observations of the ten-

year Treasury note yield for the year prior to the call

date

Default premium Difference between the yield on the Lehman Credit

Index and the Lehman Treasury Index, divided by the

yield on the Treasury Index

In-the-money percent Number of months the bond was in-the-money,

divided by the total number of months between the

first time in-the-money and the call announcement

Opportunity cost Difference between the coupon rate divided by the

effective call price, and the weighted average yield to

worst from the Lehman Brothers US Domestic Credit

Index appropriate to the bond's rating and sector

Remaining maturity Remaining maturity at time of call, in months

Utility Equals one if the bond is a power or

telecommunications utility, zero otherwise

Liquidity Natural logarithm of the sum of cash and marketable

securities

Announcement year Year of call announcement

32

Table 3

Survival analysis for in-the-money callers The semi-parametric proportional hazard models (Cox, 1972) compare the natural logarithm of the hazard function (t) =

0(t)e'x(t) for bonds called at time t with those at risk for call (those whose call protection has expired and have been in-the-

money at least once) at time t. The dependent variable is ln(hazard), where the hazard is a function of the relationship between

Delay and the independent variables x(t) as defined in Table 2. Delay is the time between the first time the bond is in-the-money

and the call announcement date. The Full model includes all covariates in Table 2, while the Final model includes only those

significant in the Full model. The table displays parameter estimates for covariates with their robust standard errors below. The

hazard rate is e, where is the maximum likelihood parameter estimate. A negative parameter estimate implies an inverse relationship to the likelihood of a call, and a positive relationship to Delay. P-values are computed based on the Wald chi-square

test using robust standard errors (Lin and Wei, 1989). Fifty-two bonds were eliminated from the sample for the Full Model and

35 were eliminated from the Final Model because they did not have enough consecutive monthly accounting data.

Full model Final model

Variable

Parameter

estimate Hazard rate

Parameter

estimate Hazard Rate

Rating change -0.51 0.599 -0.54 0.584

(0.1301)*** (0.1204)***

Book-to-market -0.16 0.848

(0.1467)

Profitability 0.03 1.029 0.03 1.030

(0.0073)*** (0.0073)***

Leverage change 0.20 1.227

(0.1485)

Yield curve slope 2.56 12.932 2.38 10.756

(0.6166)*** (0.5695)***

Interest rate volatility 0.17 1.186

(0.4107)

In-the-money percent 1.32 3.731 1.28 3.592

(0.1698)*** (0.1659)***

Opportunity cost 0.16 1.171 0.19 1.204

(0.0551)*** (0.0520)***

Remaining maturity 0.00 1.001

(0.0006)

Utility -0.48 0.621 -0.44 0.643

(0.1725)*** (0.1558)***

Liquidity 0.00 1.000

(0.0309)

Announcement year -0.54 0.581 -0.53 0.592

(0.1081)*** (0.0919)***

N 439 456

*** indicates statistical significance at the 0.01 level.

33

Table 4

Economic interpretation of hazard model parameter estimates The semi-parametric models (Cox, 1972) compare the natural logarithm of the hazard function, (t) = 0(t)e

'x(t), for bonds called

at time t with those at risk for call (those whose call protection has expired and have been in-the-money at least once) at time t.

The dependent variable is ln(hazard), where the hazard is a function of the relationship between Delay and the independent

variables x(t) as defined in Table 2. Delay is the time between the first time the bond is in-the-money and the call announcement

date. The covariates for Rating change 1 month, Rating change 3 months, Profitability, Yield curve slope, In-the-money percent,

and Opportunity cost were significant in the proportional hazard model and are defined in Table 2. The hazard ratio is ec, where

is the parameter estimate, and c is a unit of change appropriate to the covariate (Hosmer and Lemeshow, 1999). The hazard

percent change is ec- 1. The units of change are: a one-notch rating change for a A2-rated (median) issuer (a change in the rating

index of 1/7); a 34% (median) year-on-year increase in EBIT; a five percentage point increase in the slope of the yield curve

(corresponding to a 50 basis point change in the ten-year US Treasury note; one additional month in-the-money on the average

Delay of 11 months (1/11); a 50 basis point increase in the relative opportunity cost of delaying the call.

Parameter Unit of Hazard

Hazard

percent

95%

Confidence interval

estimate change rate change of hazard rate

Variable c ec

ec

- 1

Rating change -0.54 0.14 0.93 -7% 0.90 0.96

Profitability 0.03 0.34 1.01 1% 1.01 1.02

Yield curve slope 2.38 0.05 1.13 13% 1.06 1.19

In-the-money percent 1.28 0.09 1.12 12% 1.09 1.16

Opportunity cost 0.19 0.50 1.10 10% 1.04 1.15

34

Bond Issued Call

Announcement

Contractual Call

Protection Ends

t = t 0 t = T

First Time

Market Price = Call Price

Bond is At Risk of Call Bonds called in-the-money

0 Call delay in months = T – t

Bond Issued Call

Announcement

Contractual Call

Protection Ends

t = t 0 t = T

First Time

Market Price = Call Price

Bond is At Risk of Call

Bond Issued Call

Announcement

Contractual Call

Protection Ends

t = t 0 ' t = T

Bond is At Risk of Call

All callable bonds (in- and out-of-the-money)

Time to call in months = T – t 0 '

Bond Issued Call

Announcement

Contractual Call

Protection Ends

t = t 0 ' t = T

Bond is At Risk of Call

Call delay (Delay) applies only to bonds called in-the-money. Delay equals the number of

months from the time two conditions are met: (1) contractual call protection, as specified

in the bond indenture, has ended; and (2) the bond’s market price equals or exceeds its call

price (goes in-the-money), until the call announcement date (T - t0). Under this measure,

the bond is at risk of call from the first time the bond is in-the-money.

Time to call (Time to call) applies to bonds called in-the-money or out-of-the-money.

Time to call equals the number of months from the end of contractual call protection, as

specified in the indenture, until the call announcement date (T - t0′). Under this measure,

the bond is at risk of call from the end of call protection.

Figure 1

Modeling Call delay and Time to call

35

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150 175 200 225 250 275

Time to Call (months)

In-the-Money Cohort

Out-of-the-Money Cohort

Ka

pla

n-M

eie

rS

urv

iva

l F

un

cti

on

Figure 2

Survival functions for in- and out-of-the-money callers

Survival functions comparing Time to call for in-the-money and out-of-the-money callers. Time

to call is the number of months from the end of contractual call protection to the call

announcement date. The Kaplan-Meier Survival Function measures the likelihood of the bond

not being called at time t, given that it has not been called before time t. Tests of equality (not

displayed) reject the null hypothesis that the survival functions for the two samples are equal.