Are Make-Whole Call Provisions Overpriced? Theory

and Empirical Evidence

Eric Powers∗and Sergey Tsyplakov

Moore School of Business

University of South Carolina

Columbia, SC 29208

February 11, 2004

∗Corresponding author. Tel +1-803-777-4928. E-mail address: epowers@moore.sc.edu. We thank Brent

Ambrose, Frank Fehle, Shingo Goto, Brad Jordan, Steve Mann, Sattar Mansi, Ted Moore, Greg Niehaus,

Ellen Roueche, Stathis Tompaidis, and seminar participants at the University of South Carolina for helpful

comments.

Are Make-Whole Call Provisions Overpriced? Theory and

Empirical Evidence

Abstract

We use a structural model to examine whether make-whole call provisions - a recent yet

surprisingly common innovation in corporate debt markets - are fairly priced at origination.

The call provision cost is calculated as the callable bond yield minus the equivalent non-

callable bond yield, producing an incremental yield attributable to the make-whole call

provision. Model parameters are calibrated to match characteristics of the issuing firm,

bond, and yield curve at origination for a large sample of recently issued US corporate bonds.

Our analysis indicates that while our model successfully captures cross-sectional variation in

incrementals yields, observed values are significantly greater than model-generated values.

The discrepancy between model-generated and observed incremental yields persists even

after we incorporate selected market imperfections that should widen incremental yields.

Our conclusion is that make-whole call provisions at origination have been mispriced and

that issuing firms have been paying too much for the financial flexibility that the call provision

provides.

1 Introduction

It is well-known that there has been a decline in the prevalence of fixed-price call provisions

in US corporate bonds throughout the 1980s and 1990s (Brealey and Myers; 2003, p.708).

What is less well-known is that a new type of call provision, known as a make-whole call, has

recently supplanted fixed-price call provisions. For example, in 2001, the amount of newly-

issued corporate debt with make-whole call provisions was more than 30 percent greater than

the amount of non-callable and fixed-price callable corporate debt combined - see Figure 1

for the trend since 1995.

With a make-whole call provision, the call price is not determined by a price schedule,

rather, the call price floats inversely with Treasury rates. If exercised, the make-whole call

price is calculated as the maximum of par value or the present value of the bond’s remaining

payments. The discount rate used in the present value calculation is the comparable maturity

Treasury yield plus a spread (known as the make-whole premium) that is specified in the

bond’s indenture. Thus, as risk-free rates decrease, the call price increases. Conversely, as

risk-free rates increase, the call price decreases until the floor at par is hit.1

The primary benefit of make-whole call provision relative to a traditional fixed-price call

provision is that the floating call price virtually eliminates the incentive for the firm to call

when interest rates drop. Thus, interest rate risk that bondholders are exposed to via the

call option is significantly reduced. With reduced risk, bondholders should demand less

compensation for their short position in the option. The required compensation, i.e. the

cost of the call option, is further limited by the fact that make-whole premiums are always

set well below prevailing credit spreads. Since prices (both market and call) are inversely

1For more detail on the characteristics and benefits of make-whole call provisions, see Mann and Powers(2003b). Also see Emery, Hoffmeister, and Spahr (1987) who suggested indexing call prices well beforemake-whole call provisions became prevalent.

1

related to yields (risk-free rate plus credit spread or make-whole premium), this ensures that

make-whole call options will be well out-of-the-money at origination. In our sample, for

example, make-whole premiums average approximately 25 bp, but at-issue credit spreads of

the associated bonds are 150 bp greater on average. In fact, most of these call provisions are

unlikely ever to be in the money. Since January 1995 for example, the 10-year Aaa credit

spread has never dipped below 32 bp, yet 79 percent of the make-whole premiums in our

sample are less than this value.2 Furthermore, the call provision’s floor at par ensures that

the call will always be out-of-the-money whenever the bond is trading at a discount.

Our primary objective is to determine what is fair compensation for the short position

held by make-whole call bond investors. Intuitively, the cost of the call provision should be

low, but how low? Mann and Powers (2003a, 2003b) estimate that at-issue yields of bonds

with make-whole call provisions average 11 bp more than yields of comparable non-callable

bonds.3 The lack of a model, however, prevents them from assessing whether this is fair

compensation. Our second objective is to understand how characteristics of the bond such

as time-to-maturity, of the issuing firm such as leverage, and of the yield curve such as its

level should affect the incremental yield. Again, without a model, insights thus far have been

limited to simple intuition.

To accomplish these objectives we first develop a structural credit spread model. In our

model, risk-free rates and firm cash flows are given by correlated stochastic processes while

default and call decisions are endogenous. Credit spreads for both make-whole call and

non-callable bonds are then calculated numerically. As noted, our primary interest is in the

2In our sample, make-whole premiums range between 0 bp and 100 bp with a mean (median) value of25.6 bp (25 bp); 99.3 percent are less than 50 bp. In comparison, the 10-year Aaa industrials credit spreadhas ranged from a low of 32 bp in February, 1997 to a high of 130 bp in May, 2000.

3In both papers, they measure the cost of the make-whole call provision by subtracting maturity andrating-specific Bloomberg Fair Market Yields from observed at-issue yields for matched samples of make-whole call and non-callable bonds. The resulting yield differential for make-whole call bonds bonds is 11bp more than the differential for comparable non-callable bonds. In comparison, the yield differential forfixed-price callable bonds is 45 bp greater than the equivalent non-callable value.

2

incremental yield attributable to a make-whole call provision and not in credit spreads per se.

Thus, for make-whole call bonds, we disentangle the default and call option components of

the credit spread by subtracting the predicted spread of an otherwise equivalent non-callable

bond. The incremental yield resulting from this calculation is the cost of the call option.

We parameterize our model using contemporaneous risk-free yield curve information as

well as firm and bond-specific characteristics at origination for a sample of approximately

1,300 recently issued make-whole call and non-callable bonds. For each bond in the sample,

we calculate what its credit spread should be assuming that capital markets are friction-

less and that calls only occur when economically optimal. For make-whole call bonds, the

predicted incremental yield has a sample mean (median) of 2.75 bp (1.75 bp). Regression

analysis reveals that our model-generated values successfully capture cross-sectional varia-

tion in observed incremental yields. However, after controlling for a variety of other factors

such as liquidity and the macro-economic credit environment, we find that observed values

average more than 11 bp and that the difference between model-generated and observed

values is statistically significant. Thus, our frictionless model significantly underestimates

observed incremental yields.

Recent research by Elton, et al. (2001) highlights the impact of imperfections such as

state taxes on corporate credit spreads. Similarly, we hypothesize that the disparity between

predicted and actual incremental yields can be explained by market imperfections that are

likely to increase the incremental yield. Thus, we extend the model by parameterizing and

incorporating three real-world market imperfections. The first imperfection is capital gains

taxes assessed on the difference between the call price and basis price of taxable investors

if the bond is called. The second imperfection is transactions costs that are imposed on

debtholders when they are forced to rebalance their investment portfolios following a call.

The third imperfection is an exogenous event which requires the firm to retire debt for a

3

reason other than the call being sufficiently in-the-money. For example, debt assumed in an

acquisition or merger might contain covenants that restrict the ability of the firm to con-

duct business. In this situation, early retirement of the acquired debt may be desirable. A

make-whole call provision, even though it is out-of-the-money relative to the market price

of the bond, may help the firm avoid and even costlier tender offer. After incorporating all

three imperfections, the model-generated mean (median) incremental yield increases to 6.07

bp (5.44 bp), bringing results closer to empirically observed values. Nevertheless, regres-

sion results still indicate that model-generated values are statistically significantly less than

empirically observed values.

Our results could potentially be due to misspecification of the model. Extensive robust-

ness checks, however, suggest that this is not the case. Since we concentrate on incremental

yields - calculated as the difference between make-whole call and equivalent non-callable bond

yields - potential misspecification is likely to be minimized. Moreover, we believe that our

model-generated values may actually overestimate what should be the cost of a make-whole

call provision. One reason to believe this is because our structural model underestimates

credit spreads in general, a sympton common to many structural models (Eom, Helwege,

and Huang; 2002). This increases the model-generated incremental yield by pushing the call

provision closer to being in-the-money. We have also focused only on imperfections likely to

increase the incremental yield and have ignored others that might have the opposite effect.

Thus, we conclude that make-whole call provisions have been overpriced at origination and

issuing firms have paid too much for the financial flexibility provided by this innovative call

option.

The rest of our paper proceeds as follows. In section 2 we develop the model. The

data is described in section 3. In section 4 we use the data to calibrate the model for

individual bonds, calculate model-generated credit spreads, and discuss comparative statics

4

of the model. The model-generated credit spreads from section 4 are compared to real-

world at-issue credit spreads of both make-whole call and non-callable bonds in section 5.

In section 6 we extend the model and discuss alternative sources of the incremental yield.

Robustness checks of both the model and the empirics are provided in section 7, followed by

a conclusion in section 8.

2 Model

2.1 Time Line

At time zero the firm borrows an exogenous amount. The debt is a coupon bond with

principal due at maturity and is either non-callable or has a make-whole call provision. At

each instant, the firm generates cash flow by producing sales at a fixed cost. The residual cash

flow net of debt payments and production costs is paid to the equityholders as a dividend.

If cash flow is insufficient to cover debt payments, the firm can costlessly issue equity. Sales

and the risk-free rate are assumed to be correlated stochastic processes with a constant

correlation coefficient.4

At each instant, the firm decides to make the coupon payment and pay production

costs, or to default, in which case debtholders recover the firm’s value and equityholders

get nothing. For a callable bond, if default does not occur, the firm must decide whether

to call the bond or leave it in place. If called, the call price is calculated as the maximum

of par value or the present value of the remaining scheduled debt payments. The discount

rate for the present value calculation is the prevailing risk-free rate plus the make-whole-call

premium.

The firm is assumed to make optimal default and call decisions. Default occurs when

4Acharya and Carpenter (2002) use a similar setting for analyzing fixed-price call provisions with theprincipal difference being that we assume cash flows are stochastic while they assume firm value is stochastic.See their paper for a detailed discussion of the antecedent modeling literature.

5

sales decline and the market value of the firm’s equity becomes zero. In contrast, a call

occurs when sales increase and the firm is able to issue an equivalent bond with a yield that

is less than the risk-free rate plus the make-whole call premium of the existing bond. Both

equity and debt are priced fairly taking into account the optimal call and default strategies

of the firm.

2.2 Model Description

2.2.1 The interest rate process

The short-term risk-free rate rt is assumed to follow a mean-reverting square root stochastic

diffusion process, described by the one factor Cox, Ingersoll and Ross (1985) (CIR, hereafter)

model:

drt = κr(r∗ − rt)dt+ σr

√rtdWr, (1)

where κr is the mean-reversion rate, r∗ is the long-term level to which the short-term rate

reverts, σr is the instantaneous volatility for the short-term rate, and Wr is a standard

Wiener process under the risk-neutral measure.

2.2.2 The firm’s cash flow and production costs

We assume that the firm continuously generates sales s through time. All production costs p

(p ≥ 0) are assumed to be fixed through time, regardless of the level of sales. Thus, the cashflow available to pay debt and dividends is s− p. Sales for the firm are assumed to follow a

log-normal stochastic process:

ds

s= (r − α)dt+ σsdWs, (2)

where α is the convenience yield,Ws is a Weiner process under the risk-neutral measure, and

σs is the instantaneous volatility coefficient. The Wiener processesWr andWs are correlated

with correlation coefficient equal to ρ.

6

Fixed production costs imply that even an unlevered firm can become financially dis-

tressed.5 A distressed firm can either costlessly issue equity (via a negative dividend) or

can shut down operations permanently; temporary shut downs are not allowed. The sales

level at which financial distress induces the unlevered firm to shut down is endogenously

determined such that the value of the firm is always greater than zero.

2.2.3 Bond types

We assume that the firm issues a bond that has a continuous coupon payment rate of c per

unit of time and par value F at maturity T. The firm continuously pays dividends that equal

sales net of production costs and debt payments, s− p− c.We consider two types of bonds: 1) a bond with a make-whole call provision and 2) an

option-free or non-callable bond. The call price of a bond with a make-whole call provision

is determined by the remaining maturity t and by the level of the risk-free rate r. The call

price M(r, c, F,m, t), t < T at which the firm can call its debt is calculated as the present

value of the remaining coupon payments c and par value F discounted at the risk-free rate

plus some prespecified premium m > 0. There is a floor for the call price specifying that it

cannot be lower than the face value of the bond F . For a bond that has T − t remaininguntil maturity, the call price is given by

M(r, c, F,m, T − t) = max{F, [Z T

t

ce−mxP (r, t, x)dx] + F · P (r, t, T )e−m(T−t)}, (3)

where P (r, t, x) is the price of a risk-free zero coupon bond paying $1 at time x, calculated

according to the CIR formula

5This fixed production costs assumption extends Merton’s (1977) classical model of the firm and enhancesour ability to calibrate the model to match cash flow characteristics of individual firms. Brennan andSchwartz, (1984), Mello and Parsons (1992), and Mauer and Ott (2000) make similar assumptions withrespect to costs.

7

P (r, t, x) = (2γe(κr−γ)(x−t)2(κr−γ)

2γ + (κr − γ)(1− e−γ(x−t)))2κrr

∗/σ2rerB(x−t), where

B(x− t) =−2(1− e−γ(x−t))

2γ + (κr − γ)(1− e−γ(x−t)) , and γ =p

κ2r + 2σ2r. (4)

The last two terms in equation 3 are the present values of the coupon payments and of the

par value discounted at the risk-free rate plus the premium m.

2.2.4 Value of the unlevered firm

The value of the unlevered firm equals the expected present value under the risk-neutral

measure of the discounted future cash flows taking into account the option to shut down

operations if sales are sufficiently low. Given the value of the short-term interest rate r

and the sales level s, the value of the unlevered firm V (s, r) is given by the solution to the

following problem

V (s, r) = maxτEZ τ

0

(st − p)e−R t0 rsdsdt, (5)

where E is the expectation under the risk-neutral measure, and τ is the stopping time

corresponding to when sales drop to the critical lower boundary at which the unlevered firm

shuts down its operations.

2.2.5 Value of the firm’s equity and debt

For a levered firm having debt with characteristics c, F, T,M , where c is the coupon rate, F

is the face value, T is the maturity of the debt and M is the call price for each t < T and

risk-free rate r, the value of the firm’s equity is E(s, r, t). Equity’s value depends on the

optimal default and call strategies and is given by

E(s, r, t) = maxτ[E(V (s, r)−M(r, c, F,m, T − τ))e−

R τt rydy, (6)

EZ τ

t

(s− p− c)e−R xt rydydx+ δ(T − τ)e−

R Tt rydymax(0, VT (s, r)− F )],

8

where the stopping time τ either corresponds to the time of default, bond call, or maturity.

The function δ in (6) is given by δ(x) = 0 if x 6= 0 and δ(0) = 1. The details of equity

valuation are discussed in the appendix.

2.2.6 Valuation of the Debt

To calculate the value of the debt D, we need to consider the firm’s default and call strategy

(if applicable). At maturity T, the debt value is given by the minimum of par value F and

the value of the firm’s assets V :

D(s, r, T ) = min(V (s, r), F ). (7)

Prior to maturity, the value of debt satisfies

σ2rr

2Drr +

σ2ss2

2Dss + ρσsσrs

√rDrs + κr(r

∗ − r)Dr + (r − α)Ds+

+Dt − rD + c = 0.(8)

In the equation the subscripts denote partial derivatives. There is a boundary condition for

the value of debt when equity is valueless and the firm defaults:6

D(s, r, t) = V (s, r), if E(s, r, t) = 0. (9)

For a callable bond there is another free boundary condition that corresponds to the case

where the firm buys the debt back at the make-whole call price M(r, c, F,m, t):

D(s, r, t) =M(r, c, F,m, t) if E(s, r, t) = V (s, r)−M(r, c, F,m, t). (10)

In the absence of taxes, financial distress costs and bankruptcy costs, the value of the firm

V , the equity value E, and the value of the debt D, satisfy

V = E +D. (11)

6This boundary condition assumes that assets of the levered firm are transferred to bondholders followingdefault. Note that the sales level at which the levered firm will default is greater than the sales level atwhich the unlevered firm shuts down its operations.

9

3 Data

We calibrate and test our model using a sample of bonds drawn from the Fixed Income

Securities Database (FISD). The selected bonds have the following characteristics: (1) issued

on or after January 1, 1995, (2) maturity of at least one year, (3) denominated in US dollars,

(4) offering amount of at least $25 million, (5) fixed semi-annual coupon, (6) not asset backed,

(7) not putable, (8) without a sinking fund, (9) not a Yankee bond, (10) not a Medium Term

Note, (11) not part of a unit offering, (12) not convertible, and (13) listed as a Corporate

Debenture. These screens result in an initial sample of 2,511 non-callable bonds, 2,800 bonds

with fixed-price call provisions, and 2,447 bonds with make-whole call provisions.

We exclude bonds with fixed-price call provisions and those for which there is no infor-

mation in the FISD on the at-issue yield-to-maturity. We also eliminate make-whole call

bonds for which we are unable to determine the make-whole premium via either Bloomberg

or by direct inspection of the bond prospectus. These requirements reduce our sample to

2,262 non-callable bonds and 1,870 bonds with make-whole call provisions.

Using the 6-digit Cusip of the issuer provided in the FISD, we match each observation

to the corresponding prior fiscal year record in Compustat, the source for the issuer-specific

information required for our pricing model. Observations are lost either because the firm

is not listed in Compustat or because the bond was issued by a subsidiary of a firm rather

than the actual parent firm.

In columns one and two of Table 1, Panel A, we present means and medians for character-

istics of the firms responsible for issuing the 1,662 non-callable bonds and 1,583 make-whole

call bonds for which we have at least sales data for the issuing firm. In calculating these

statistics, we allow only one observation per firm, per bond type in each issue year. With

the exception of sales, all characteristics are winsorized at the 1st and 99th percentiles for

10

the entire Compustat universe in order to limit extreme outliers. Column three contains

p-values for t-tests and Wilcoxon Rank-Sum tests (in parentheses) of the null hypothesis

that means and medians for the associated variables are the same for the two samples.

As can be seen from the summary statistics, the typical issuer of a make-whole call bond

is smaller, more profitable, and appears to have greater growth opportunities (as proxied

by Tobin’s Q) than the typical non-callable bond issuer. Make-whole call issuers also have

greater book leverage. Average historical sales growth and volatility of sales growth are

significantly greater for the make-whole issuers (both variables are highly skewed), but there

is no significant difference in the respective medians. Finally, the volatility of the firm’s

daily excess equity return for the prior six months is significantly greater for make-whole

call issuers. Note that make-whole call bonds are more prevalent in the later half of our

sample period. Thus, some univariate differences are potentially due to different economic

conditions prevailing at the issue date.

Our initial sample includes 1,662 non-callable bonds and 1,583 make-whole call bonds.

Our final sample, however, is limited to 775 non-callable bonds and 612 make-whole call

bonds. Observations are lost/discarded when we parameterize our model for reasons such as

no equity price available which makes calculating a proxy for Tobin’s Q impossible, insuffi-

cient information for calculating the standard deviation of sales growth, or extremely high or

low input parameters. For the issuers of bonds that make it into our final sample, we report

all of the same summary statistics in columns four and five. All of the prior comparisons

that were significant remain statistically significant (p-values not reported in the table).

Panel B shows means and medians for characteristics of the actual bonds in the sample

(no bonds are excluded). The summary statistics indicate that the typical make-whole call

bond has a worse rating, longer maturity, and moderately larger offering amount than the

typical non-callable bond. The median make-whole call bond has a rating of BBB, 10 years

11

to maturity, and an offering amount of $300 million. In contrast, the median non-callable

bond has a rating of A-, 9 years to maturity, and an offering amount of $250 million.

Following Eom, Helwege, and Huang (2002), we calculate the credit spread as the bond’s

yield-to-maturity at issue minus the equivalent maturity Constant Maturity Treasury (CMT)

yield. In situations where an equivalent maturity CMT yield is unavailable, we interpolate

linearly using the two closest maturity CMT yields.7 The mean and median credit spreads

for the non-callable bonds are 117 basis points and 88 basis points, respectively. Consistent

with their lower ratings, longer maturities, and prevalence later in the sample period when

credit spreads are wider, the mean and median credit spreads for the make-whole call bonds

are statistically significantly greater at 179 basis points and 155 basis points, respectively.

Comparisons are similar for the final sample bonds reported in columns 4 and 5.

4 Model Output

4.1 Calibration

To use the model, we require parameter values for the risk-free interest rate process (r,κr, r∗,σr),

the sales process of the firm (σs, ρ, p,α), and the capital structure of the firm (F, T,m, c). To

estimate the parameters of the risk-free process, we solve for the short-term rate r, the mean

reversion rate κr, the long-term rate r∗, and the volatility σr which minimize the sum of

squared deviations between the 1, 2, 3, 5, 10, and 30 year yields implied by the closed-form

solution of the CIR model and the real-world Constant Maturity Treasury (CMT) yields for

the same maturities. This is done independently for each bond origination date.

For the firm, we approximate the volatility of the sales process σs using the standard

deviation of annual sales growth for the prior 10 years. For ρ, the correlation between the

7Duration bias is a potential concern since we are making a comparison to the equivalent maturity (notduration) CMT yield. Our model-generated credit spread, however, will be reported on the same basis,minimizing potential bias.

12

Wiener processes driving the risk-free rate and sales, we calculate the median correlation

between sales growth and changes in the short-term risk-free rate over the prior 10 years for

the firm’s industry. To approximate production costs for the firm p, we calculate the firm’s

5 year average of (Sales−EBITSales

).

Technically, the parameter α is the payout rate (or convenience yield) of the firm. The

primary effect of α, however, is that it adjusts the risk-neutral growth rate of firm sales;

when α is small (large), the growth rate is large (small). To set α, therefore, we need

an estimate of growth expectations for the firm. While the ratio of EBITTotal Market V alue

is a

theoretically appealing measure of growth in the context of the model, it is a noisy measure

in real-world data. Instead, we use a proxy for Tobin’s Q, (Total Market V alueTotal Book V alue

) to measure

growth opportunities. This proxy for growth is common in the corporate finance literature

(see e.g. Shin and Stultz; 1998). Furthermore, regression analysis (results not presented in

tables) indicates that Q and observed credit spreads are significantly negatively related.

To map Q into α, we first calculate average observed credit spreads and Q for twelve

representative non-callable bonds. Characteristics of these representative bonds correspond

to typical 5, 10, and 30 year bonds in our sample with ratings of either Aa, A, Baa, or Ba.8

We then assume that the mapping between Q and α for these representative bonds has the

following functional form:

α = a+ b ∗ ln (Q) . (12)

Finally, we solve for a and b such that the sum of squared relative prediction errors ((model-

generated spread - average observed spread) / average observed spread)2 is minimized for

8To calculate average observed credit spreads, we first regress actual at-issue credit spreads for our entiresample of non-callable bonds on a variety of observed characteristics, the most important being issuing firmleverage and bond maturity. The estimated coefficients from this regression are then used to calculate averagecredit spread values for our twelve representative bonds. For a medium term Baa bond for example, we setleverage equal to the average leverage value for medium term non-callable Baa bonds in our sample, setmaturity equal to 10 years, hold all other values constant at sample averages, and then calculate a predictedvalue. A similar process is used to calculate average Q for the representative bonds.

13

the representative bonds. The resulting values are a = 0.0501 and b = −0.0136. Thesevalues are then used in mapping Q into α for all sample bonds, including the make-whole

call bonds.9

For the capital structure of the firm, we first establish the degree of financial leverage by

setting the face value of debt F . Note that in the model there are no physical assets per se

and thus no book value of assets. We do, however, calculate the value of the firm. Thus,

leverage in the model corresponds to market leverage, DebtTotal Market V alue

. While we could set

F to match observed market leverage, the observed value tends to be noisy and affected by

exogenous market-wide variation in equity prices. We therefore set F to match observed

book leverage, DebtTotal Assets

.10

Debt maturity T is taken directly from the bond that we are analyzing; we are implic-

itly assuming that the bond’s maturity is representative of all debt in the firm’s capital

structure.11 Similarly, if the bond has a make-whole call provision then m is set equal to the

make-whole premium given in the bond’s indenture. To get the coupon rate c, we numerically

solve for the value such that the bond is priced at par. Thus, c is also the yield-to-maturity

of the bond.

9While our transformation of Q into α may seem ad-hoc, it is a parsimonious method of getting ourmodel to approximate real-world credit spreads. This is a necessary first step if we want to value the creditspread option given by the make-whole call provision. Other papers use similar methods to set appropriateparameters (see Anderson and Sundaresan; 2000 or Huang and Huang; 2002).10In our data, book leverage ( Debt

Total Assets ) is more highly correlated with at-issue credit spread (ρ=0.34)

than is market leverage ( DebtTotalMarket V alue ) (ρ =0.27).

11Jones, Mason, and Rosenfeld (1984) note that contingent claims models are difficult to implement whenpricing individual bonds since the models must assume simple capital structures while real-world capitalstructures are often quite complex. Empirical studies that analyze the effectiveness of structural modelssuch as Jones, Mason, and Rosenfeld (1984), Ogden (1987), and Eom, Helwege, and Huang (2003) finessethis issue by focusing on firms with very simple capital structures.

14

4.2 Model-Generated Spreads

For each bond in the final sample, we parameterize the stochastic processes to match observed

characteristics of the risk-free yield curve, firm, and bond at the origination date. Table 2

displays the predicted credit spread relative to the model-generated comparable maturity

risk-free yield. For non-callable bonds, the mean (median) predicted spread is 81 (38) basis

points. For make-whole bonds, the predicted spread includes the incremental yield associated

with that bond’s make-whole call provision. The predicted spread for the make-whole call

bonds is significantly higher at 145 (114) basis points.12,13

To assess the general fit of our model, we provide summary statistics on prediction error

calculated as predicted spread minus observed spread. For non-callable bonds the mean

(median) value of the prediction error is -26 (-44) bp with a standard deviation of 98 bp.

For make-whole call bonds the prediction error is -35 (-48) bp with a standard deviation of

127 bp. We also report percentage prediction errors, calculated as prediction error divided

by observed spread.

While our model underpredicts credit spreads on average, its predictive ability is on par

with the structural models tested by Jones, Mason, and Rosenfeld (1984), Wei and Guo

(1997), Lyden and Saranti (2000), and Eom, Helwege, and Huang (2003). For example,

the absolute percentage prediction error is of similar magnitude to the two best performing

models tested by Eom et al. and reported in their Table 3.14 This is particularly notable

12As will be seen later, most of the difference in predicted spreads between the non-callable and the make-whole call bonds is not due to the make-whole call provision. Rather, it is due to systematic differences inother characteristics as illustrated in Table 1.13A potential concern is our assumption that maturity of the individual bond is representative of all of the

firm’s debt. We calculate a weighted-average maturity of the firm’s debt listed in the FISD, excluding bankdebt and commercial paper, and subtract it from the maturity of the individual bond. The differential isapproximately the same for both types of bonds and has a mean (median) value of 1.2 (0.6) years. Therefore,while our simplifying assumption will induce noise in our estimates, it should not induce bias.14The models tested by Eom et al. are an extended version of Merton (1974), Geske (1977), Leland

and Toft (1996), Longstaff and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). Their bestperforming models are Merton (1974) and Geske (1977).

15

given that all of the previously mentioned empirical studies limit their samples to bonds

issued by firms with simple capital structures, i.e., samples where structural models are

expected to work best.

Regression analysis of the prediction errors (results not presented in tables) shows that

they are positively related to most of the firm and bond-specific model inputs such as lever-

age, volatility of sales, costs/sales, the payout ratio α, and maturity. The result is that we

tend to underestimate credit spreads for short-term and highly rated bonds and overestimate

credit spreads for long-term and poorly rated bonds. Eom, Helwege, and Huang (2003), An-

derson and Sundaresan (2000) and Huang and Huang (2002) all show that this is a common

characteristic of structural models.

Intuitively, the total spread can be thought of as compensation demanded by bondholders

for the two options owned by the issuer: (1) the option to default and (2) the option to call.

To estimate the incremental cost of the option to call, we subtract the predicted spread

for an equivalent non-callable bond from the predicted spread for the make-whole call bond.

Taking the difference in this manner should substantially reduce any unobserved bias possibly

introduced by the model. After differencing, we calculate the sample mean (median) model-

generated incremental yield to be 2.75 (1.75) basis points with a maximum of 22.1 basis

points and a minimum of 0 basis points.

In a perfect capital market, the comparatively small incremental yield reflects two facts.

First, the firm will call only when it can profitably refund the existing bond with an equivalent

bond at lower cost. For this to occur, the credit spread on new borrowing for the firm must

be less than the make-whole premium and the market price of the bond must be above

par (or else the call price floor at par is binding). Given the small magnitude of make-

whole premiums, however, the likelihood of such a refunding opportunity is small. Second,

the small incremental yield reflects that the payoff to the firm from exercising the call is

16

capped.15

4.3 Comparative Statics

In this section, we examine how changes in underlying parameter values affect the incremen-

tal yield attributable to a make-whole call provision. To provide meaningful comparative

statics, we first parameterize a base case for our model. The parameter values for the base

case correspond to a typical bond in our sample and are as follows: r=4.77%, κr=0.171

per year, r∗=6.01%, and σr=10% annualized. For the sales process, values are σs=11.4%,

ρ=0.027, p=78%, and α=4.56%. Finally, for capital structure, values are FV=18.5%, T=10

years, and m=24 bp. For these parameter values, the predicted credit spread for the equiva-

lent non-callable bond is 65.21 bp and the incremental yield attributable to the make-whole

call provision is 3.89 bp. Next, holding all other parameters constant, we vary each pa-

rameter by reducing it to approximately its 25th percentile value and then increasing it

to approximately its 75th percentile value. The resulting non-callable credit spreads and

incremental yields are reported in Table 3.

The comparative statics indicate that in most cases, the incremental yield and the non-

callable credit spread are inversely related. The incremental yield is larger while the non-

callable credit spread is smaller for firms that have lower volatility of sales, lower leverage,

lower production costs, and greater growth opportunities. Given the competing nature of

the default and call options, these results are intuitive. As the option to default becomes

more valuable, the non-callable credit spread increases - a first order effect. The second

order effect, however, is a reduction in the value of the call option since firms that are more

likely to default have less incentive to exercise the call option. This leads to a decline in

15If the make-whole premium is 25 bp, the most that the firm can save when refunding is 25 bp of yield.For a bond with five years until maturity and a 7 percent coupon, discounting at 6.75 percent rather thanat 7 percent implies a savings of $10.46 per $1,000 of face value.

17

the incremental yield. For example, an increase in sales volatility from 11.4% to 17.4%

increases the non-callable credit spread from 65.21 bp to 170.04 bp while the incremental

yield declines from 3.89 bp to less than 1 bp. The inverse relationship between incremental

yield and non-callable credit spread also holds as the level of the yield curve varies; as the

risk-free yield increases, the non-callable credit spread narrows and the incremental yield

increases.

In most cases, there is little that issuing firms can do to adjust the parameters for which we

present comparative statics. This is not true, however, for the make-whole premium; issuing

firm are free to choose any value that they desire. Because of the practical importance of

the relationship between the make-whole premium and the incremental yield, we plot the

relationship in Figure 2. A larger make-whole premium is tantamount to a lower exercise

price. This results in a larger incremental yield. For the base case bond for example, an

increase in the make-whole premium from 24 bp to 30 bp leads to a substantial increase in

the incremental yield from 3.89 bp to 5.44 bp.

5 Empirical Analysis of Incremental Yields

We have two primary objectives in our empirical analysis. The first is to determine whether

our model captures the cross-sectional variation in the incremental yield associated with a

make-whole call provision. If so, then this helps to validate the comparative statics discussed

in section 4.3. The second objective is to compare the magnitude of observed incremental

yields to the model-generated incremental yields.

To accomplish both objectives, we rely on regression analyses where the dependent vari-

able is the observed credit spread CSpo at origination. To control for the default component

of credit spreads, we include the model-generated non-callable bond credit spread as an

independent variable NC CSpm. Note that for a make-whole call bond, this is the model-

18

generated credit spread for an equivalent non-callable bond. To capture the incremental

yield associated with a make-whole call provision, we include the model-generated incre-

mental yield for make-whole call bonds MW IYm. For non-callable bonds, MW IYm is set

equal to zero.

As our primary analysis, we estimate the following equation using Ordinary as well as

Robust Least-Squares:

CSpo = a0 + a1 ∗NC CSpm + a2 ∗MW IYm + a03 ∗ (Controls) + ε. (13)

If our model is a perfect representation of reality and our parameterization process is without

error, then we expect estimated coefficients of 0 for a0 and 1 for a1 and a2. We also include

a variety of controls in the regression for bond, firm, and economy-wide factors which have

been shown to affect credit spreads but which are not incorporated in our structural model.

5.1 Exogenous Control Variables

To account for exogenous variation in the credit environment due to macroeconomic fluc-

tuations, we include the difference between Moody’s Seasoned 10-year Baa corporate yield

and the 10-year Constant Maturity Treasury (CMT) rate (Baa CMT Sp). Throughout the

sample period, there is wide variation in the seasoned credit spread ranging from 124 to 383

basis points.16

Elton et al. (2001) show that low credit quality bonds expose investors to systematic

risk in addition to default risk. While this additional risk is reflected in real-world credit

spreads, it is not incorporated in our model and must be controlled for separately. Following

Eom, Helwege, and Huang (2003), we use an ordinalized rating variable (Aaa = 1, Aa+ =

2, Aa = 3, etc.) Since actual rating is correlated with our model-generated credit spread, we

16During the sample period, there was a “flight to quality” during the Asian debt crisis of 1997 and theLong-Term Capital Management and Russian debt crises of 1998. There was also a significant increase inidiosyncratic equity volatility (Campbell and Taksler; 2003).

19

first orthogonalize the ordinal rating variable before including it in our primary regression.

We do this by estimating an ordered logit regression with ordinal rating as our dependent

variable and NC CSpm as the independent variable.17 The residual from this regression

Residual Rating is then included in our analysis of CSpo and functions as a proxy for all of

the characteristics of the bond and firm that we are unable to observe. For non-rated bonds

(71 cases), we replace the missing value for Residual Rating with a zero and then code a

dichotomous variable Not Rated to one.

Our model already incorporates a measure of firm volatility, however, Campbell and

Taksler (2003) find that the relationship between observed credit spreads and the volatility

of daily excess stock returns is significantly stronger than what is found when simulating

the Merton (1974) model. We expect that much of the extra explanatory power of idiosyn-

cratic equity volatility will already be controlled for via our inclusion of Residual Rating and

Baa CMT Sp.18 Nevertheless, we include EquityVolatility as an independent variable. Since

idiosyncratic volatility is positively correlated with MW IYm, we report regression results

both with and without the volatility measure.

Chaplinsky and Ramchand (1997), Fenn (2000), and Livingston and Zhou (2002) find

that credit spreads for bonds issued privately under Rule 144a are significantly greater than

for comparable publicly issued bonds. The latter two papers also find that credit spreads are

greater for first-time bond issuers (see also Datta, Iskandar-Datta and Patel; 1997) and, after

controlling for rating, for bonds classified as senior. To control for private versus public, we

include a dichotomous variable Rule 144A that is coded one for the 13.8 percent of our bonds

that are privately issued. First Bond is coded one for the 17.5 percent of our sample where

17Discussions with representatives of the two major bond rating agencies (Moody’s and Standard andPoors) indicate that the existence of a make-whole call provision does not impact the rating assigned to abond. Thus, we do not include MW IYm when we orthogonalize.18In addition to finding a cross-sectional relationship, Campbell and Taksler (2003) show that aggregate

corporate yield spreads widen during periods of higher idiosyncratic volatility.

20

no earlier bond issued by the same firm is recorded in the FISD. Finally, Senior is coded

one for 94.9 percent of our bonds that are designated as either senior or senior-secured.

Elton et al. (2001), and Campbell and Taksler (2003) document that yield spreads for

bonds issued by financial service firms are between 10 and 20 basis points greater than yield

spreads for industrial bonds. Therefore, we include a dichotomous variable Finance that is

coded one for the 21.3 percent of our bonds that are issued by financial service firms and zero

otherwise. Bonds issued by utility firms comprise 6.8 percent of our sample. Since utility

firms are often regarded as distinctly different credit risks, we also include a dichotomous

variable Utility for utility issuers.

Chen, Lesmond, and Wei (2002) show that bond liquidity is negatively related to credit

spreads. Their measure of liquidity is beyond the scope of this paper, however, they find that

their liquidity measure is negatively related to maturity and positively related to amount

outstanding. We include LogOfferingAmount and LogMaturity, therefore, as controls for

liquidity. Including the log of maturity is also motivated by research indicating that the

observed term structure of credit spreads widens with maturity (Litterman and Iben; 1991,

Fons; 1994, and Duffee; 1999).19

5.2 Regression Results

Results from estimating equation (13) for the entire sample are displayed in Table 4. The

first column presents OLS estimates. The second and third columns present robust least

squares estimates.20 Inclusion of EquityVolatility distinguishes the specification in the third

19Our model generates an upward-sloped credit spread term structure. It is unclear, though, whether theobserved slope is entirely due to the default risk captured by our model. Thus, it is prudent to includelog of maturity as an exogenous control. Subsequent results are robust to including dichotomous variablesdistinguishing short-term, medium-term and long-term bonds.20The robust regression procedure available in Stata 7.0 R° is an iterative weighted least squares process

where the weights are inversely proportional to residuals from a previous pass. This reduces the influence ofoutliers.

21

column from the specification in the second column.

In each specification, the signs of estimated coefficients for the exogenous control vari-

ables are generally as expected and values are statistically significant. At-issue credit spreads

increase with Moody’s seasoned bond credit spread. The estimated coefficients for Resid-

ual Rating, our proxy for unobserved characteristics outside the scope of our structural model,

are positive and highly significant. Credit spreads are greater for: longer maturity bonds,

privately issued bonds, bonds that represent the first debt issue of the firm, and for bonds

issued by firms with volatile equity prices. Credit spreads are lower when the yield curve is

steeply sloped, the offering amount is large, and when the bond has seniority. The impact

of issuer industry (Finance and Utility) depends on the specification.

The more important results are those that pertain to the model estimates. In the OLS

results of the first specification, The estimated coefficient for NC CSpm is 0.257 with a

heteroscedasticity-consistent t-statistic of 12.22. While the estimated coefficient is substan-

tially less than one - the value that would be expected if our model and its parameterization

were a perfect representation of reality - the statistical significance suggests that our struc-

tural model does capture a significant amount of real-world variation in credit spreads.

The estimated coefficient for MW IYm is 6.219 with a highly significant t-statistic of

6.07. We caution that these results are sensitive to outliers in the data. Indeed, analysis

of the regression residuals shows that the variance of the residuals increases noticeably with

the predicted credit spreads.21

The difficulty with outliers can be almost totally eliminated by replacingCSpo, NC CSpm,

and Baa CMT Sp with their respective logs and MW IYm with log(1+MW IYm).22 Inter-

21This is consistent with Elton et al. (2001) who note that greater bond default risk leads to greatercredit spreads and to greater uncertainty as to the appropriate value of the bond. Similarly, Nejadmalayeri(2002) and Joutz, Mansi, and Maxwell (2002) show that variation in credit spreads increases as bond ratingdeteriorates.22Taking the log of MW IYm without first adding one is problematic since MW IYm is equal to zero for

22

preting coefficient in this regression, however, is not straightforward (results available from

authors.) Instead, we report robust OLS results in the second and third regression specifi-

cations. In the second specification, the estimated coefficient for NC CSpm declines from

0.257 to 0.184, but the t-statistic increases to more than 18. The estimated coefficient for

the incremental yield MW IYm also declines from 6.219 to 4.359 with a t-statistic of 8.46.

Including idiosyncratic equity volatility as is done in specification 3 has minimal effect on

the estimated coefficients for the model-generated values. Including a dichotomous variable

identifying make-whole call bonds in addition to MW IYm (results not presented in tables)

does not alter results significantly either.

Given our results, how do we interpret the estimated coefficients forMW IYm? If the real

world pricing of make-whole call provisions perfectly coincides with our model’s predictions,

then we expect an estimated coefficient of one for MW IYm. Instead, estimated coefficients

are significantly greater than one for MW IYm; the p-value of an F-test for MW IYm =

1 is .0000 for both specifications two and three. For the average make-whole call bond in

our sample, the baseline model predicts an incremental yield of 2.75 basis points. Empirical

results from the robust OLS regressions suggest incremental yields of 4.359×2.75 bp = 11.99bp for specification two and 3.866×2.75 bp = 10.63 bp for specification three. Both valuesare significantly greater than what is predicted by the model.

6 Potential Sources of Additional Incremental Yield

The incremental yield generated by our model reflects the pure economic value of the make-

whole call provision. By pure economic value we mean the gains that the firm can seize

when credit spreads narrow to the point that the make-whole call provision is in-the-money.

In practice, there are alternative sources of incremental yield that are not captured in the

over half of the observations.

23

model. In the following subsections, we discuss and incorporate three market imperfections

that we believe might account for the disparity between model-generated and observed in-

cremental yields. These imperfections are capital gains taxes, transactions costs imposed

on investors when calls are executed, and exogenous events requiring the firm to retire debt

early. Other market imperfections such as transactions costs imposed on the firm when a

call is exercised might reduce the model-generated incremental yields. We choose, however,

to focus only on those that we think will increase model-generated values. Moreover, we try

to be conservative in parameterizing the imperfections so that we do not underestimate the

effect that imperfections have on incremental yields.

6.1 Capital Gains Taxes

If a make-whole call is exercised, a taxable investor will owe capital gains taxes whenever the

call price is greater than the investor’s basis value. For every make-whole call bond in our

sample, its offering price is at par or below — the mean (median) is 99.59 (99.70) percent of

par. Since the call price has a floor at par, taxable investors who purchased the bond when

issued will invariably owe capital gains taxes if the bond is called. Incorporating capital

gains taxes of 20 percent into our model has no impact on the non-callable credit spread. If

we assume that the marginal investor is taxed, however, the incremental yield for the base

case make-whole call bond increases by almost 2 bp from 3.89 bp to 5.83 bp.

6.2 Transactions Costs

A significant percentage of corporate bonds are held by institutional investors who often have

well-defined investment strategies. For example, the institution might follow a passive strat-

egy designed to match the risk profile and return of a benchmark portfolio. Alternatively,

the institution might follow an active strategy designed to capitalize on risk-arbitrage op-

24

portunities. In either case, exercise of a make-whole call provision can upset the investment

strategy and force the institution to rebalance the portfolio at an inopportune time.

We adjust the model by incorporating this “inconvenience”, assuming that if the firm

calls its debt, bondholders must pay transaction costs proportional to the face value of the

bond. In model terms, at the call boundary (eq. 10) the bond value is the following:

D(s, r, t) = (1− TransactionCosts)×M(r, c, F,m, t). (14)

Schultz (2001) presents evidence that round-trip transactions costs for investment grade

bonds average $2.70 per $1,000 of par value. Bondholders subject to the call of a bond are

presumably faced with one-way transactions costs when they reinvest call proceeds since

cash proceeds from the call are likely to be directly deposited into one of the investor’s bank

accounts. Thus, for the one-way trip bondholders experience when reinvesting proceeds from

a called bond, we assume that transactions costs are $1.35 per $1,000 of par value.23

When transactions costs of this magnitude are incorporated in our model in addition to

capital gains taxes, the non-callable credit spread again stays constant, but the incremental

yield attributable to the make-whole call provision increases by 0.37 bp from 5.83 bp to 6.20

bp.

6.3 Make-Whole Call Provisions as a Substitute for Tender Offers

Survey results from Graham and Harvey (2001) make it clear that firms value financial

flexibility. While their results imply that firms keep leverage low in order to be able to

23We impose an artificial restriction that no calls can occur within three months of the bond’s maturitydate. We do this because model-generated credit spreads decline to zero for all but the riskiest bonds as thematurity date approaches. This is a common outcome for structural models. If the bond has a make-wholecall provision, then the likelihood of a call approaches one as long as the make-whole premium is greater thanzero. This has minimal impact on the incremental yield of a make-whole call provision in a world devoid ofimperfections. However, when we include transactions costs, the result is that these costs are imposed fartoo frequently unless something like the three month barrier is applied.

25

issue debt in the future, survey results from Mann and Powers (2003b) indicate that firms

also value the flexibility to retire debt early. Specifically, they document that CFO’s value

make-whole call provisions because the call provision gives the firm ”the ability to retire 100

percent of a debt issue” without having to resort to a potentially costlier tender offer.

This cap on the price of a successful tender offer pays off in situations where a tender

offer would have otherwise occurred. Mann and Powers (2003c) find that tender offers are

primarily driven by exogenous events. For example, debt issues acquired during a merger or

acquisition may contain restrictive covenants that the surviving firm finds inconvenient and

desires to eliminate. They document that in the typical successful tender offer, the median

tendering firm pays bondholders a premium above market value of approximately $40 per

$1,000 of face value. The yield corresponding to this average tender price is approximately

50 bp above the equivalent maturity risk-free Treasury yield.

We conservatively assume that all tender offers occur at a spread of 10 bp above Trea-

suries. Thus, any make-whole call provision with a premium of 10 bp or more will reduce

the ex-post wealth transferred to debtholders, resulting in a corresponding increase in the

ex-ante incremental yield. Obviously, the greater the likelihood of situations requiring early

redemption, the greater should be the increase in incremental yield.

To estimate the likelihood of such an exogenous event, we search the transactions data in

the FISD for sales of bonds where the name of the purchaser includes the word “tender”.24

For all non-callable bonds and make-whole call bonds that mature after January 1, 1995 and

which pass the screening criteria described in the data section, we are able to identify 244

tender offers.

This number is likely to be an under-estimate of the true number of tender offers due

24The FISD has a field denoting whether a tender or exchange offer has ever been made for each bond,but the field is dormant and unused.

26

to data entry errors and a lack of data standardization. To estimate the degree of under-

estimation, we match this sample of FISD-identified tender offers to a sample of confirmed

tender offers provided by Mann and Powers (2003c). Our sample identifies 73.5% of their

confirmed tender offers. Thus, we suspect that our sample of FISD-identified tender offers

understates the true number by approximately 36% ( 10.735− 1) and that the true number

should be approximately 332 tender offers. In addition, we are able to identify 13 actual calls

of bonds with make-whole call provisions, making the total number of early redemptions 345.

The total number of bond-years from which redemptions are identified is 41,631. Thus, we

estimate that redemptions occur in approximately 0.83 percent of bond-years. The median

number of bond years per bond is 5. On an annualized basis, therefore, the likelihood of

observing an early redemption is only 0.17 percent per year (1 — (1-0.0017)5=0.0083).

With this information, we further modify the model by incorporating a Poisson arrival

process for an exogenous event that induces the firm to retire the bond early. The probability

of such an event is assumed to be constant per unit of time and independent of the remaining

maturity. If such an event arrives, the firm with a non-callable bond tenders for its bond

at the risk-free rate plus 10 bp while the firm with a make-whole call bond can call at the

make-whole call price. Note that we still assume that the firm with a make-whole call bond

can also call its bond endogenously, i.e., for economic reasons.

With an exogenous retirement requirement, imposed in addition to the two prior imper-

fections, the non-callable credit spread for the base case bond decreases slightly from 65.21

bp to 64.83 bp due to the potential windfall that a tender offer will generate.25 The windfall,

however, is capped in the case of the make-whole call bond. Thus, the incremental yield

attributable to the make-whole call provision increases by 0.40 bp from 6.20 bp to 6.60 bp.

25For consistency, one-way transactions costs as well as capital gains taxes are imposed when a tenderoccurs, moderating the benefit of the windfall.

27

6.4 Empirical Results Incorporating Imperfections into the Model

In Table 5, we present the same summary statistics as given in Table 2 for sample bonds.

In Table 5, however, model-generated credit spreads incorporate the imperfections of capital

gains taxes, transactions costs, and exogenous events requiring redemption. To save space,

we mention only the model-generated incremental yield, noting that after incorporating

imperfections, the incremental yield has a mean (median) value of 6.07 (5.44) bp.

Regression results using the new model-generated values are reported in Table 6. We

confine our discussion to the robust regression results presented in the second and third

specifications. As expected, estimated coefficients for the various exogenous control vari-

ables do not change significantly. Estimated coefficients for the non-callable credit spread

NC CSpm are also quite similar to Table 4 values. This is expected since the incorporated

market imperfections have minimal impact on the non-callable credit spread.

Of greater importance are the estimated coefficients for the incremental yield attributable

to the make-whole call provision MW IYm. Coefficient estimates for this variable are no-

ticeably smaller with values of 2.393 and 2.130. In both cases, however, F-tests indicate

that estimated coefficients for MW IYm are still significantly different from one (p-values <

.0001). Even after incorporating imperfections that likely increase the cost of make-whole

call provisions, our results still suggest that the call provisions are overpriced.

7 Robustness Checks

7.1 Analysis of More Homogenous Subsamples

Despite all of the control variables used in the regression analysis, one might still criticize our

analysis by suggesting that there are unobserved factors which explain the greater offering

spread for bonds with make-whole call provisions and that these factors are simply correlated

28

with the presence of a make-whole call provision. One way to reduce the likelihood of

unobserved heterogeneity within the issuing firms is to limit our sample to bonds with

similar characteristics.

In Table 7, we replicate the second specification in Table 6 (robust OLS using model-

generated values which incorporate imperfections) on various subsamples of the data. In the

first specification in Table 7, we restrict the sample to bonds that have ratings of Baa- or

better, eliminating the low grade and unrated bonds where heteroscedasticity is greatest. In

the second specification we further eliminate bonds issued by finance or utility companies

since it is conceivable that these firms use call provisions in a different manner than do

industrial firms. In both specifications, results are similar to those presented in Table 6.

In the third specification we reduce heterogeneity between the non-callable and make-

whole call bonds by matching them such that for each make-whole call bond there is one

non-callable bond with the same rating, similar maturity, and the same industry group.

Estimated coefficients for this matched subsample are also quite similar to the results shown

in Table 6.

In the final specification in Table 7, our subsample is restricted to non-callable and make-

whole call bonds issued by firms represented by at least one of each type of bond in our

sample. Again results are similar to those presented in Table 6 and the estimated coefficient

for MW IYm is significantly different from one. To summarize, these subsample robustness

checks suggest that the greater at-issue yield of bonds with make-whole call provisions is due

to the make-whole call provision, not to other unobserved differences between non-callable

and make-whole call bonds. Thus, results still suggest that make-whole call provisions are

overpriced at origination.

29

7.2 Alternative Models

For the majority of structural models it is not sales or cash flow that is stochastic, rather,

firm value V is assumed to be stochastic. To ensure that our results are not dependent on

our most basic modeling assumption, we replace the stochastic process for ds/s in equation

(2) with

dV

V= (r − α)dt+ σV dWV . (15)

To parameterize the firm value variant of our model we first calculate the annual volatility

of equity σE using the past 6 months of daily stock returns. The volatility of firm value σV

is related to σE by

σE = σVV

E

dEtdVt

. (16)

Following Eom, Helwege, and Huang (2003), we approximate dEtdVtusing the Merton (1974)

model where,

σE = σVN(d1(Kt, t))VtEt, (17)

d1(x, t) =ln( V0

xD(0,t)) + (−α+ σ2V

2)t

σV√t

, (18)

and where D(0, t) is the present value of a risk-free zero-coupon bond maturing at t, α is

the payout rate, and Kt is the amount of the firm’s debt.

The cash flows available to service debt are assumed to be a linear function of firm value.

As before, we use a representative group of non-callable bonds and solve for an optimal

mapping of Q into α using the functional form given in equation 12. All other characteristics

of the model and the resultant solutions remain the same.

Predicted spreads and more importantly incremental yields are quite similar when com-

pared to our original results. For example, with the baseline model that does not incorporate

30

imperfections, the average incremental yield using firm value as the stochastic process is 2.36

bp as compared to 2.75 bp. (results not presented in tables). In subsequent regression anal-

ysis (results not presented in tables) where NC CSpm and MW IYm are calculated using

the stochastic firm value process, results are similar in magnitude and significance to those

presented in Table 4.

7.3 Is Mispricing Independent of Bond Characteristics?

In our final robustness check, we investigate whether perceived mispricing is independent

of basic bond characteristics. To do this, we split the sample based on issue date, time

to maturity, and rating. We then estimate regression specification 2 from Table 6 for each

subsample. Results are presented in Table 8.

We first split the sample based on whether the bond was issued before or after 10/1/1999.

This split-date is chosen because it allocates roughly the same number of make-whole call

bonds to each subsample. Results for specification 1 show that there is no significant dif-

ference in the estimated coefficients for the the incremental yield MW IYm, suggesting that

mispricing at origination has been present across the entire time-span of the sample.

In specification 2, we split the sample based on whether the time-to-maturity of the

bond is more or less than 10.1 years. Again, estimated coefficients for MW IYm are not

significantly different from one another.

Finally, in specification 3, we split the sample based on whether the rating of the bond is

Baa+ or better as opposed to Baa or worse. For this sample split, estimated coefficients for

MW IYm of 1.626 for highly rated bonds and 3.485 for poorly rated bonds are significantly

different from one another (p-value=0.002). The larger estimated coefficient for the poorly

rated bonds indicates that investors require significantly greater compensation than predicted

by our model when a make-whole call provision is attached to a poorly rated bond.

31

One potential explanation for this result could be our assumption that the likelihood

of an exogenous event requiring early redemption is the same for all firms. Nuttall (1999),

however, finds that the likelihood of being a takeover target for UK quoted companies is

greater for more levered and more poorly performing firms. Poorly rated bonds are also

more likely to contain restrictive covenants (Nash, Netter, and Poulsen; 2003) which, if they

become binding in the future, will provide an incentive for the firm to retire debt early. In

either case, it is possible that the likelihood of our exogenous event should increase as credit

quality deteriorates. The alternative reason for the greater observed incremental yields for

poorly rated make-whole call bonds is that investors are unneccesarily penalizing poorly

rated make-whole call issuers. This alternative, however, is strictly speculation.

8 Conclusion

Make-whole call provisions have become quite common in corporate debt over the past

five years. The call provision’s primary benefit is that it gives the issuing firm substantial

financial flexibility without the high up-front cost of a fixed-price call provision. The lower

cost is directly attributable to the fact that the make-whole call price floats inversely with

contemporaneous risk-free interest rates. This greatly reduces the interest rate risk that is

associated with a potential future call.

Despite the prevalence of make-whole call provisions, we are the first to provide a model

for valuing them. In a frictionless market environment, our model predicts that the average

bond with a make-whole call provision should have a yield that is approximately 2.75 bp

greater than a comparable non-callable bond. When real-world market imperfections such

as capital gains taxes, transactions costs, and exogenous requirements to retire debt early

are taken into account, our model indicates that the incremental yield should average ap-

proximately 6.1 bp. Extensive empirical analysis of at-issue credit spread data for a large

32

sample of corporate bonds with make-whole call provisions, however, indicates that the ob-

served incremental yield is more than 11 bp. Moreover, the difference between observed and

predicted incremental yields is statistically significant. Our conclusion is that make-whole

call provisions to date have been overpriced at origination and that issuing firms have been

paying too high of a yield on their newly issued make-whole call bonds. An additional 5 bp

in yield may seem negligible, however, it is substantial when compared to the typical credit

spread at origination of 125 bp. In dollar terms, for a representative par bond with 15 years

to maturity, a 7 percent coupon, and an offering amount of $500 million, an additional 5 bp

in yield reduces offering proceeds by $2.3 million - to us a sum that should not be casually

disregarded.

Like all structural models, our’s is an abstraction from reality and incremental yields

are potentially predicted with error. We feel, however, that our model likely overestimates

what incremental yields should be, further strengthening our empirical results. One reason

why we believe this is because our underlying model is strictly a default model. In practice,

however, corporate credit spreads incorporate other factors such as liquidity risk, systematic

risk, and differential state taxation relative to Treasury securities (Elton et al.; 2001). These

other factors lend an additional component to credit spreads, ensuring that even the most

credit-worthy corporate bonds have yields that are significantly greater than risk-free yields.

For example, since 1954, Moody’s seasoned Aaa corporate bond yield has averaged 75 bp

more than the 10-year Constant Maturity Treasury yield. In this environment, the typical

make-whole call provision with a make-whole premium of 25 bp will have minimal economic

value since it is almost always out-of-the-money.

The second reason why our model might overestimate incremental yields is that in the

extended version, we have only included imperfections that generate an increase in incremen-

tal yields. Alternative imperfections, however, could conceivably have the opposite effect.

33

For example, firms might delay calls due to transactions costs incurred when calling (Mauer;

1993), concerns about wealth transfers resulting from temporary capital structure changes

(Longstaff and Tuckman; 1994), or simply because a suboptimal call policy is employed

(King and Mauer; 2000). Anything which delays calls beyond the point predicted by our

model will necessarily reduce model-generated incremental yields.

The final reason why model-generated incremental yields might be too high is because we

have been conservative in our assumptions regarding the three incorporated imperfections.

For example, we assume that the marginal investor is taxed. This is highly debatable when

the investment is a corporate bond. In addition, we assume a worst-case scenario when firms

are exogenously required to tender for non-callable debt. Thus, the additional incremental

yield due to both imperfections is likely to be overstated in the model.

It is unclear whether this perceived pricing anomaly will continue. Longstaff (1992)

for example, shows that there has been persistent mispricing of fixed-price call options on

older Treasury securities, despite the apparent existence of arbitrage opportunities. For

make-whole call provisions we see little opportunity for arbitrage opportunities due to the

incompleteness of the corporate bond market. Without arbitrage opportunities, there is no

obvious mechanism that will drive down the at-issue incremental yield of make-whole call

provisions.

Note that we test our model only against at-issue bond data. Primarily, this is be-

cause at-issue data is significantly cleaner, verifiable, and easily worked with than the sparse

transactions data available for corporate bonds. An interesting extension for future research,

however, would be to apply our model to transactions data in a manner similar to that done

by Duffee (1998) for bonds with fixed-price call provisions. This would enable us to deter-

mine whether the perceived mispricing persists in the after-market. In addition, analysis of

how make-whole call bond yields evolve relative to non-callable bond yields as characteristics

34

of firms, the bond market, and the macroeconomy change would improve our understanding

of how these innovative call provisions are priced.

9 Appendix

9.1 Valuation of the unlevered firm

The value of the unlevered firm V is given as the solution to the following PDE

σ2rr

2Vrr +

σ2ss2

2Vss + ρσsσrs

√rVrs

+ κr(r∗ − r)Vr + (r − α)Vs + s− p− rV = 0, V ≥ 0.

(19)

The boundary condition V ≥ 0 reflects the firm’s option to shut down its operations assoon as its value becomes negative.

9.2 Valuation of the Equity

Given the value of the short-term interest rate r, and the price level s, the value of equity

E(s, r, t) can be determined by maximizing the expected value of equity, over all possible

call and default strategies:

E(s(t), r(t), t) = max {0, max (V (s, r)−M(r, c, F, t), [s− p− c]dt

+ e−r(t)dtEQ[E(s(t+ dt), r(t+ dt), t+ dt)]}.(20)

At the debt maturity date T , the value of the firm’s equity is the greater of zero and the

difference between the value of the firm’s assets and the par value,

E(s, r, T ) = max(V (s, r)− F, 0). (21)

Any time prior to maturity, t < T, the value of equity E is given as the solution to the

following PDE:

35

σ2rr

2Err +

σ2ss2

2Ess + ρσsσrs

√rErs + κr(r

∗ − r)Er + (r − α)Es+

+Et + s− p− c− rE = 0, E ≥ 0(22)

with additional free boundary conditions that characterize the boundaries where debt is

called and where the firm defaults. The call boundary (if applicable) should satisfy

E(s, r) > max(0, V (s, r)−M(r, c, F, T )). (23)

36

References

[1] Acharya, Viral V., and Jennifer Carpenter, 2002, Corporate bond valuation and hedging

with stochastic interest rates and endogenous bankruptcy, Review of Financial Studies,

15, 1355-1383.

[2] Anderson, Ronald, and Suresh Sundaresan, 2000, A comparative study of structural

models of corporate bond yields: an exploratory investigation, Journal of Banking and

Finance 24, 255-269.

[3] Black, F., and M. Scholes, 1973, The theory of options and corporate liabilities, Journal

of Political Economy 81, 637-654.

[4] Baker, Malcolm, Robin Greenwood, and Jeffrey Wurgler, 2002, The maturity of debt

issues and predictable variation in bond returns, Harvard University working paper.

[5] Bliss, Robert R., and Ehud I. Ronn, 1998, Callable U.S. Treasury bonds: optimal calls,

anomalies, and implied volatilities, Journal of Business 71, 211-252.

[6] Brealey, Richard A., and Stewart C. Myers, 2003, Principles of Corporate Finance,

McGraw-Hill Irwin Press, New York, NY.

[7] Brennan, Michael J., and Eduardo S. Schwartz, 1984, Optimal financial policy and firm

valuation, Journal of Finance 39, 593-607

[8] Campbell, John Y., and Glenn B. Taksler, 2003, Equity volatility and corporate bond

yields, forthcoming Journal of Finance.

[9] Chaplinsky, Susan and L. Ramchand, 1997, The Rule 144A debt market: success or

failure?, University of Virginia, Charlottesville working paper.

37

[10] Chen, Long, David A. Lesmond, and Jason Wei, 2002, Bond liquidity estimation and

the liquidity effect in yield spread, Michigan State University working paper.

[11] Collin-Dufresne, Pierre, Robert S. Goldstein, 2001, Do credit spreads reflect stationary

leverage ratios?, Journal of Finance 56, 1929-1957.

[12] Collin-Dufresne, Pierre, Robert S. Goldstein, and J. Spencer Martin, 2001, The deter-

minants of credit spread changes, Journal of Finance 56, 2177-2207.

[13] Cox J.C., J.E. Ingersoll and S.A. Ross, An intertemporal general equilibrium model of

asset prices, Econometrica 53, 1985, pp. 385—407.

[14] Crabbe, Leland E, and Jean Helwege, 1994, Alternative test of agency theories of callable

corporate bonds, Financial Management 23, no. 4 3-20.

[15] Datta, Sudip, Mai Iskandar-Datta, and Ajay Patel, 1997, The pricing of initial public

offers of corporate straight debt, Journal of Finance 52, 379-396.

[16] Duffee, Gregory R., 1998, The relation between treasury yields and corporate bond yield

spreads, Journal of Finance 53, 2225-2241.

[17] Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann, 2001,

Explaining the rate spread on corporate bonds, Journal of Finance 56, 247-277.

[18] Emery, Douglas, Ronald Hoffmeister, and Ronald Spahr, 1987, The case for indexing a

bond’s call price, Financial Management, 57-64.

[19] Eom, Young Ho, Jean Helwege, and Jing-Zhi Huang, 2002, Structural models of corpo-

rate bond pricing, an empirical analysis, forthcoming The Review of Financial Studies.

38

[20] Fenn, George W., 2000, Speed of issuance and the adequacy of disclosure in the 144a

high-yield debt market, Journal of Financial Economics 56, 383-405.

[21] Fons, Jerome S., 1994, Using default rates to model the term structure of credit risk,

Financial Analysts Journal, Sept/Oct 25-32.

[22] Geske, Robert, 1977, The valuation of corporate liabilities as compound options, Journal

of Financial and Quantitative Analysis 12, 541-552.

[23] Graham, John R., and Campbell Harvey, 2001, The theory and practice of corporate

finance: evidence from the field, Journal of Financial Economics 60, 187-243.

[24] Helwege, Jean, and Christopher M. Turner, 1999, The slope of the credit yield curve

for speculative grade issuers, Journal of Finance 54, 1869-1884.

[25] Huang, Jing-zhi, and Ming Huang, 2002, How much of the corporate-treasury yield

spread is due to credit risk?: a new calibration approach, Pennsylvania State University

working paper.

[26] Jones, E. Phillip, Scott P. Mason, and Eric Rosenfeld, 1984, Contingent claims analysis

of corporate capital structures: an empirical analysis, Journal of Finance 39, 611-625.

[27] Joutz, Fred, Sattar A. Mansi, and William F. Maxwell, 2002, The dynamics of corporate

credit spreads, George Washington University working paper.

[28] King, Tao-Hsien Dolly, and David C. Mauer, 2000, Corporate call policy for noncon-

vertible bonds, Journal of Business 73, 403-444.

[29] Leland, Hayne E., and Klaus B. Toft, 1996, Optimal capital structure, endogenous

bankruptcy, and the term structure of credit spreads, Journal of Finance, 51, 987-1019.

39

[30] Litterman, Robert, and Thomas Iben, 1991, Corporate bond valuation and the term

structure of credit spreads, Journal of Portfolio Management, Spring, 52-64.

[31] Livingston, Miles and Lei Zhou, 2002, The impact of rule 144a debt offerings upon bond

yields and underwriter fees, Financial Management 31, 5-27.

[32] Longstaff, Francis A., 1992, Are negative option prices possible? The callable U.S.

Treasury-Bond puzzle, Journal of Business 65, 571-592.

[33] Longstaff, Francis A., and Eduardo S. Schwartz, 1995, A simple approach to valuing

risky fixed and floating rate debt, Journal of Finance 50, pp. 789—821.

[34] Longstaff, Francis A., and Bruce A. Tuckman, 1994, Call nonconvertible debt and the

problem of related wealth transfer effects, Financial Management 23, 21-27.

[35] Mann, Steven V, and Eric A. Powers, 2003a, What is the cost of a make-whole call

provision?, Journal of Bond Trading and Management 1, no. 4 315-325.

[36] Mann, Steven V, and Eric A. Powers, 2003b, Indexing a bond’s call price: an analysis

of make-whole call provisions, Journal of Corporate Finance 9, 535-554.

[37] Mann, Steven V., and Eric A. Powers, 2003c, Determinants of bond tender offer premi-

ums and tendering rates, University of South Carolina working paper.

[38] Mauer, David C., 1993, Optimal bond call policies under transactions costs, Journal of

Financial Research 16, 23-27.

[39] Mauer, David C., and Stephen H. Ott, 2000, Agency costs, investment policy, and op-

timal capital structure: the effect of growth options, in M.J. Brennan and L. Trigeorgis

(eds.), Project Flexibility, Agency, and Competition: New Developments in the Theory

and Application of Real Options, Oxford University Press, 151-179.

40

[40] Mello, Antonio S., and John E. Parsons, 1992, Measuring the agency costs of debt,

Journal of Finance 47, 1887-1904.

[41] Merton, Robert C., 1974, On the pricing of corporate debt: the risk structure of interest

rates, Journal of Finance 29, 449-470.

[42] Nash, Robert C., Jeffry M. Netter, and Annette B. Poulsen, 2003, Determinants of

contractual relations between shareholders and bondholders: investment opportunities

and restrictive covenants, Journal of Corporate Finance 9, 201-232.

[43] Nejadmalayeri, Ali, 2002, The determinants of credit spread deviations, University of

Nevada-Reno working paper.

[44] Nuttal, Robin, 1999, Takeover likelihood for UK quoted companies, Oxford University

working paper.

[45] Ogden, Joseph P., 1987, Determinants of the ratings and yields on corporate bonds:

tests of the contingent claims model, The Journal of Financial Research 10, 329-339.

[46] Schultz, Paul, 2001, Corporate bond trading costs: a peek behind the curtain, Journal

of Finance 56, 677-698.

[47] Shin, Hyun-Han, and Rene M. Stulz, 1998, Are internal capital markets efficient?,

Quarterly Journal of Economics 113, 531-552.

41

42

The columns display the nominal dollar amount of corporate debt issued in the U.S. per year. Included issues have the following characteristics: maturity of at least one year, denominated in U.S. dollars, offering amount greater than $25 million, fixed semi-annual coupon, not asset-backed, not putable, without a sinking fund, not a Yankee bond, not a Medium Term Note, not part of a unit offering, and listed as a corporate debenture. Note that the 2002 data stops at 10/01/2002.

43

Plot points show the model-generated incremental yield attributable to the make-whole call provision as a function of the make-whole premium. All other parameters for the model are held fixed at base case values.

44

Table 1

Panel A: Issuing Firm Characteristics. Means (medians) for issuing firm characteristics. We allow one observation per firm, per bond type, per year. Columns two and three present results for the entire universe of straight bond and make-whole call bond issuers screened from the FISD. Column four displays p-values for a T-test and a Wilcoxon Rank-Sum test comparing straight issuers to make-whole issuers from columns two and three. Columns five and six present results for the subset of bond issuers where we were able to calculate a model-generated credit spread. Data definitions: Sales: total firm sales, EBITDA/MKT: earnings before interest, taxes, and depreciation divided by market value of firm, EBITDA/AT: EBITDA divided by total assets, Q: (total assets – book equity + market equity) divided by total assets, Book Leverage: long-term debt divided by total assets, Sales Growth: 10 year average annual sales growth, σ Sales Growth: standard deviation of 10 year annual sales growth, Equity Volatility: standard deviation of daily excess stock return for the prior 6 months.

Initial Sample Final Sample Straight Make-whole T-test

(Rank-Sum)Straight Make-whole

Sales

$10,111 ($3,758)

$7,712 ($3,145)

.0016 (.0049)

$10,988 ($4,683)

$8,797 ($4,415)

EBITDA/MKT

7.4% (7.7%)

8.3% (8.2%)

.0001 (.0001)

8.1% (8.5%)

8.9% (8.8%)

EBITDA/AT

12.1% (11.6%)

13.5% (13.1%)

.0009 (.0001)

12.9% (13.0%)

14.0% (13.1%)

Q

1.63 (1.32)

1.76 (1.41)

.0185 (.0001)

1.58 (1.34)

1.58 (1.37)

Book Leverage

28.1% (26.4%)

30.1% (29.3%)

.0090 (.0004)

23.2% (24.9%)

31.4% (30.2%)

Sales Growth

13.5% (9.3%)

16.3% (9.3%)

.0195 (.5278)

10.6% (8.6%)

11.9% (9.2%)

σ Sales Growth

15.4% (11.8%)

16.6% (11.5%)

.0685 (.9804)

12.0% (11.0%)

12.8% (11.5%)

Equity Volatility

0.020 (0.017)

0.022 (0.020)

.0000 (.0000)

0.019 (0.017)

0.022 (0.021)

# of Obs. 966 1083 520 435

45

Panel B: Bond Characteristics. Data definitions: Rating: ordinalized bond rating (AAA = 1, AA+ = 2, etc.), Maturity: years to maturity, Offering Amount: total face value in millions of nominal dollars, Offering Spread: actual yield-to-maturity at issue minus the equivalent maturity Constant Maturity Treasury yield.

Initial Sample T-test Final Sample Straight Make-whole Rank-Sum Straight Make-whole Rating

7.0 (7.0)

8.3 (9.0)

.0001 (.0001)

7.0 (7.0)

8.5 (9.0)

Maturity

10.7 (9.0)

13.0 (10.0)

.0001 (.0001)

11.1 (10.0)

12.2 (10.0)

Offering Amount

$403 ($250)

$392 ($300)

.4909 (.0001)

$336 ($244)

$365 (281)

Offering Spread 117 bp (88 bp)

179 bp (155 bp)

.0001 (.0001)

108 bp (88 bp)

180 bp (163 bp)

# of Obs. 1,612 1,583 775 734

46

Table 2 Model-Generated Credit Spreads

Predicted Spread is the model-generated yield-to-maturity minus the model-generated risk-free rate. For make-whole call bonds, Predicted Spread incorporates the inclusion of a make-whole call provision. Prediction Error is Predicted Spread minus observed Offering Spread and σ Prediction Error is the associated standard deviation. Relative Prediction Error is Prediction Error divided by observed Offering Spread and σ Relative Prediction Error is the associated standard deviation. Both signed values for errors and absolute values are presented. Incremental Yield is reported only for make-whole call bonds and is the Predicted Spread for the make-whole call bond minus the Predicted Spread for a straight bond that, with the exception of the make-whole call provision, is equivalent in all respects.

Non-callable Make-whole Signed

Value Absolute

Value Signed Value

Absolute Value

Predicted Spread 81 bp (38 bp)

145 bp (114 bp)

Prediction Error -26 bp (-44 bp)

81 bp (67 bp)

-35 bp (-48 bp)

104 bp (89 bp)

σ Prediction Error 98 bp 61 bp 127 bp 80 bp

Relative Prediction Error

-18% (-60%)

85% (87%)

-10% (-31%)

64% (63%)

σ Relative Prediction Error

106% 65% 81% 49%

Incremental Yield

2.75 bp (1.75 bp)

# of Obs. 775 612

47

Table 3 Comparative Statics

The model parameters for the base case bond are as follows: make-whole premium (Premium) = 0 bp for base case non-callable bond and 24 bp for base case make-whole call bond, Maturity = 10 years, long-term debt divided by total assets (Leverage) = 18.5%, payout rate of firm (Alpha) = 4.56%, 10 year historical variance of annual sales (Sales Volatility) = 11.4%, yield of model derived 10 year risk-free note (Yield Curve Level) = 5.64%, correlation of stochastic processes for risk-free rate and cash flows (Stochastic Correlation) = 0.027. The model-generated Credit Spread for the base case non-callable bond is 65.21 bp and the Incremental Yield of the equivalent make-whole call bond is 3.89 bp. Each row of the table reports the Credit Spread and Incremental Yield as one of the parameters, for example Premium, is varied below and then above the base case value. The low and high values for the respective parameters roughly correspond to 25th and 75th percentile sample values.

Parameter low value high value

Credit Spread

Incremental Yield

18 bp 65.21 bp 2.33 bp Premium: 30 bp 65.21 bp 5.44 bp

Maturity: 8 yrs 58.16 bp 3.95 bp 15 yrs 72.59 bp 2.33 bp Leverage: 14.5% 56.91 bp 4.13 bp 22.5% 71.95 bp 3.26 bp Alpha: 4.16% 38.04 bp 4.27 bp 4.76% 84.24 bp 3.49 bp Sales Volatility: 8.4% 27.95 bp 5.82 bp 17.4% 170.04 bp 0.78 bp Yield Curve Level: +1% 42.41 bp 4.61 bp -1% 78.24 bp 3.62 bp Stochastic Correlation: -0.037 62.16 bp 3.83 bp 0.077 67.93 bp 3.88 bp

48

Table 4 Empirically Observed Credit Spreads Versus "Pure" Model-Generated Values

The dependent variable is the bond's actual credit spread at issue. Independent variables are as follows. NC_CSpm is the model-generated credit spread for a non-callable bond. For make-whole call bonds, it is the credit spread of an equivalent straight bond. MW is coded one for bonds with a make-whole call provision, zero otherwise. MW_IYm is the model generated make-whole call provision incremental yield and is set to zero for straight bonds. Baa_CMT_Sp is Moody's seasoned Baa yield minus the 10-year CMT yield. Rule 144a is coded one for privately issued bonds, zero otherwise. Finance and Utility are coded one for financial services and utility firms, respectively, zero otherwise. Residual Rating is the difference between actual ordinal rating of the bond and a predicted rating obtained via an ordered logit regression (see text for details). Not Rated is coded one for unrated bonds, zero otherwise. First Bond is coded one when the observation represents the first bond issue for the firm, zero otherwise. Senior is coded one if the bond is denoted senior or senior-secured, zero otherwise. Equity Volatility is standard deviation of the firm's excess stock returns for the 183 days prior to the offering. Specification 1 is OLS while 2 and 3 are robust OLS (weighted least squares is used to limit impact of outliers). Below each coefficient estimate is the t-statistic (for specification 1 the t statistics are calculated using White standard errors.) Significance at the 10%, 5% and 1% levels is denoted by *, **, ***, respectively.

Spec. 1 Spec. 2 Spec. 3 Constant 0.390

(1.34) -0.556

(2.72)** -0.075 (0.40)

NC_CSpm

0.257 (12.22)***

0.184 (18.16)***

0.184 (19.76)***

MW_IYm

6.219 (6.07)***

4.359 (8.46)***

3.866 (8.19)***

Baa_CMT_Sp 0.731 (28.80)***

0.684 (27.48)***

0.509 (20.98)***

Residual Rating

0.153 (17.07)***

0.126 (20.62)***

0.129 (23.05)***

Not Rated

-0.610 (4.90)***

-0.750 (13.99)***

-0.443 (8.48)***

Rule 144A

0.467 (7.76)***

0.385 (11.57)***

0.329 (10.76)***

Finance -0.018 (0.41)

0.081 (2.81)***

0.094 (3.54)***

Utility -0.020 (0.30)

0.018 (0.40)

0.104 (2.52)**

Log Maturity 0.046 (2.01)**

0.107 (6.08)***

0.135 (8.32)***

Log Offering Amt -0.047 (2.10)**

-0.006 (0.35)

-0.062 (4.14)***

First Bond 0.134 (2.74)***

0.144 (4.79)***

0.097 (3.52)***

Senior -0.492 (4.02)***

-0.080 (1.56)

-0.149 (3.18)***

Equity Volatility 30.031 (19.05)***

# of OBS 1339 1339 1339 Adj. R2 .6169 .5647 .6458

49

Table 5 Model-Generated Credit Spreads Incorporating Imperfections

Predicted Spread is the model-generated yield-to-maturity minus the model-generated risk-free rate. For make-whole call bonds, Predicted Spread incorporates the inclusion of a make-whole call provision. Prediction Error is Predicted Spread minus observed Offering Spread and σ Prediction Error is the associated standard deviation. Relative Prediction Error is Prediction Error divided by observed Offering Spread and σ Relative Prediction Error is the associated standard deviation. Both signed values for errors and absolute values are presented. Incremental Yield is reported only for make-whole call bonds and is the Predicted Spread for the make-whole call bond minus the Predicted Spread for a straight bond that, with the exception of the make-whole call provision, is equivalent in all respects.

Straight Make-whole Signed

Value Absolute

Value Signed Value

Absolute Value

Predicted Spread 81 bp (37 bp)

147 bp (117 bp)

Prediction Error -27 bp (-44 bp)

81 bp (67 bp)

-33 bp (-45 bp)

102 bp (86 bp)

σ Prediction Error 97 bp 61 bp 125 bp 80 bp

Relative Prediction Error

-19% (-60%)

85% (85%)

-9% (-29%)

63% (61%)

σ Relative Prediction Error

105% 64% 79% 49%

Incremental Yield

# of Obs. 775

6.07 bp (5.44 bp)

612

50

Table 6 Empirically Observed Credit Spreads Versus Model-Generated Values with Imperfections

The dependent variable is the bond's actual credit spread at issue. Independent variables are as follows. NC_CSpm is the model-generated credit spread for a non-callable bond. For make-whole call bonds, it is the credit spread of an equivalent straight bond. MW is coded one for bonds with a make-whole call provision, zero otherwise. MW_IYm is the model generated make-whole call provision incremental yield and is set to zero for straight bonds. Baa_CMT_Sp is Moody's seasoned Baa yield minus the 10-year CMT yield. Rule 144a is coded one for privately issued bonds, zero otherwise. Finance and Utility are coded one for financial services and utility firms respectively, zero otherwise. Residual Rating is the difference between actual ordinal rating of the bond and a predicted rating obtained via an ordered logit regression (see text for details). Not Rated is coded one for unrated bonds, zero otherwise. First Bond is coded one when the observation represents the first bond issue for the firm, zero otherwise. Senior is coded one if the bond is denoted senior or senior-secured, zero otherwise. Equity Volatility is standard deviation of the firm's excess stock returns for the 183 days prior to the offering. Specification 1 is OLS while 2 and 3 are robust OLS (weighted least squares is used to limit impact of outliers). Below each coefficient estimate is the t-statistic (for specifications 1 the t-statistic is calculated using White standard errors.) Significance at the 10%, 5% and 1% levels is denoted by *, **, ***, respectively.

Spec. 1 Spec. 2 Spec 3. Constant 0.331

(1.13) -0.582

(2.83)*** -0.124 (0.66)

NC_CSpm

0.242 (11.67)***

0.176 (17.50)***

0.176 (19.15)***

MW_IYm

3.239 (5.85)***

2.393 (8.22)***

2.130 (8.01)***

Baa_CMT_Sp 0.734 (18.85)***

0.682 (27.12)***

0.507 (20.75)***

Residual Rating

0.158 (17.62)***

0.129 (21.23)***

0.131 (23.64)***

Not Rated

-0.587 (4.65)***

-0.738 (13.63)***

-0.433 (8.24)***

Rule 144A

0.476 (7.88)***

0.386 (11.59)***

0.328 (10.75)***

Finance -0.025 (0.58)

0.076 (2.60)***

0.089 (3.36)***

Utility -0.036 (0.55)

0.005 (0.10)

0.090 (2.17)**

Log Maturity 0.065 (2.80)***

0.119 (6.66)***

0.146 (8.91)***

Log Offering Amt -0.044 (1.99)**

-0.004 (0.26)

-0.059 (3.93)***

First Bond 0.146 (3.04)***

0.148 (4.89)***

0.101 (3.64)***

Senior -0.505 (4.12)***

-0.091 (1.76)*

-0.159 (3.39)***

Equity Volatility 30.07 (19.03)***

# of OBS 1339 1339 1339 Adj. R2 .6129 .5618 .6421

51

Table 7 Robustness Checks for Empirically Observed Credit Spreads

The dependent variable is the bond's actual credit spread at issue. Independent variables are as follows. NC_CSpm is the model-generated credit spread for a non-callable bond. For make-whole call bonds, it is the credit spread of an equivalent straight bond. MW is coded one for bonds with a make-whole call provision, zero otherwise. MW_IYm is the model generated make-whole call provision incremental yield and is set to zero for straight bonds. Baa_CMT_Sp is Moody's seasoned Baa yield minus the 10-year CMT yield. Rule 144a is coded one for privately issued bonds, zero otherwise. Finance and Utility are coded one for financial services and utility firms, respectively, zero otherwise. Residual Rating is the difference between actual ordinal rating of the bond and a predicted rating obtained via an ordered logit regression (see text for details). Not Rated is coded one for unrated bonds, zero otherwise. First Bond is coded one when the observation represents the first bond issue for the firm, zero otherwise. Senior is coded one if the bond is denoted senior or senior-secured, zero otherwise. All specifications are robust OLS (weighted least squares is used to limit impact of outliers). The subsamples for each regression are as follows: specification 1: rating of Baa- or better, specification 2: Rating of Baa- or better and excluding bonds issued by finance or utility companies, specification 3: matched subset of the sample where make-whole and straight bonds have been matched on the basis of rating, maturity and industry group, specification 4: bonds issued by firms that are represented by at least one straight bonds and at least one make-whole call bond in the sample. Below each coefficient estimate is the t-statistic. Significance at the 10%, 5% and 1% levels is denoted by *, **, ***, respectively.

Spec. 1 Spec. 2 Spec. 3 Spec. 4 Constant -1.043

(5.79)*** -0.118 (0.30)

-0.222 (0.79)

0.659 (2.27)**

NC_CSpm

0.133 (13.53)***

0.152 (11.79)***

0.185 (14.45)***

0.145 (11.17)***

MW_IYm

2.092 (7.57)***

2.750 (7.95)***

2.462 (7.47)***

2.009 (5.42)***

Baa_CMT_Sp 0.699 (31.00)***

0.643 (24.16)***

0.693 (22.11)***

0.613 (20.19)***

Residual Rating

0.094 (15.95)***

0.091 (13.33)***

0.134 (17.89)***

0.093 (12.45)***

Not Rated

-0.673 (9.34)***

Rule 144A

0.286 (8.93)***

0.275 (7.67)***

0.363 (9.75)***

0.187 (4.58)***

Finance 0.153 (5.90)***

0.043 (0.93)

0.140 (2.65)**

Utility -0.037 (0.86)

-0.109 (1.46)

0.098 (1.34)

Log Maturity 0.152 (9.92)***

0.150 (8.68)***

0.112 (5.08)***

0.145 (7.14)***

Log Offering Amt

0.007 (0.52)

-0.004 (0.21)

-0.027 (1.26)

0.034 (1.60)

First Bond 0.140 (4.96)***

0.169 (4.64)***

0.184 (5.02)***

0.127 (2.19)**

Senior 0.105 (1.98)**

-0.601 (1.84)*

-0.202 (2.42)**

-1.787 (12.33)***

# of OBS 1126 815 779 548 Adj. R2 .6184 .6046 .5643 .5178

52

Table 8 Split Sample Comparisons

The dependent variable is the bond's actual credit spread at issue. Independent variables are as follows. NC_CSpm is the model-generated credit spread for a non-callable bond. For make-whole call bonds, it is the credit spread of an equivalent straight bond. MW is coded one for bonds with a make-whole call provision, zero otherwise. MW_IYm is the model generated make-whole call provision incremental yield and is set to zero for straight bonds. Baa_CMT_Sp is Moody's seasoned Baa yield minus the 10-year CMT yield. Rule 144a is coded one for privately issued bonds, zero otherwise. Finance and Utility are coded one for financial services and utility firms, respectively, zero otherwise. Residual Rating is the difference between actual ordinal rating of the bond and a predicted rating obtained via an ordered logit regression (see text for details). Not Rated is coded one for unrated bonds, zero otherwise. First Bond is coded one when the observation represents the first bond issue for the firm, zero otherwise. Senior is coded one if the bond is denoted senior or senior-secured, zero otherwise. All specifications are robust OLS (weighted least squares is used to limit impact of outliers). For specification 1, the sample is split into bonds issued before versus after 10/1/1999. For specification 2, the sample is split into bonds with maturity less than versus more than 10.1 years. For specification 3, the sample is split into bonds with ratings of Baa+ or better versus Baa or worse. Below each coefficient estimate is the t-statistic Significance at the 10%, 5% and 1% levels is denoted by *, **, ***, respectively.

Spec. 1 Spec. 2 Spec. 3 Early Late Short Mat. Long Mat. Good Rating Poor Rating Constant -0.668

(3.55)*** 3.690

(6.32)*** 0.244 (0.62)

-1.064 (4.28)***

-1.031 (5.57)***

0.998 (1.73)*

NC_CSpm

0.136 (14.39)***

0.217 (9.95)***

0.166 (9.45)***

0.177 (14.16)***

0.135 (11.52)***

0.290 (10.62)***

MW_IYm

2.137 (7.33)***

1.828 (3.03)***

2.209 (5.09)***

2.697 (6.03)***

1.626 (5.52)***

3.485 (5.80)***

Baa_CMT_Sp 0.665 (24.09)***

0.054 (0.73)

0.707 (16.79)***

0.674 (21.16)***

0.673 (28.16)***

0.860 (14.80)***

Residual Rating

0.116 (22.23)***

0.180 (10.94)***

0.150 (13.76)***

0.115 (15.82)***

0.093 (12.41)***

0.225 (9.39)***

Not Rated

-0.551 (2.78)***

-0.523 (6.12)***

-0.982 (10.34)***

-0.491 (7.54)***

Rule 144A

0.354 (11.18)***

0.469 (6.68)***

0.478 (8.55)***

0.314 (7.60)***

0.253 (6.46)***

0.491 (7.27)***

Finance 0.085 (3.35)***

0.071 (0.98)

0.080 (1.70)*

0.090 (2.35)**

0.170 (6.25)***

-0.160 (1.85)*

Utility 0.022 (0.45)

0.024 (0.27)

-0.106 (1.28)

0.057 (1.07)

0.029 (0.63)

-0.092 (0.88)

Log Maturity 0.135 (8.92)***

0.182 (3.90)***

0.202 (3.10)***

0.124 (4.29)***

0.159 (10.02)***

-0.001 (0.03)

Log Offering Amt -0.007 (0.47)

-0.189 (4.58)***

-0.035 (1.23)

0.027 (1.35)

0.005 (0.72)

-0.103 (2.12)**

First Bond 0.162 (5.84)***

0.031 (0.43)

0.107 (1.90)*

0.147 (4.16)***

0.113 (3.46)***

0.202 (3.01)***

Senior -0.000 (0.00)

-0.303 (2.22)**

-0.684 (4.43)***

-0.016 (0.30)

0.147 (2.92)***

-0.843 (6.92)***

# of OBS 887 452 539 800 810 458 Adj. R2 .5821 .4517 .5532 .6073 .6361 .5717