Three Essays in Corporate Bond Contract Design and Valuation

THREE ESSAYS IN CORPORATE BOND CONTRACT DESIGN AND VALUATION

JOHN C. BANKO

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2003

This document is dedicated to my parents, John and Sandy Banko; and to my wife, Khanh-Lien.

ACKNOWLEDGMENTS

I thank the students and professors at the University of Florida and in the

Department of Finance for seeing me through this endeavor. Joel Houston and M.

Nimalendran provided support at many points during my education. I am fortunate to have Rich Romano from the Department of Economics serve on my committee.

Chungrong Ai also provided keen insight at many points. I am especially thankful to

Dave Brown and Mark Flannery for their counsel, support, and friendship over the years.

iii TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...... iii

LIST OF TABLES...... vi

LIST OF FIGURES ...... viii

ABSTRACT...... ix

CHAPTER

1 INTRODUCTION ...... 1

2 PUTABLE DEBT IN AGENCY THEORY...... 6

2.1 Previous Research...... 7 2.2 Agency Conflict Models: the Equivalence of the Call and Put Option...... 10 2.2.1 Asymmetric Information ...... 11 2.2.1.1 Model setup...... 12 2.2.1.2 Equilibrium strategies under asymmetric information...... 14 2.2.1.3 Discussion ...... 16 2.2.2 Future Investment Opportunities...... 17 2.2.2.1 Model setup...... 18 2.2.2.2 Straight debt and callable debt-financing...... 18 2.2.2.3 Putable debt-financing...... 19 2.2.2.4 Discussion ...... 21 2.2.3 Risk-shifting ...... 21 2.2.3.1 Solution with callable and putable debt ...... 22 2.2.3.2 Discussion ...... 23 2.2.4 Summary of Theoretical Findings ...... 24 2.3 Empirical Summary...... 25 2.3.1 Issues in Empirical Tests...... 25 2.3.2 Data, Sample Selection, and Description ...... 26 2.4 Conclusions...... 29 2.4.1 Findings ...... 29 2.4.2 Future Research...... 30

3 DIRECTIONALITY OF CREDIT-SPREADS REVISITED...... 50

3.1 Data and the Time Series of Credit Spread Volatility ...... 53 3.2 Regression Analysis of Credit Spreads and Rate Changes...... 57

iv 3.2.1 Choice of Interest Rate Variable ...... 57 3.2.2 Analysis of Full Sample Period...... 58 3.2.3 Analysis of the Pre-1994 Sample Period...... 59 3.2.4 Analysis of the Post-1991 Period ...... 61 3.3 Stock Market Evidence of Interest Rates and Issuer Prospects...... 63 3.4 Directionality of Agency Spreads...... 65 3.5 Conclusions...... 66

4 SERIAL CORRELATION IN U.S. CORPORATE BOND EXCESS RETURNS....84

4.1 Sources of Serial Correlation in Excess Bond Returns ...... 86 4.1.1 Zero-coupon Bond Example...... 87 4.1.2 The Relation between Excess Returns and Past Excess Returns ...... 89 4.2 Data and Bond Excess Return Calculations ...... 92 4.2.1 Sample Selection Criteria...... 93 4.2.2 Excess Returns...... 95 4.3 Empirical Results...... 96 4.3.1 Empirical Specification ...... 96 4.3.2 Results of the Empirical Analysis ...... 98 4.4 Implications for Risk Pricing...... 99 4.5 Conclusions and Future Research...... 100

5 CONCLUSION...... 109

APPENDIX

A PROOF OF PROPOSITION 1 ...... 111

B PROOF OF EQUIVALENT SECURITY HYPOTHESIS 2...... 114

C REGRESSIONS USING DIFFERENT BENCHMARK TREASURIES...... 117

LIST OF REFERENCES...... 120

BIOGRAPHICAL SKETCH ...... 123

LIST OF TABLES

Table page

2-1. Debt financing with required rates...... 32

2-2. Debt financing allowing firm separation ...... 33

2-3. State-dependent payoffs to the project...... 34

2-4. State-dependent payoffs to putable bond investors ...... 35

2-5. Summary statistics: U.S. corporate debt issues, 1980-1999 ...... 36

2-6. Summary Statistics by firm-type: U.S. corporate debt issues, 1980-1999 ...... 37

2-7. S&P rating numerical conversion ...... 38

3-1. Credit-spread summary statistics for U.S. corporate debt ...... 68

3-2. Credit-spread summary statistics for U.S. agency debt ...... 69

3-3. Directionality of credit-spreads for the entire sample period ...... 70

3-4. Directionality of credit-spreads for the pre-1994 sample period, short-maturity .....71

3-5. Directionality of credit-spreads for the pre-1994 sample period, medium-maturity...... 73

3-6. Directionality of credit-spreads for the pre-1994 sample period, long-maturity...... 75

3-7. Directionality of credit-spreads for the post-1991 sample period, short-maturity....77

3-8. Directionality of credit-spreads for the post-1991 sample period, medium-maturity...... 78

3-9. Directionality of credit-spreads for the post-1991 sample period, long-maturity ....79

3-10. Relation between stock returns and interest-rate changes ...... 80

3-11. Directionality of credit-spreads for long-maturity agency bonds...... 81

4-1. Regression results from simulated price paths...... 101

vi 4-2. Summary statistics for U.S. corporate debt issues, 1990-1997...... 102

4-3. Additional summary statistics for U.S. corporate debt issues, 1990-1997 ...... 103

4-4. Regression results for investment-grade debt, 1990-1997...... 104

4-5. Regression results for junk debt, 1990-1997 ...... 105

4-6. Regression results by grade, 1990-1997 ...... 106

4-7. S&P ratings for initial bond issuance...... 107

C-1. Directionality of credit-spreads with different treasury yields ...... 119

vii

LIST OF FIGURES

Figure page

2-1. Uncertainty about changes in project value ...... 39

2-2. Project with a future investment opportunity...... 40

2-3. Changes in equity value from risk-shifting...... 41

2-4. Changes in call option value from risk-shifting...... 42

2-5. Changes in put option value from risk-shifting...... 43

2-6. Debt covenant preferences with multiple agency conflicts...... 44

2-7. Percentage of call options in corporate debt issues...... 45

2-8. Percentage of put options in corporate debt issues ...... 46

2-9. Percentage of straight debt in corporate debt issues ...... 47

2-10. Initial debt yield in corporate debt issues...... 48

2-11. Initial debt rating for corporate debt issues...... 49

3-1. Yield spreads on U.S. corporate bonds ...... 82

3-2. Treasury bill yields...... 83

4-1. Simulated bond price paths ...... 108

viii

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

THREE ESSAYS IN CORPORATE BOND CONTRACT DESIGN AND VALUATION

John C. Banko

May 2003

Chair: David T. Brown Major Department: Finance, Insurance, and Real Estate

The chapters that comprise this dissertation examine three topics in corporate bond structure and pricing. Chapter 2 addresses why financial theory fails to explain the propensity of firms to include a call provision in long-term debt. I argue that this failure is possibly because the hypothesis is flawed. I offer theoretical support that a put option exists offering outcomes identical to a call option. I also describe a certain agency conflict that cannot be resolved with a call provision. These findings raise serious questions concerning previous investigations of the call option and suggest interesting future research.

Chapter 3 provides an analysis of monthly credit-spread data on noncallable and nonputable investment-grade corporate bonds. In contrast to prior research, I find little evidence of a negative relation between credit-spreads and interest-rate changes in the

1990s. There is a positive relation between interest-rate changes and credit-spread changes for short-maturity, investment-grade portfolios. There is no significant relation between interest-rate changes and spread changes for medium-maturity portfolios. A

ix negative relation between interest-rate changes and spread changes occurs for top-rated short-term portfolios and for all credit-quality long-maturity portfolios. The chapter goes on to explore three additional areas: the relation between credit-spread changes and interest-rate changes over time, the relation between interest-rate changes and monthly returns on major stock indices, and the causes of credit-spread changes in long-maturity corporate bonds.

Chapter 4 explores the time-varying structure of changes in corporate bond yields and yields on similar Treasury bonds. The difference between corporate bond yields and similar-maturity Treasury bond yields varies considerably over time. I show that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. Empirical analysis offers evidence that corporate bond excess returns are negatively related to lagged excess returns. Results suggest that the volatility in corporate bond excess returns is driven by time-varying risk premiums. The implications for the equilibrium pricing of credit risk are also discussed.

x CHAPTER 1 INTRODUCTION

The structure of corporate debt offerings and their subsequent prices remain an important topic in financial economics. The chapters that comprise this dissertation examine three of these topics and offer new evidence supporting and challenging current views in the literature. Chapter 2 addresses an important disparity in the financial literature. Why does financial theory fail to explain the propensity of firms to include a call provision in long-term debt? Over the last 2 decades, significant contributions were made to our theoretical understanding of the call provision in corporate debt issues

(Bodie and Taggart 1978; Barnea, Haugen, and Senbet 1980; and Robbins and

Schatzberg 1986). These researchers show that callable debt consistently reduces or eliminates the agency cost of debt by allowing management to renegotiate the terms of the debt before maturity.

Unfortunately, empirical evidence offers little support for theory. Kish and

Livingston (1992) and Güntay, Prabhala, and Unal (“Callable Bonds and Hedging,”

Working Paper 1-1, University of Maryland) empirically test both the call provision hypothesis and the hypothesis that firms simply hedge future interest-rates (the “hedging hypothesis”). These papers found limited support for agency explanations, favoring hedging arguments. Crabbe and Helwege (1994) found the agency hypothesis incapable of predicting the propensity of firms to issue callable debt.

I argue that the failure to support the call provision hypothesis is possibly because the hypothesis is flawed. I develop the “equivalent security hypothesis.” I allow the put

1 2 provision to compete with the call provision in various agency settings. I offer theoretical support for the equivalent security hypothesis in several agency settings. I show that a put option exists offering outcomes identical to a call option, in terms of both ex ante expected and ex post actual outcomes. I also describe a certain agency conflict that cannot be resolved with a call provision. The equivalent security hypothesis fails; however, the put provision alone exhibits the ability to resolve the situation. Combined, these findings raise serious questions about previous empirical investigations of the call option and suggest an interesting avenue of future research.

Chapter 3 provides an analysis of monthly credit-spread data on noncallable and nonputable investment-grade corporate bonds. Prior examinations of corporate bond yields by Longstaff and Schwartz (1995), Duffee (1998) and Collin-Dufresne, Goldstein and Martin (2003) found a negative relation between corporate bond yield spread changes and changes in Treasury bond yields: yield spreads tighten when interest-rates rise. An initial examination of credit-spreads and interest-rates reveals that credit-spreads are very volatile during the late 1980s and a dramatic credit-spread widening is associated with an increase in rates. After 1990 credit-spreads are much less volatile and it appears that credit-spread changes are positively related to rate changes.

We used Duffee’s (1998) approach (the same data source from 1985 through March

1995) to examine twelve portfolios of different credit quality and maturity. During the

1985 through 1991 period, the coefficients on the change in interest-rate variable are negative for all twelve portfolios. Further, when the model is estimated on progressively shorter sample periods, the explanatory power of the interest-rate variable increases and the coefficients become much more negative. The negative relation between

3 credit-spreads and interest-rate changes is very strong during the initial years of the sample period (1985-1987).

In contrast, estimating the relation between credit-spread changes and interest-rate changes for the period from 1991-1997 finds very little evidence of a negative relation between credit-spreads and interest-rate changes. There is a positive and significant relation between interest-rate changes and credit-spread changes for AA, A and BBB- rated short-maturity portfolios. There is no significant relation between interest-rate changes and spread changes for the medium-maturity portfolios. A negative and significant relation between interest-rate changes and spread changes occurs for

AAA-rated short-term portfolios and for all credit quality long-maturity portfolios.

Further, the coefficients are very similar across the four different credit quality portfolios.

We go on to explore why the relation between credit-spread changes and interest-rate changes is different over the sample period. A simple analysis of the relation between stock returns and interest-rates suggests that the relationship between asset values supporting corporate bonds and interest-rates changed during the sample period.

Chapter 3 further examines the relation between interest-rate changes and monthly returns on major stock indices over the sample period. The chapter concludes with an investigation of the causes of credit-spread changes in long-maturity corporate bonds.

Some evidence is found that the negative relation between credit-spread changes and interest changes in long-maturity corporate bonds during the latter part of the sample is result of changes in the liquidity value of Treasuries rather than changes in credit quality.

Chapter 4 explores the time-varying structure of changes in corporate bond yields and yields on similar Treasury bonds. The difference between corporate bond and

4 similar-maturity Treasury bond yields (yield spreads) exhibit considerable variation over time. There are two potential sources of this variation: changes in credit quality and changes in risk or liquidity premiums. Changes in credit quality represent changes in expected cash flows. Risk or liquidity premium changes are changes in the rate at which expected corporate bond cash flows are discounted (expected return premium) that result from changes in the market price of credit risk or changes in the liquidity premium in

Treasury bond prices.

There is reason to believe that time variation in the expected return premium on corporate bonds is significant. For example, Liu, Longstaff, and Mandell (“The Market

Price of Credit Risk: An Empirical Analysis of Interest-rate Swap Spreads,” Working

Paper 1-2, UCLA) found that most of the time variation in LIBOR swap spreads is due to changes in the liquidity of Treasury bonds rather than changes in default risk. Casual observation of the quality spread suggests time variation in required corporate bond returns.

Chapter 4 shows that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. The intuition is straightforward. An increase in the expected return premium reduces bond prices and results in a low holding-period return. However, after an increase in the expected return premium and a low realized holding-period return, the excess return is expected to be higher. In contrast, when excess returns are driven by changes in investor perceptions of default probabilities, excess returns are generally uncorrelated.

The empirical analysis examines the relation between excess corporate bond returns and lagged excess corporate bond returns over the 1990-1997 period. Strong evidence is found that corporate bond excess returns are negatively related to lagged excess returns.

Results suggest that much of the volatility in corporate bond excess returns is driven by time-varying risk or liquidity premiums. We also give limited evidence that below investment-grade (junk) bonds excess returns display negative serial correlation. This result is not surprising since innovations in expected default probabilities are probably a more important determinant of junk bond holding-period returns.

Results of this analysis have important implications for the equilibrium pricing of credit risk. We argue that the structure of excess return premia offers investors the ability to insulate their holding-period returns from much of the monthly variation in the price of risk. In this framework, earlier research may overstate the true holding-period risk to a bond portfolio.

CHAPTER 2 PUTABLE DEBT IN AGENCY THEORY

This chapter addresses an important disparity in the financial literature. Why does financial theory fail to explain the propensity of firms to include a call provision in long-term debt? Over the last 2 decades, several papers made significant contributions in our understanding of the call provision in corporate debt issues (Bodie and Taggart 1978;

Barnea, Haugen, and Senbet 1980; and Robbins and Schatzberg 1986). Exploiting the seminal work of Jensen and Meckling (1976), these papers consider agency explanations to justify the call option in corporate debt. This “call provision hypothesis” argues that a firm financed with debt exhibits behavior potentially inconsistent with firm value maximization. Callable debt is consistently shown to reduce or eliminate this agency cost of debt by allowing management to renegotiate the terms of the debt before maturity.

The hypothesis also shows that callable debt dominates a strategy of simply issuing short-maturity debt.

Unfortunately, empirical evidence offers little support for this hypothesis. Kish and

Livingston (1992) and Güntay, Prabhala, and Unal (Working Paper 1-1) empirically tested both the call provision hypothesis and the hypothesis that firms simply hedge future interest-rates (the “hedging hypothesis”). They found limited support for agency explanations, favoring hedging arguments. Crabbe and Helwege (1994) found the agency hypothesis incapable of predicting the propensity of firms to issue callable debt.

A recent trend in the use of the call option creates a further problem for the call provision hypothesis. Before 1990, over 50% of all new corporate debt included a call

6 7 provision, regardless of the initial credit risk. By 1990, a dramatic shift occurred (Figure

2-7). For several years around 1990, only 20% of all new issues incorporated a call provision. For the remainder of the 1990s, investment-grade debt issues maintained this low incidence of including a call provision. During the same period, newly issued junk bonds increased their use of the call provision, returning to a pre-1990 level by 1993.

This dramatic change between investment-grade and below investment-grade issues remains difficult to explain with any existing hypothesis.

I argue that the failure to support the call provision hypothesis is possibly because the hypothesis is flawed. I show that the call provision in corporate debt is not unique in its ability to reduce or eliminate certain agency conflicts. To show this, I develop the

“equivalent security hypothesis.” I allow another debt covenant (the put provision) to compete with the call provision in various agency settings. Results are two-fold. First, I offer theoretical support for the equivalent security hypothesis in several agency settings.

I show that a put option exists offering outcomes identical to a call option, in terms of both ex ante expected and ex post actual outcomes. Secondly, I describe a certain agency conflict that cannot be resolved with a call provision. The equivalent security hypothesis fails; however, the put provision alone exhibits the ability to resolve the situation.

Combined, these findings raise serious questions about previous empirical investigations of the call option and suggest an interesting avenue of future research.

2.1 Previous Research

The seminal work of Jensen and Meckling (1976) pioneered the exploration of the call provision in the context of agency problems. Earlier research sought to explain the high frequency of the call option via divergent interest-rate expectations (Bowlin 1966;

Jen and Wert 1967; and Kidwell 1976), divergent risk preferences between bondholders

8 and shareholders (Barnea, Haugen, and Senbet 1985), and tax considerations (Boyce and

Kalotay 1979). Bodie and Taggart (1978) [BT hereafter] were the first to exploit the agency story, exploring the ability of callable debt to restore the full value of future investment opportunities. In their model, a firm financed partly with debt bypasses some positive NPV projects when the bondholder benefits from reduced risk. Callable debt offers the firm’s entrepreneur an opportunity to renegotiate the terms of the debt when favorable information arrives. With callable debt, the debt holder is compensated with an interest-rate consistent with her risk exposure, without compromising the firm’s investment incentives. Barnea, Haugen, and Senbet (1980) [BHS hereafter] extend the work of BT, examining future investment opportunities along with modeling asymmetric information and risk-shifting. Both papers show that the inclusion of a call provision resolves the conflict between managers/owners and debt holders. A call provision offers the firm the ability to re-contract debt based on new, favorable information not available at the original debt issuance.

These early papers fail to show a clear advantage of callable debt over a short-term debt policy. As constructed, the models rely on issuance costs to generate a separating equilibrium. To address this criticism, Robbins and Schatzberg (1986) found that risk-averse managers prefer callable debt to a short-term debt policy as a signaling mechanism when the value of the firm’s investment quality is uncertain. Other papers, notably Flannery (1986), can show that callable debt dominates short-term debt, even absent transaction costs, when considered as a financing option.

Kish and Livingston (1992) empirically tested both agency and nonagency hypotheses, examining callable and noncallable bonds issued from 1977-1986. They ran

9 a series of logit regressions using firm characteristics such as leverage, growth, and book-to-market ratio to predict the presence of a call option in debt issued by the firm.

They found mixed support for the call provision hypothesis. Growth firms are more likely to include a call provision. This is consistent with the predictions of BT. The findings of BT could not confirm any of the other agency theories. However, simple interest-rate hedging stories also gain support. The call feature is more prevalent during periods of high interest-rates and for longer maturity bonds. Crabbe and Helwege (1994) found the call provision hypothesis incapable of predicting the propensity of firms to issue callable bonds. Looking at industrial debt issues from 1987 through 1991, they found evidence against the call provision hypothesis. They conclude that the prevailing agency theories are not of first order importance in prompting firms to include a call provision in their debt issues. Güntay, Prabhala, and Unal (Working Paper 1-1) found strong support for the hedging hypothesis; and limited evidence favoring the call provision hypothesis.

Put options received relatively little attention in the literature, perhaps consistent with their rare occurrence in debt covenants. No paper has examined the role of the put covenant in the general context of agency theory, or compared the relative merit of the put option versus the call option in resolving agency conflicts. Brick and Palmon (1993) proposed a bond contract that facilitates an alternative refunding policy. This bond contract gives each bondholder a put option as part of the bond covenants. Crabbe and

Nikoulis (1997) examined the market for putable debt, looking at the historical features of these bonds. Although the article challenges the pricing of putable debt, it does not compare putable debt with its callable counterpart. Crabbe (1991) examined the advent

10 of the event-risk covenant (poison put) in corporate debt in response to the risk-shifting activities during the late 1980s. Cook and Easterwood (1994) examined the impact of the poison put on the outstanding securities of a firm. They conclude that a poison put benefits managers and bondholders, but at the expense of stockholders. Gibson and

Singh (“Using Put Warrants to Reduce Corporate Financing Costs,” Working Paper 2-1,

Cornell University) examined put warrants in a situation with adverse selection costs.

This paper is closest in spirit to the present work, but examines put options on equity instead of debt.

2.2 Agency Conflict Models: the Equivalence of the Call and Put Option

In this section, I show that a variety of agency conflicts arising from debt-financing are resolved using either a call option or a put option in the debt covenants. I show that either option results in identical ex ante expected outcomes and identical ex post state-dependent outcomes for debt investors. An analogous result holds for the firm. I focus specifically on asymmetric information, future investment opportunities, and risk-shifting. Previous models, such at BT and BHS, have shown that a call option resolves these agency conflicts. I show here that a put option offers equivalent outcomes.

I call this result the equivalent security hypothesis. By demonstrating that a specific put option is equivalent in these models, I show that the debate over the dominance of callable debt is incomplete. Essentially, the previous models explain why an embedded option is useful when questions of agency conflict arise. However, the dominance of the call option is not resolved.

I consider the case of asymmetric information in a setting not previously explored in the literature. I exploit the model in Flannery (1986), which considered short-term and long-term financing (straight debt) in a 2-period model with asymmetric information. By

11 adding a call and a put option as financing opportunities, I derive scenarios where a call or a put option is preferred over other financing alternatives. I also show that equivalent contracts exist using either a call or a put option under some circumstances. With this evidence supporting the equivalent security hypothesis, I then turn to models of future investment opportunities and risk-shifting. In these cases, I extend the work previously completed by BT and BHS, respectively. In each scenario, I show that the equivalent security hypothesis holds. Lastly, I explore a situation where a call option and a put option are not comparable. This setting entails risk-shifting under conditions of asymmetric information. In this case, the equivalent security hypothesis fails, but not in favor of a call option. A put provision is favored.

2.2.1 Asymmetric Information

Flannery’s original model is cleverly designed to capture the pure signaling motivation for debt design by maintaining fixed future values for the firm. In the model,

“Good” and “Bad” firms (described in Section 2.2.1.1) enter the market for debt, issuing either short-term or long-term debt. If Good firms cannot successfully signal their true quality to investors, they pool with Bad firms, forced to accept a required rate on their debt that exceeds a fair rate of compensation based on their true risk. I modify the original model in two ways:

• I eliminate transaction costs from the model • I allow firms to include either a call option or a put option in the debt offered

As modified, the model offers several interesting insights. First, firms with favorable private information will issue debt including an embedded option. By using either a call option or a put option, Good firms separate in a situation where straight debt alone fails.

Second, it is shown that the debt investor receives an equilibrium payout that exceeds the

12 market’s required payout. The excess payout is the mechanism Good firms use to achieve a separating equilibrium. This proves less costly than suffering under a pooling equilibrium. Lastly, the equilibrium payout to the debt investor is shown to be identical using either a call or a put option. The same holds for the residual payout to the entrepreneur.

2.2.1.1 Model setup

At time zero, an entrepreneur wishes to proceed with a positive NPV project. The project is indivisible and nontransferable. The project lasts for 2 periods, and all cash flows from the project are received at the end of the second-period. The value of the project, however, is uncertain through time (Figure 2-1). The value follows a binomial process where, during each period, the value of the project increases with probability p or decreases with probability (1-p). At time t=1 and t=2, the firm's value becomes public information.

Throughout the project life, the individual firms in the market are impossible to tell apart. However, the market knows that θ% of the firms are Good firms, and (1-θ)% of the firms are Bad firms. Good firms differ from Bad firms in that their “up” probability, pG, is higher than that for Bad firms, pB. That is, pG > pB. Good firms cannot directly reveal their true type. To avoid pooling, Good firms must find some market mechanism to signal their true quality. Knowledge of θ, pG, and pB is public information. All market participants are risk-neutral wealth maximizers, and the risk-free rate of interest is zero for both periods.

The cost of the project exceeds the entrepreneur’s wealth, forcing her to borrow an exogenously determined amount D from the investor. The risk assumed by the investor is determined by both the debt maturity and the project value through time. The firm can

issue short-term debt, long-term debt, or long-term debt including either a call or put

option. Short-term debt involves issuing one-period debt, both in the first-period and in

the second-period. As constructed, the expected project value always exceeds the

outstanding debt at t=1, suggesting that short-term debt at t=0 is default-free. The firm

will pay exactly zero interest for this debt. Since the firm is solvent at t=1, I assume that

it will reissue debt. The second-period interest-rate depends on the project value at time

t=1. If the project value increases during the first-period, the subsequent one-period

F rate, RS , is zero. When unfavorable information arrives, the investor charges an

R appropriate interest-rate, RS . Long-term debt (2-period debt) always exhibits some

probability of default. Investors charge a coupon rate RL , based on the equilibrium probability of default1. Finally, the firm can issue callable or putable debt, promising to

pay a rate of RC or RP, respectively, in 2 periods. With callable (putable) debt, the firm

(investor) may buy (sell) the debt from (back to) the investor (firm) for the face value of the debt, D. If either option is exercised, the firm reissues the debt at a short-term rate

consistent with the risk characteristics of the future cash flows. Liquidity is not a concern

in this model.

It is simple to show that the required rate for 2-period callable debt, RC, is a

R 2-period rate equivalent to RS . In accepting callable debt, the investor assumes that the

firm refrains from exercising the call option if first-period results are poor, and that the

firm exercises the call option when first-period results are positive. With these

assumptions, the debt exhibits risk characteristics consistent with a short-term debt

1 R Both rate RL and RS are equivalent to the rates established in Flannery (1986), equations (4) and (5), respectively.

R rollover strategy. A rate consistent with this level of risk (a 2-period RS -equivalent rate) is required. This rate is consistent with actual firm behavior. When first-period results are positive, the firm exercises the call option and reissues the debt at the risk-free rate.

Under poor first-period conditions, the firm finds the call option worthless and avoids calling the debt. The putable debt holder needs no assumptions since the option to redeem the debt is under her control. Accordingly, it can be shown that the firm offers a rate, RP, equal to the risk-free rate. With good first-period performance, the debt exhibits no risk. The debt holder is perfectly compensated for the actual risk of the investment.

The put option has no value and is not exercised. If, however, the debt becomes risky, the investor exercises the put option, forcing the firm to reissue debt at a rate reflecting

R the true risk ( RS ).

2.2.1.2 Equilibrium strategies under asymmetric information

Absent embedded options, Flannery found that a pooling equilibrium in short-term debt. All market rates reflect the “average” risk of the market participants. Good firms suffer, losing value from required market rates on debt that exceed rates consistent with their true risk characteristics. Bad firms benefit, paying a lower rate than they would under a separating equilibrium. Can either a call option or a put option resolve this? As constructed, a call strategy or a put strategy is equivalent to a short-term debt policy.

Neither offers Good firms the ability to separate from Bad firms (Table 2-1). The required rates offer no explanation for the use of embedded options to reduce asymmetric information in this context. Robbins and Schatzberg (1986, page 935) discussed this problem: “The theory of financial economics has failed to distinguish advantages of

callable bonds from those of short-term debt.” Absent transaction costs, embedded

options in debt covenants simply mimic financing options available to the firm.

To distinguish either option-based strategy from a short-term strategy, Good firms

are forced to change the terms of the offering, diverging from the market’s required rates.

Any change must also benefit Good firms, allowing them to create a separating

equilibrium with a cost lower then their loss in value under a pooling environment. I first

show that this is possible with callable debt. I then focus on a solution including a put

option.

R Although the required rate for callable debt is RS , equilibriums exist where Good

firms issue callable debt including a call premium to separate from Bad firms. The call

premium discourages Bad firms from mimicking the debt-financing choice of Good

firms.

• Proposition 1. Under asymmetric information with zero transaction costs, a separating equilibrium exists where firms with favorable private information issue callable debt. Firms with poor prospects issue short-term debt, despite revealing 2 2 (1− pB ) M 5 + DR1 ( pB − pB ) − D their true condition. A call premium, RC = , is − pB D included in the contact. If the firm exercises the call option, debt investors are repaid DC = D RC.

• Proof. See Appendix A.

Good firms offer terms that exceed the market’s demands. Bad firms avoid callable

debt with a call premium2 because of their higher probability of losing value in the

2 Investors in a separating equilibrium are willing pay upfront for the expected call premium, or (p RC), in addition to the contract amount D, partially offsetting the cost of signaling to Good firms. Assuming that firms act homogenously within a given type, the lower actual cost will maintain a separating equilibrium. This holds analogously for putable debt. However, as long as firms can issue debt with a face value of D, and also offer the premium, the separating equilibrium will result. Secondary market prices for the debt, however, will exceed the proceeds to the firm.

first-period. They cannot afford the call premium under good conditions and the

R short-term rate RS under poor first-period performance.

Given that a solution exists using callable debt, an equivalent strategy using putable

debt is easily constructed. Putable debt is offered with the following terms: if the put

option is exercised, the firm will pay debt holders D RP; otherwise, if the debt is held for

R the full 2 periods, the firm will pay debt holders D RS . This strategy is equivalent to a

callable debt strategy if RC = RP (Table 2-2). Existence, then, is a simple contractual

2 2 (1− pB ) M 5 + DR1 ( pB − pB ) − D matter of setting RP = . This leads to the following − pB D

hypothesis:

• Equivalent security hypothesis 1. Conflicts between the debt holder and the firm arising from debt-financing under asymmetric information can be resolved using either a call option or a put option3. Further, for a given debt contract including a call option, an equivalent contract including a put option can be written, despite shifting the option value from the firm to the investor.

2.2.1.3 Discussion

This section offers several interesting outcomes concerning callable debt and

agency conflicts. First, the call provision hypothesis holds. By showing that callable

debt offers a mechanism to avoid the agency conflict arising from debt-financing under

asymmetric information, I offer further support for the call provision hypothesis in a

model not previously explored. Further, I show callable debt dominates short-term debt

when a call premium is included. This offers support for firms issuing callable debt

including a call premium.

3 Public information on firm condition is essential for this result. Results under uncertainty may lead to a different solution.

This section also shows that putable debt (including a put premium) offers the firm

an equivalent financing option. Although putable debt shifts the option value to the debt

holders, the equilibrium contract outcomes are identical to a callable debt strategy. Using

either callable or putable debt, the firm faces the same expected costs ex ante and identical state-dependent residual payoffs ex post. This holds analogously for debt holders. The equivalent security hypothesis is established.

This result suggests that the firm is indifferent between using a call option and a put option in the their debt covenants. If asymmetric information drives the firm to include a call option, an equal number of put options should also be observed in debt issues.

Figure 2-7 shows this is not the case, with callable debt dominating putable debt significantly each year. Is the model here correct, suggesting that asymmetric information is not pushing firms to include a call option? Or, is asymmetric information important, but the model fails to capture an essential element in the decision? These questions are revisited later in the chapter.

2.2.2 Future Investment Opportunities

When a firm’s prospects include future investment opportunities, BT found the

benefit of callable debt. Using their model, I show that callable debt or putable debt

restores the full future investment incentives of the equity holders, garnering further

support for the equivalent security hypothesis. I initially review the findings of BT for

callable debt. I then extend the argument, considering putable debt. The putable debt

contract maintains incentives consistent with callable debt. The full value of the

investment attains with either option. Second, I alter the original model of BT, including

asymmetric information regarding possible future projects. If the debt holder is unaware

of (some) upcoming opportunities, either contract may include an unforeseen cost to the

18 firm. If this cost is high enough, the project may be bypassed, despite any potential benefit to the firm.

2.2.2.1 Model setup

A firm invests $100 in a 2-period project (Figure 2-2). The condition of the economy is either good or bad in the first-period, with equal probability. If first-period conditions are good, the firm invests an additional $X at the beginning of the second-period, and that investment generates an additional revenue of $15.75 ln(X) for certain at the end of the second-period. Otherwise, first-period conditions are bad; consequently, no additional investment is made. Conditions and final payoffs during the second-period depend on first-period results (Table 2-3). For simplicity, the risk-free rate is 5% in both periods, and all participants are risk-neutral expected wealth maximizers.

The firm has several investment choices. The project can be financed with all equity or

50% debt. If limited capital forces the use of debt-financing, the debt issuance options include 2-period (straight) debt and debt including an embedded option (call or put).

2.2.2.2 Straight debt and callable debt-financing

With all equity financing, it is simple to show that the firm will invest $15 at the end of the first-period, if conditions are good. Further, the project has an expected net present value of approximately $36.92. For the remainder of this section, I assume that the firm’s entrepreneur has limited capital, and partial debt-financing is required. I first consider straight 2-period debt, and then include a call option in the offering.

By issuing straight debt, a portion of the future investment opportunity will be bypassed. The increase in firm value from the future investment accrues partly to the debt holders in the form of reduced risk. Unlike the case of all equity financing, the firm will only invest $9 at t=1. Based on the required rate on the debt, the expected residual

firm value falls to $36.12, a loss of roughly $0.80 due to agency issues. Callable debt

resolves this under investment problem, allowing the equity holder to refinance the debt

if favorable information arrives at t=1. In equilibrium, the debt holder expects to retain

the debt if first-period results are bad, while forced to redeem the debt if the first-period

results are good. The mean expected return4 to the callable debt holder is

2 2 0.5[50(1.05) ] + 0.3(25) + 0.2[50(1+rC) ]. (2-1)

Since the risk-neutral investor requires, on average, the risk-free rate, setting Eq.

2 2-1 equal to 50(1.05) allows us to derive rC. This results in a callable rate rC = 40.3%.

This rate is consistent with debt holder expectations. The debt will be called if

first-period results are good, but not when first-period results are bad5. Further, when the

debt is called, the firm will reissue debt at the risk-free rate of 5%. This restores the

optimal investment at t=1 to $15. This, in turn, guarantees the debt holder repayment in

full, consistent with the risk-free rate. From the firm’s perspective, the optimal future

investment of $15 also restores the full value of the firm under 100% equity financing.

2.2.2.3 Putable debt-financing

The firms again issues $50 in debt. However, the bond contains a put provision

allowing the investor to redeem the debt at t=1. If the option is exercised, the firm must

pay the full principal amount plus accrued interest for one period, and then reissue the

debt. The stated rate on the debt, rP, must fully reflect all expected losses to the

bondholder. The firm’s optimal future investment decision depends critically on the

4 This is a modification to BT. I assume that the debt is callable at par plus the risk-free rate. This adjusts the second-period rate on callable debt to reflect the risk of holding debt following poor first-period performance.

5 Indifference attains if first-period results are bad. The debt can be called for $52.50, but new debt will be issued with a coupon rate of 87.5%. Thus, the firm realizes no benefit from a call policy in this state.

required rate for putable debt, rP. Putable debt in this model is viewed as a full guarantee of principal to the debt holder. The firm expects the debt holder to retain the debt if the first-period is good, while she redeems the debt if first-period results are bad. The mean return to putable the debt holder is

2 0.5[50(1+rP) ]+0.3(25)+0.2[50(1+rP)(1.05)]. (2-2)

Unlike callable debt, the putable debt investor sets the optimal put policy, considering her expected payoff. The corresponding payoff structure to the investor at t=1 is found in Table 2-4. With business in the first-period good, the debt is risk less, and the debt holder (ex ante) requires the risk-free rate of 5%. For any coupon rate greater than or equal to the risk-free rate, the debt holder does not redeem the debt. I assume, then, that rP=5%. With this rate, the optimal value of the future investment at t=1 is $15, and the expected value of the firm at t=1 is consistent with results from issuing callable debt. However, I must show that rP=5% is also the equilibrium rate with poor first-period performance.

Assuming that rP = 5%, the putable debt holder redeems the debt if first-period performance is poor. By redeeming the debt, the investor forces the firm the finance the second-period at the required rate of 87.5%. This is consistent with our expectations.

The putable debt holder retains the debt if first-period performance is good, but will redeem the debt is first-period performance is poor.

• Equivalent security hypothesis 2. Debt-financing can distort future investment opportunities when a portion of the value of the future investment accrues to the debt holder in the form of reduced risk. This appropriation of value from the shareholder to the debt investor is eliminated using either a call option or a put option in the debt covenants. With either debt covenant, the all-equity value of the firm is fully restored.

• Proof. See Appendix B.

2.2.2.4 Discussion

This section confirms the call provision hypothesis and the equivalent security hypothesis. Callable debt with a rate rC = 40.3% restores the full value of the future project to the firm. Putable debt with a putable rate rP = 5% (the risk-free rate) achieves the same end. The equilibrium putable debt contract offers outcomes identical to a callable debt strategy. The agency conflict is resolved using either option contract. The firm is indifferent between using a call option and a put option. Asymmetric information or a future investment opportunity (when explored separately) theoretically results in an equal use of either option in corporate debt covenants.

Results also hold in a model including asymmetric information and future investment opportunities. Consider a scenario where first-period results are bad, but the firm (somehow) creates the ability to pursue the identical future investment opportunity.

To introduce asymmetric information, the debt investor (for some reason) is unaware of this opportunity, and it is costly for the firm to credibly educate them. Neither callable debt nor putable debt offers a superior solution. Callable debt is called, new investors are educated, and new debt is issued at the risk-free rate. With putable debt, the firm educates the investor. Since the investment retains its risk-free characteristics, none of the debt is redeemed. In either scenario, the investment opportunity remains viable as long as the cost to educate is low enough. If the cost exceeds the benefit of the project, the firm may forego (part of) the project, despite its benefit to the firm.

2.2.3 Risk-shifting

Risk incentives may induce a debt-financed firm to shift away from a high value project (A) to a low value project (B). The value of the firm under project B is lower than the alternative project A (Figure 2-3). Although both projects require the same

initial outlay, project B is riskier than project A [i.e., σ(B) > σ(A)]. This creates the

incentive for the firm to raise debt in the amount of VD(A), claiming that project A will be undertaken. Once debt-financing is secured, the firm shifts to project B. Although the value of the firm falls, by ∆V = V(B) – V(A) < 0, the firm’s equity increases in value, by

∆S = S(B) – S(A) > 0. A transfer of wealth occurs from the debt holder to the firm’s

equity holder because the value of the debt falls by more than the value of the firm.

Without a credible mechanism signaling that project A will be pursued, the debt holder

must assume that project B is undertaken. Debt-financing only in the amount of D(B) is

made available to the firm. Consequently, the firm’s equity holder suffers from the

additional capital requirements.

2.2.3.1 Solution with callable and putable debt

BHS found that a call option can be constructed as a credible mechanism to

indicate that project A is pursued. The value of a call option on debt6 will fall (by ∆C) as

the value of the underlying debt diminishes, as in the case of shifting to project B (Figure

2-4). Recall that the value of a call option on debt fully accrues to the firm’s shareholder.

The shareholder solves the risk-shifting incentive problem by constructing the call option

(i.e., setting the strike price) such that any gains from shifting to project B result in an

equal or greater offsetting loss in the value of the call option. That is, set the strike price

such that |∆C| ≥ |∆S| holds. Putable debt also achieves the same goal. The value of a put

option on debt will rise (by ∆VP) as the value of the underlying debt diminishes (Figure

2-5). Unlike the call option, the value of a put option on debt fully accrues to the debt

holder. The risk-shifting incentive problem in this scenario is solved by constructing the

6 This assumes that option pricing follows the Black-Scholes (1973) pricing model.

23 put option such that any loss to debt holders as the firm shifts to project B results in an equal or greater gain in the value of the put option. Set the strike price such that |∆P| ≥

|∆D| holds.

2.2.3.2 Discussion

Clearly, callable debt resolves this class of agency problems, and is often sited as strong theoretical support for the existence of the call option in corporate debt. As shown, however, a put option achieves the same end. Further, a put option provides additional protection that a call option cannot. Consider a scenario where a third project

Project C is riskier than project B [i.e., σ(C) > σ(B)], and by shifting to project C, the shareholder gains additional value from risk-shifting. Is the debt holder protected?

Under callable debt, if the strike price is set such that |∆C| = |∆S| assuming only the existence of project B, the answer may be no. Beyond a limit, a loss in debt value cannot correspond to an offsetting decrease in call value (Figure 2-4). The shareholder, once the strike price is set, may have an incentive to undertake a project risky enough such that debt holder wealth is expropriated in her favor. In the limit, the debt holder requires a strike price on the call option of zero. Of course, the debt holder pays nothing for such debt (since it can be called at zero), and the firm is forced to issue new equity. Putable debt avoids the problem of unknown, riskier projects. Figure 2-5 shows that any incremental loss in value of the underlying debt is exactly offset by a corresponding increase in put value. By setting the strike price such that |∆P| ≥ |∆D| for any known, possible shift in risk, the debt holder is fully protected from any incremental shift to unknown riskier projects. The shareholder has nothing to gain from risk-shifting alone.

• Equivalent security hypothesis 3. Debt-financing can create an incentive for the shareholder to shift into riskier projects, if the riskier project results in a wealth transfer from the debt holder to the firm’s shareholder. This appropriation of wealth to the shareholder is eliminated using either a call option or a put option in the debt covenants. However, if uncertainty exists regarding unknown, riskier projects, putable debt may dominate callable debt in resolving the conflict.

2.2.4 Summary of Theoretical Findings

When the firm and the investor face a single agency problem (Figure 2-6), they are

indifferent between callable and putable debt. In these cases, the equivalent security

hypothesis holds, and either embedded option resolves the agency conflict equally well.

Further, either option offers a first-best solution in cases of future investment

opportunities and risk-shifting (Figure 2-6, shaded cells). The firm retains its full wealth

maximization incentives as with all-equity financing. Although asymmetric information

does not exhibit this characteristic, a call options and a put option offer the firm a less

costly alternative than a pooling equilibrium.

Mixed agency environments are a different matter, and either callable debt or

putable debt may dominate in some scenarios. Future investment opportunities under

conditions of asymmetric information favor neither option. The firm may forego the

future project, despite any benefit, if the cost to resolve the information asymmetry is too

high. The scenario of risk-shifting combined with asymmetric information lends itself to

a putable debt covenant. A putable bond offers the investor a full guarantee. The riskiest

project offers the shareholder no opportunity to transfer wealth away from the

bondholder. Any gain to the shareholder from risk-shifting is exactly offset by an

incremental loss to the shareholder as the value of the put option grows. With callable

debt, the firm retains the incentive to shift to risky projects. Any project with a variance

higher than the riskiest, known alternative may offer the shareholder the ability to

25 expropriate wealth from the debt investor. In the limit, the debt investor will not invest in corporate debt. Finally, a mixed environment including future investment opportunities and potential risk-shifting is ambiguous. Although this setting is not explored, it is conjectured that the solution depends on the relative degree of investment opportunities versus debt holder exploitation via risk-shifting in the model. In some cases, callable debt may be favored, while putable debt dominates other scenarios.

2.3 Empirical Summary

This section explores the impact of results from the last section on past studies of the call provision hypothesis. Given the methodological questions raised, I offer only a summary of the market for putable and callable debt over the last 2 decades. Even ignoring the implications of the equivalent security hypothesis, the actual data reveal interesting changes in the market for corporate debt in recent years.

2.3.1 Issues in Empirical Tests

Results of the last section highlight two potential issues with previous tests of the call provision hypothesis. First, the empirical design may have a bias since the studies test only for a call option in limited-dependent variable analysis. The second issue relates to the variables used to measure agency problems in firms.

The studies of Kish and Livingston (1992) and Crabbe and Helwege (1994) exhibited call provision myopia. Both papers examined the propensity of firms to issue either callable or noncallable debt. By limiting the scope of their investigation in this fashion, an important class of equivalent securities is ignored. This paper shows that the put provision may be comparable in many settings, and needs to be included in the studies. I do offer on caveat to this issue. I later show the paucity of putable issues over the last 2 decades. A natural conclusion is that any impact from excluding putable debt

26 in the previously mentioned studies is minimal. But, the preference for a call option is more than just an interesting puzzle. The equivalent security hypothesis posits that firms will issue an equal number of callable and putable issues. But firms do not, favoring callable issues. The reason for this behavior certainly has implications for the call provision hypothesis, the equivalent security hypothesis, and any empirical test based on them.

The second issue deals with empirical proxies for the distinct agency conflicts. For example, proxies for asymmetric information, such as asset opaqueness (Flannery, Kwan, and Nimalendran 2003) and variation in analyst forecasts (Thomas 2002) are often sited as proxies for potential risk-shifting. Using these proxies now requires the distinction between a firm dominated by risk-shifting issues and one also suffering from asymmetric information. The former situation implies that any security satisfying the equivalent security hypothesis should be included as a left-hand side independent variable in discrete regression models. The latter suggests that only putable debt is used. Disentangling these joint measures of asymmetric information and risk-shifting remains a challenge for empirical finance.

2.3.2 Data, Sample Selection, and Description

Due to the issues raised concerning empirical tests of the call and put option, I offer only a summary of characteristics of the market for embedded options in U.S. corporate debt issues. The data I examine comes from the Fixed Income Securities Database

(FISD) constructed by LJS Global Information Services, Inc. I identify debt issues by

U.S. corporations from January 1, 1980 through December 31, 1999. Debt issues are considered for inclusion if they are a fixed-coupon corporate debt issue. I also require that the issue not be one of the following: convertible; asset-backed; Yankee bond;

Canadian issue; denominated in a foreign currency; unit deal; private placement; exchangeable; rule 144a issue; a securitized lease obligations; or an event-driven put.

A total of 23,549 issues are included in the sample. Table 2-5 describes the debt issues in terms of year of issue, embedded options, rating, and size. Note that rating information in FISD is reported for debt issues as AAA+ (best rating) through D (worst rating). These are translated into numerical values according to Table 2-7. Higher numbers are associated with worse conditional ratings. For the sample, bonds with a rating of D or worse are adjusted to 25, and bonds with a rating of either Suspended (26) or No Rating (27) are excluded. In addition, Figures 2-7, 2-8, and 2-9 show the distribution by year for callable, putable, and straight debt issues, respectively.

Table 2-5 and Figure 2-7 reveal interesting facts about the market for corporate debt over the last 20 years. Figure 2-7 shows a recent trend away from callable debt, replacing it with straight debt, as seen in Figure 2-9. From 1980 through 1986, roughly

70% of the issues included a call option. By 1990, callable debt represented only 20% of the market. This is true for investment-grade and junk debt issues. During the same time periods, callable debt is essentially replaced with straight debt. Also interesting, during the period 1991 through 1999, the percentage of callable, investment-grade issues continues to decline, reaching a low of approximately 10% in 1994, but climbing back somewhat to its 1990 level of 20% by the end of 1999. During that same nine-year period, the percentage of junk bonds including a call option rises dramatically, reaching over 50% by 1992, and increasing to sustained levels above 60% by 1996. During the entire 20-year period, putable debt represents, on average, less than 2% of the market for

28 corporate debt issues (Figure 2-8). Table 2-6 further examines debt issues, dividing the sample into industrial, financial, and public utility sectors.

Figure 2-10 shows the initial debt yield and Figure 2-11 shows the initial debt rating for bonds issued from 1980 through 1999 for investment-grade issues. The yields on callable and noncallable debt maintain a consistent relationship over the period.

Callable debt requires a yield in excess of the yield on similar, straight debt. Further, the average rating on callable debt has fallen during the latter part of the sample period relative to its straight counterpart. This is consistent with the trend of high quality debt to avoid the call option in the 1990s. Most likely, AA issues include fewer call options, leaving more BBB debt in the sample.

The yield on putable debt offers a riddle. Although the average rating on putable issues is consistent with straight debt (and sometimes better), the issues offer no average yield improvement for the debt issuers. The inclusion of the put option, all else equal, should result in a lower yield. Yet we do not observe this. Separate results by industry group and rating (not reported) offer little insight into this problem. It is conjectured that these issues (or issuers) are somehow different in a dimension not captured here.

A number of important empirical questions arise, and will be the focus of future research. First, the divergence between investment-grade and below investment-grade issues in the use of call options is striking, meriting further consideration. The data suggests that lower credit quality firms experience more trouble with agency concerns than their higher quality counterparts. Neither the call provision hypothesis nor the equivalent security hypothesis offers any insight into this significant change over the last decade. Second, the relatively rare presence of putable issues remains difficult to explain

with the equivalent security hypothesis. Assuming that the put option is fairly priced, a

firm is indifferent between issuing debt with a put option and a call option where a single

agency problem exists. Yet, relatively few firms use them. Unless some other equivalent

security replicates the structure of callable debt, the data remains difficult to explain with

the current theoretical framework.

2.4 Conclusions

2.4.1 Findings

Firms often seek external debt-financing to fund projects, creating potential

distortions in firm behavior. Unchecked, these distortions result in sub optimal

debt-financing, but theoretical work (Barnea, Haugen, and Senbet 1980,1985; and

Robbins and Schatzberg 1986) shows that a solution exists. The call provision

hypothesis argues that a call option resolve several agency conflicts created through the

use of debt-financing. Perplexing, though, empirical tests of the call provision hypothesis

(Kish and Livingston 1992; Crabbe and Helwege 1994; and Güntay, Prabhala, and Unal

Working Paper 1-1) offered limited support for the premise.

This chapter concludes that the call provision hypothesis is incomplete and offers a

theoretical justification why the call provision hypothesis may fail in empirical

investigations. Examining asymmetric information, future investment opportunities, and

risk-shifting, I develop what I term the equivalent security hypotheses. This hypothesis

shows that these three agency conflicts arising from debt-financing are resolved using

either a call option or a put option in the debt covenants. I further show that either option

will result in identical ex ante expected outcomes and identical ex post state-dependent outcomes for debt issuers and investors. I conjecture that other securities (perhaps convertible debt) may also have a role in understanding the limits of the equivalent

30 security hypotheses. This continued research is important to understand the puzzle presented in actual empirical investigations. I also offer empirical data on the combined use of straight debt as well as debt including either a call or a put provision. In light of the equivalent security hypothesis, the evidence suggests a number of important empirical questions that will be the focus of future research.

2.4.2 Future Research

As suggested in this paper, empirical investigations of the call provision hypothesis must consider any other bond covenant that fulfills the equivalent security hypothesis.

This paper shows that put options are equivalent in many scenarios, such as environments where a single agency problem dominates. Other debt covenants may be equivalent as well. Although a call option and a put option represent the most common debt covenants, a complete understanding of the equivalent security hypothesis is a prerequisite to a thorough empirical investigation of corporate debt issuances. A compelling area not explored in this paper is the relation of a call and a put option in hedging. Güntay,

Prabhala, and Unal (Working Paper 1-1) found strong empirical support for the use of the call option in various hedging environments. Whether a put option (or some other security feature) is equivalent in these setting is an open question.

Any future empirical investigations of the call provision hypothesis must identify situations where multiple agency problems exist. In these scenarios, one type of provision may dominate others. For example, this paper shows that risk-shifting under conditions of asymmetric information favor putable debt; otherwise, callable or putable debt works equally well. Empirically, however, distinguishing between these scenarios is problematic. Measures of asymmetric information, such as asset opaqueness (Flannery,

Kwan, and Nimalendran 2003) and variation in analyst forecasts (Thomas 2002), are

31 often sited as proxies for potential risk-shifting. Disentangling these joint signals, or finding pure signals for asymmetric information and risk-shifting potential, remains a challenge for empirical finance.

Lastly, a more complete agency theory including interest-rates needs to be considered. Until interest-rate levels are formally explored in agency settings, results from any empirical investigation of the call provision hypothesis and the equivalent security hypothesis remains ambiguous. Empirical finding, such as Kish and Livingston

(1994) and Güntay, Prabhala, and Unal (Working Paper 1-1), offered support for simple interest-rate hedges, but pricing theory suggests that indifference attains. An embedded option is fairly priced, offering no net advantage. But, does indifference hold when agency problems plague the market for corporate debt? Important links may remain undiscovered that explain why empirical investigations offer results that differ, sometimes sharply, from the expected results couched precisely in pricing and agency paradigms.

Table 2-1. Debt financing with required rates. Debt-holder payout is shown in a 2- period model with asymmetric information under four different financing opportunities: long-term, short-tern, callable, and putable. When embedded options offer contract rates at the required rates, the contracts are equivalent to a short-term debt policy. Debt holders expect the same state-dependent payoffs using short-term, callable, and putable debt. Required Period 1 Resulting Period 2 Debtholder Strategy rate results action results payout Good D R Good N/A 2 Bad D R2 Long-term R2 Good D R Bad N/A 2 Bad M5 Issue new short-term debt, Good D Good rate = 0. Bad D Short-term 0 Issue new short-term debt, Good D R Bad 1 rate = R1. Bad M5 Call debt. Issue short-term debt, Good D Good rate = 0. R - Bad D Callable 1 equivalent Good D R Bad Don't call debt. 1 Bad M5 Good D Good Don't put debt. Bad D Putable 0 Put debt. Issue short-term debt, Good D R Bad 1 rate = R1. Bad M5

Table 2-2. Debt financing allowing firm separation. Debt holder payout is shown in a 2- period model with asymmetric information under four different financing opportunities: long-term, short-tern, callable, and putable. Callable and putable debt can differ from a short-term debt contact when rates in excess of the required rates are offered. Required Period 1 Resulting Period 2 Debtholder Strategy rate results action results payout Good D R Good N/A 2 Bad D R2 Long-term R2 Good D R Bad N/A 2 Bad M5 Issue short-term debt, Good D Good rate = 0. Bad D Short-term 0 Good D R1 Bad Issue short-term debt, rate = R1. Bad M5 Call debt at D R . Issue new Good D R R - Good C C 1 short-term debt, interest rate = 0. equivalent Bad D R Callable C with a call Good D R premium Bad Don't call debt. 1 Bad M5 Good D R Period 1: Good Don't put debt. P 0 Bad D R Putable P period 2: Debt put at D. Issue new short-term Good D R1 RP Bad debt, interest rate = R1. Bad M5

Table 2-3. State-dependent payoffs to the project. State-dependent payoffs to the firm are shown. First-period conditions follow a binomial process, with an equal probability of being good or bad. The business conditions in the second- period are conditioned on first-period results. The final column shows that actual payoffs. 1st period 2nd period Expected payoff conditions Probability conditions Probability at t=2 Good 60% $250 + 15.75 ln X Good 50% Bad 40% $ 25 + 15.75 ln X Good 40% $250 Bad 50% Bad 60% $25

Table 2-4. State-dependent payoffs to putable bond investors. State-dependent payoffs to the putable bond investor are shown. First-period conditions follow a binomial process, with an equal probability of being good or bad. The business conditions in the second-period are conditioned on first-period results. The last column shows the actual payoff to the putable bond investor. 1st period Put policy Expected payoff at t=2 conditions 2 Put 50(1 + rP) Good No put 50(1 + rP)(1.05)

Put 50(1 + rP)(1.05) or 50(1 + rP)(1.75) Bad 2 No put 0.40[50(1+rP) ] + 0.60[25]

Table 2-5. Summary statistics: U.S. corporate debt issues, 1980-1999. Summary statistics for U.S. corporate debt issues from 1980 though 1999 are shown. The Fixed Income Securities Database is the source of the data. Rating scores correspond to the rating scale in Table 2-7.

Percent Issue Period N Putable Callable Straight Rating Amount 80 - 99 23,549 0.01 0.21 0.77 6.76 78,634 80 - 89 2,786 0.03 0.51 0.46 7.45 130,563 90 - 99 20,763 0.01 0.18 0.81 6.68 71,667

Investment Grade Issues Sub-investment Grade Issues

Percent Issue Percent Issue Year N Putable Callable Straight Rating Amount N Putable Callable Straight Rating Amount 36 80 - 99 20,871 0.02 0.17 0.82 5.99 75,492 2,678 0.01 0.59 0.40 13.19 103,124 80 - 89 2,291 0.04 0.48 0.48 6.08 128,966 495 0.01 0.65 0.34 15.64 137,956 90 - 99 18,580 0.01 0.13 0.86 5.98 68,898 2,183 0.01 0.57 0.42 12.76 95,226

Table 2-6. Summary Statistics by firm-type: U.S. corporate debt issues, 1980-1999. Additional summary statistics for U.S. corporate debt issues from 1980 though 1999 are shown. The Fixed Income Securities Database is the source of the data. For each firm-type, statistics are reported for the entire sample (1980 - 1999), and the 2 periods of 1980 - 1989 and 1990 through 1999. Rating scores correspond to the rating scale in Table 2-7.

Investment Grade Issues Sub-investment Grade Issues Percent Issue Percent Issue Firms Years N Putable Callable Straight Rating Amount N Putable Callable Straight Rating Amount Industrial 80 - 99 5,862 0.02 0.16 0.82 6.61 110,802 2,317 0.01 0.60 0.39 13.17 99,823 Industrial 80 - 89 1,087 0.03 0.46 0.51 6.23 123,710 389 0.01 0.66 0.33 15.51 140,308 Industrial 90 - 99 4,775 0.02 0.09 0.89 6.70 107,863 1,928 0.01 0.59 0.40 12.81 91,655 Financial 80 - 99 12,306 0.01 0.13 0.86 5.60 60,769 223 0.02 0.60 0.39 14.28 115,917 Financial 80 - 89 861 0.06 0.40 0.54 5.55 147,304 80 0.04 0.55 0.41 17.11 114,253

Financial 90 - 99 11,445 0.01 0.11 0.89 5.60 54,260 143 0.01 0.62 0.37 12.89 116,848 37 Utility 80 - 99 2,681 0.02 0.36 0.62 6.47 65,236 135 0.03 0.34 0.63 11.96 137,241 Utility 80 - 89 338 0.01 0.73 0.27 6.92 99,936 24 0.00 0.75 0.25 13.14 184,083 Utility 90 - 99 2,343 0.02 0.31 0.67 6.41 60,230 111 0.04 0.25 0.71 11.73 127,113

Table 2-7. S&P rating numerical conversion. The conversion from numerical to alpha ratings for bond ratings is shown. The ratings are S&P bond ratings as listed in the Fixed Income Securities Database.

Numerical rating Alpha rating 1 AAA 2 AA+ 3AA 4 AA- 5A+ 6A 7A- 8 BBB+ 9 BBB 10 BBB- 11 BB+ 12 BB 13 BB- 14 B+ 15 B 16 B- 17 CCC+ 18 CCC 19 CCC- 20 CC 21 C 25 D 26 Suspended 27 NR

Figure 2-1. Uncertainty about changes in project value. The project will last for 2 periods, and all cash flows from the project will be received at the end of the second-period. The value of the project, however, is uncertain through time, as shown. The value follows a binomial process where, during each period, the value of the project will increase will probability p or decrease with probability (1-p).

Figure 2-2. Project with a future investment opportunity. The project lasts for 2 periods, and all cash flows from the project will be received at the end of the second- period. The value of the project, however, is uncertain through time, as shown. Further, if prospects are good during the first-period, the entrepreneur can invest additional capital into the project.

Figure 2-3. Changes in equity value from risk-shifting. The value of the firm falls as management shifts from Project A to Project B, as depicted along the horizontal axis. However, the value of the equity increases. This suggests that the value of the debt falls by more than the loss in the value of the firm. Equity holders expropriate value from debt holders by shifting to Project B.

Figure 2-4. Changes in call option value from risk-shifting. As a risk shift occurs, the value of the firm’s debt falls from D(A) to D(B). However, the value any call option on the debt also falls. Since the value of the call option on debt accrues to the firm’s equity holder, the presence of the call option diminishes the value of risk-shifting on the part of the firm.

Figure 2-5. Changes in put option value from risk-shifting. As a risk shift occurs, the value of the firm’s debt falls from D(A) to D(B). However, the value any put option on the debt increases. Since the value of the put option on debt accrues to the firm’s debt investors, the presence of the put option diminishes the value of risk-shifting on the part of the firm.

Future Asymmetric Investment Risk-Shifting Information Opportunties

Asymmetric Either Either Putable Information

Future Investment Either Either ? Opportunties

Risk-Shifting Putable ? Either

Figure 2-6. Debt covenant preferences with multiple agency conflicts. When firms and investors are faced with pure agency problems (the diagonal squares from top- left to bottom-right), firms and investors are indifferent between callable and putable debt. Further, pure environments of future investment opportunities and risk-shifting offer first-best solutions (shaded cells). If a mixed agency environment exists, either callable debt or putable debt may dominate in some scenarios.

0.8

0.6 Investment Grade 0.4 Junk Grade

0.2 Percent of Issues 0

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 Year

Figure 2-7. Percentage of call options in corporate debt issues. The percentage of callable debt issues from 1980-1999 for U.S. corporate debt issues changes dramatically over the 20-year period.

0.14 0.12 0.1 0.08 Investment Grade 0.06 0.04 Junk Grade 0.02

Percent of Issues 0

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 Year

Figure 2-8. Percentage of put options in corporate debt issues. The percentage of putable debt issues from 1980-1999 for U.S. corporate debt issues remains relatively stable over the 20-year period.

1 0.9 0.8 0.7 0.6 Investment Grade 0.5 0.4 Junk Grade 0.3 0.2

Percent of Issues 0.1 0

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 Year

Figure 2-9. Percentage of straight debt in corporate debt issues. The percentage of straight debt issues from 1980-1999 for U.S. corporate debt issues changes dramatically over the 20-year period.

16 14 12 10 Straight 8 Callable Yield 6 Putable 4 2 0

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 Year

Figure 2-10. Initial debt yield in corporate debt issues. The initial yield of debt issues for straight, callable, and putable debt is shown from 1980-1999 for U.S. corporate debt issues.

9 8 7 6 Straight 5 Callable 4 Rating Putable 3 2 1 0

0 2 4 6 8 0 2 4 6 8 198 198 198 198 198 199 199 199 199 199 Year

Figure 2-11. Initial debt rating for corporate debt issues. The initial rating of debt issues for straight, callable, and putable debt for U.S. corporate debt issues is shown from 1980-1999.

CHAPTER 3 DIRECTIONALITY OF CREDIT-SPREADS REVISITED

Empirical examinations of corporate bond yields by Longstaff and Schwartz

(1995), Duffee (1998) and Collin-Dufresne, Goldstein and Martin (2003) found a negative relation between corporate bond yield spread changes and changes in Treasury bond yields: yield spreads tighten when interest-rates rise. This result supports the theoretical models of Longstaff and Schwartz (1995) and Acharaya and Carpenter (2002).

Interestingly, Kavvathas (“Estimating Credit Rating Transition Probabilities for

Corporate Bonds”, Working Paper 3-1, University of Chicago) found that corporate bond credit ratings are more likely to be downgraded when interest-rates rise.

In this chapter, our analysis of monthly credit-spread data on noncallable and nonputable investment-grade corporate bonds provided by Lehman Brothers via the

Fixed Income (or Warga) Database from 1985 through 1997 reveals that the relation between credit-spread changes and interest-rates has changed dramatically over time.

Examining plots of credit-spreads (Figure 3-1 and Figure 3-2) and interest-rates reveals that credit-spreads are very volatile during the 1985-1989 period and a dramatic credit- spread widening (tightening) is clearly associated with an increases (decreases) in rates.

After 1990 credit-spreads are much less volatile and it appears that credit-spread changes are positively related to rate changes.

We use Duffee’s (1998) approach (the same data source from 1985 through March

1995) to examine twelve portfolios of different credit quality and maturity. During the

1985 through 1991 period the coefficients on the change in interest-rate variable are

50 51 negative (significantly different from zero at the 1% level) for all twelve portfolios. The coefficients range from approximately -0.1 for the highest credit quality and shortest maturity portfolio to -0.4 for the lowest credit quality and longest maturity portfolio.

Further, when the model is estimated on progressively shorter sample periods (1985 through 1990, then 1985 through 1989 and so on), the explanatory power of the interest-rate variable increases and the coefficients become much more negative. The negative relation between credit-spreads and interest-rate changes is very strong during the initial years of the sample period (1985-1987). Further, consistent with Longstaff and

Schartz (1985) and Acharaya and Carpenter (2002), the relation between credit-spread changes and interest-rate changes is stronger for lower credit quality portfolios.

AAA-rated short-term portfolios and for all credit quality long-maturity portfolios. The coefficients on the interest-rate change variable for the long-maturity portfolios are around -0.06, much smaller then the magnitudes estimated in the 1985-1991 period. It is important to note that the coefficients are very similar across the four different credit quality long-maturity portfolios.

We go on to explore why the relation between credit-spread changes and interest-rate changes is different over the sample period. In the Longstaff and Schwartz

(1995) model, a negative relation between credit-spreads and interest-rates occurs because the rate of growth of the borrower’s asset value increases with interest-rates. In

Acharya and Carpenter (2002), credit-spreads tightened as interest-rates rose because of a change in the value of the liability (and hence the value of the option to default) not because of change in the value of the assets supporting the liability. A simple analysis of the relation between stock returns and interest-rates suggests that the relationship between asset values supporting corporate bonds and interest-rates changed during the sample period in a manner consistent with the changing relation between credit-spread and rate changes.

We examine the relation between interest-rate changes and the monthly returns on major stock indices over the sample period. Over the entire sample period, stock returns are negatively related to changes in interest-rates, equity market values decrease with interest-rates. However, this relation is significantly stronger during the 1991-1997 period. Thus, during the 1991-1997 period, interest-rate declines are associated with large increases in equity values and mixed changes in credit-spreads. Interest-rate declines are associated with small increases in equity value and large increases in credit-spreads during the 1985-1991 period.

Finally, we find some evidence that the negative relation between credit-spread changes and interest changes in long-maturity corporate bonds during the latter part of the sample is result of changes in the liquidity value of Treasuries rather than changes in credit quality. Specifically, we find a similar negative relation between long-maturity

53 agency bond yield spreads and interest-rate changes during the latter part of the sample period. Agency securities have almost no credit risk during the period.

3.1 Data and the Time Series of Credit Spread Volatility

This section begins with a description of how the sample is constructed. Next, the methodology for creating credit-spreads for the sample bonds and how the individual bond observations are aggregated into portfolios is presented. Finally, this section provides summary statistics for the sample and a preliminary look at the relation between credit-spread and interest-rate innovations over the sample period.

The Fixed Income Database from the University of Houston provides month-end pricing data for bonds found in the Lehman Brothers Bond Indexes. Warga (1995) provides a detailed description of the data. Specifically, month-end trader-quoted prices and yields, maturity, and Standard and Poor’s (S&P) rating are available for investment-grade corporate issuers for January 1973 through March 1998.

We limit our study, using data from January 1985 through December 1997. This is for several reasons. To eliminate the effect of changes in the value of imbedded options on bond yields as interest-rates change, the sample excludes all callable and putable bonds and bonds with sinking fund provisions. Further, debt with structured payoffs

(CMOs, convertibles, etc.) and debt structured as lease obligations are excluded. Finally, we require that the debt include semi-annual coupon payments. These objectives eliminate most debt before 1985, since most of the bonds issued in the pre-1985 period include a call option. Using the identical criteria, U.S. agency debt is also extracted from the database.

Lastly, the database also includes Treasury bonds, which are used to calculate the difference in yield between the corporate bonds and Treasury bonds (the “spread”).

Using similar criteria as the corporate bonds, we select Treasury bonds from January

1985 through December 1997. For each month-end, the selected Treasury bonds are group by maturity. An average yield is calculated for Treasuries with a remaining maturity (in years) as follows: ½, 1, 2, 3, 5, 7, 10, and 30. These monthly averages are then matched with the corporate data for each bond-month. For a given bond in a given month, a “Treasury yield” is then calculated by using the remaining maturity of the corporate bond to extrapolate between two of the calculated Treasury averages. The difference between the yield on the corporate bond and the “yield” on the Treasury is recorded as the spread for that bond-month. An analogous spread is calculated for U.S.

Agency bonds.

The corporate bonds from each issue-month are grouped into one of 48 categories constructed as follows: four different business sector categories (all bonds, industrial bonds, financial bonds, and utility bonds); four S&P rating categories (AA+ or better, AA and AA-, A+ and A, and A- and BBB+); and three categories of remaining years to maturity (2-7 years, 7-15 years, and 15-30 years). Within each category, a time series of yield spreads is developed for each month-end on the study. Accordingly, at month-end t, the yield spread for sector s, rating r, and maturity m, denoted SPREADt,s,m, is constructed as the equal-weighted mean spread for all debt issues identified in that category. ∆SPREADt,s,m is defined as the change in spread from month t to month t+1.

The U.S. agency bonds from each issue-month are grouped into one of three categories of remaining years to maturity (2-7 years, 7-15 years, and 15-30 years). A time series of yield spreads and spread changes is calculated as well.

Note further that the indexes of spread changes are not based on “refreshed” yield indexes. Neither the S&P rating category nor the maturity grouping is assumed fixed from month t to month t+1, so the bonds comprising SPREADt and SPREADt+1 can change from one month to the next. Duffee (1998) discussed possible problems with not holding these fixed from one period to the next. However, for comparability with previously published results, the methodology is employed.

The summary statistics for the corporate bond yield spreads and U.S. agency yield spreads used in the analysis are provided in Table 3-1 and Table 3-2, respectively. The average monthly spread calculated for the rating-maturity match results in over 120 monthly observations for most groups. However, there are less than 80 monthly observations for the long-maturity AAA and AA portfolios, as well as the A medium-maturity group. This occurs because there are two or fewer noncallable bonds in these portfolio categories during some of the early months of the sample period. For U.S. agency debt, only AAA-rated debt is of interest.

Before proceeding to the regression analysis of yield spread changes, graphs of credit-spreads and interest-rates over the sample period are presented. These graphs suggest that the relations between interest-rates and credit-spreads changes may be specific to the sample period examined. Figure 3-1 graphs monthly levels of credit-spreads for the AAA, AA, A and BBB-rated short-maturity portfolios over the sample period. The same patterns emerge in the medium and long-maturity portfolios.

The short-maturity portfolios are presented because there are observations for short-maturity portfolios during each month of the sample period.

These plots clearly show that yield spread volatility is much higher from the start of the sample period through the end of 1990 and declines dramatically during the latter part of the sample period. This analysis does not attempt to explain why credit-spread volatility has declined during the latter part of the sample period, however, it is important to note that interest-rate volatility did not similarly decline over the sample period, and time series models of credit-spread innovations are likely to be strongly influenced by observations during the initial part of the sample period.

Figure 3-2 plots the 2-year bond yield over the sample period. Again, very similar patterns are observed in other maturity Treasury yield series. Comparing Figure 3-1 and

Figure 3-2 reveals that spikes in credit-spreads occur at the same time as declines in interest-rates during the first part of the sample period. First, from January 1985 through early 1986 there is a dramatic (almost 400 basis point) decline in the 2-year rate and a very large (approximately 100 basis point) widening in spreads for each credit quality portfolio. The opposite pattern is observed from the 1986 peak through mid-1987: the yield on the 2-year Treasury bond yield rises and spreads tighten. Finally, the decline in the five-year Treasury bond rate from late 1987 through mid-1988 is associated with a tightening in yield spreads. The negative relation between credit-spreads and interest-rates are very clear during the three years of the sample period.

After 1988, other than the widening in credit-spreads from mid-1989 through early

1990 that occurs when rates are falling, the graph does not reveal any obvious negative relation between interest-rates and spreads. In fact, as spreads decline from peak levels in late 1990 through mid-1993, the 2-year Treasury bond yield is also largely declining.

From late 1990 through mid-1993, credit-spreads and interest-rates are positively related.

Further, the large increase in interest-rates during 1994 and subsequent decline in 1995 is associated with a widening and then tightening of credit-spreads. Again, credit-spreads and interest-rates appear positively correlated in the later part of the sample period.

3.2 Regression Analysis of Credit Spreads and Rate Changes

This section presents results of estimated models of the relation between credit-spread and interest-rate changes. First, the choice of interest-rate variable used to characterize changes in interest-rates is presented. Second, results of models estimated over the entire sample period are presented. Third, it is shown that estimating models over the early part of the sample period results in very a different relation between credit-spread changes and changes in interest-rates.

3.2.1 Choice of Interest Rate Variable

Exploring the relation between credit-spread changes and changes rates, i.e. the directionality of credit-spreads, requires creating variables that specifying the change in

Treasury bond yield curve from one month to the next. This analysis regresses spread changes on the change in a single Treasury yield change rather than using multiple

Treasury yield changes to more fully characterize changes in the Treasury curve.

Specifically, changes in credit-spreads for short-maturity portfolios are regressed against changes in the 2-year Treasury bond yield; changes in credit-spreads for medium-maturity portfolios are regressed against changes in the five-year Treasury bond yield; and changes in credit-spreads for short-maturity portfolios are regressed against changes in the ten-year Treasury bond yield. In contrast, Duffee (1998) used changes in the three-month Treasury bill rate and changes in difference between the thirty-year

Treasury bond and three-month Treasury bill yield to characterize changes in the interest-rate environment from one month to the next. None of the central results of the

58 analysis are different when multiple yields along the Treasury yield curve are used (see

Appendix C for more details). This is not surprising since principal components analysis shows that most of the variation in Treasury yields are captured the “shift” factor (Dybvig

“Bond Option and Bond Pricing Based on the Current Term Structure,” Working Paper

3-2, Washington University; and Axel and Vankudre 1998).

3.2.2 Analysis of Full Sample Period

The estimated models of the directionality of credit-spreads for the entire sample period are presented in Table 3-3. Results presented in Table 3-3 confirm the findings of earlier work: there is a negative and significant relation between credit-spread changes and changes in interest-rates. While the interest-rate change variable and sample period are not the same as Duffee (1998), the coefficients on the rate change variables are of similar magnitudes and display the same patterns.

The relation between the magnitude of the coefficient on the interest-rate variable and credit quality is important to note. The coefficients on the interest-rate variable increase as credit quality decreases with only one exception: the coefficient on short-maturity AAA-rated bonds is larger than the coefficient on short-maturity AA and

A-rated bond portfolios and nearly as large as the coefficient on BBB-rated short-maturity bonds. This pattern, other than the exception, is consistent with the

Longstaff and Schwartz (1995) and Acharya and Carpenter (2002) models, assuming that the change in interest-rates has a similar effect on the underlying asset growth rates across issuers: the impact of a change in interest-rates has a larger impact on lower credit quality issuer credit-spreads.

The exceptional case, relatively highly sensitive AAA-rated credit-spreads, is interesting in light of the findings of Kavvathas (Working Paper 3-1) that the relation

59 between credit rating upgrade likelihoods and interest-rates over the January 1985 to

March 1993 period is different for higher versus lower credit quality bonds. Kavvathas

(Working Paper 3-1) found that the probability that AAA and AA are rated bonds are upgraded is positively but insignificantly related to interest-rates while A and lower rated upgrade probabilities are inverse related to rates.

3.2.3 Analysis of the Pre-1994 Sample Period

Based on the plots of credit-spreads and interest-rates provided previously, one would expect a stronger negative relation between interest-rate changes and changes in credit-spreads for the earlier years of the sample period. Results presented in Table 3-4,

3-5, and 3-6, which focus on data before the end of the 1993, show a considerably stronger negative relation between interest-rate changes and credit-spread changes during the earlier years of the sample than those estimated for the full sample. The three tables reports estimates for the model over five successively shorter sample periods:

1985:03-1991:12, 1985:03-1990:12, 1985:03-1989:12, 1985:03-1988:12 and

1985:03-1987:12. A year is dropped from the end of the sample period in each model since the plots provided in Section 3.2.2 indicate greater negative directionality of credit-spreads during the first part of the sample period, and that this negative directionality might by most acute during the first years of the sample period.

First, focusing on short-maturity portfolios in Table 3-4, the slope coefficients for the AAA-rated portfolios are similar to the entire sample period estimates, around -0.10, other than for the 1985:3-1988:12 and 1985:3-1987:12 periods where the slope coefficients are -0.16 and -0.18. More striking are results for the lower (AA, A and BBB- rated) credit quality sectors.

For AA-rated bonds, the full sample slope coefficient is -0.08 and the single factor model has an R-squared of 12%. In the pre-1994 sample periods, the slope coefficients are -0.11 (R-squared of 18%) for the 1985:3-1993:12 period and become more negative as the sample period shrinks by one year to -0.17 (R-squared of 39%) for the

1985:3-1988:12 period. The standard errors of the slope coefficients are around 0.03.

With A-rated portfolios, the full sample period slope coefficient is -0.08 and the model R-squared is 9%. In the pre-1994 sample periods, the slope coefficients are -0.13

(R-squared of 18%) for the 1985:3-1993:12 sample period and increase as the sample period shrinks to -0.18 (R-squared of 42%) as the sample period shrinks to

1985:3-1987:12. Finally, the full sample period slope coefficient for the BBB-rated short-maturity portfolio is -0.14 and the R-squared is 8%. In the pre-1994 sample periods, the slope coefficients are -0.19 (R-squared of 12%) for the 1985:3-1993:12 sample period and increase as the sample period shrinks to -0.27 (R-squared of 54%) as the sample period shrinks to 1985:3-1987:12. The slope coefficient standard errors for the A and BBB-rated portfolio models range from 0.03 to 0.06.

In summary, there is a much stronger inverse relation between interest-rate changes and credit-spread changes in the earlier part of the sample period and the negative relation is particularly strong during the first few years of the sample period. Changes in interest-rates are also able to explain a much greater proportion of the variation in credit-spreads during the earlier years of the sample period. The single factor model

R-squared is over 39% or higher for AA, A and BBB-rated portfolios when the sample period is limited to the initial years of the sample period.

The same three patterns are observed with AA, A and BBB-rated medium (Table

3-5) and long-maturity (Table 3-6) portfolios7. First, there is a stronger negative relation between credit-spread changes and interest-rate changes for the earlier part of the sample period than for the entire sample period. Second, the negative relation between credit-spread changes and interest-rate changes is particularly strong during the first few years of the sample period: the slope coefficients are more than twice as large in absolute value than for the whole sample period. Third, interest-rate changes are able to explain a much larger proportion of credit-spread changes during the first part of the sample period, and particularly so for the first few years of the sample period where interest-rate changes explain over 40% of the variation in credit-spreads in many of the models.

3.2.4 Analysis of the Post-1991 Period

Estimated models of the relation between interest-rates and credit-spreads for the post-1991 period show very limited evidence of a negative relation between credit-spread changes and changes in interest-rates. These models are reported in Table 3-7, 3-8, and

3-9. The tables present models for each of the twelve corporate bond portfolios over three sample periods: 1991:12-1997:12, 1992:12-1997:12 and 1993:12-1997:12.

The model estimates for the short-maturity portfolios reported in Table 3-7 show a positive, statistically significant relation between credit-spreads and interest-rate changes for the AA, A, and BBB-rated portfolios in the 1991:12 to 1997:12 and 1992:12 to

1997:12 periods. The relation between interest-rate changes and spread changes goes from negative during the pre-1992 period to positive in the post-1993 period. This is not surprising given the patterns observed in Figures 3-1 and 3-2. However, there is a

7 No long term AAA debt exists in the sample.

62 negative and significant relation between credit-spread changes and interest-rate changes from AAA-rated bonds. The estimated slope coefficients vary between -0.7 and -0.10 during the post-1991 sample periods as compared to between -0.12 and -0.18 in the earlier sample period.

Results for medium-maturity portfolios are reported in Table 3-8. There are no significant relationships between credit-spread changes and interest-rate changes in the later part of the sample period.

Results for long-maturity portfolios reported in Table 3-9 indicate a significant and negative relation between credit-spread changes and changes in interest-rates. However, there are two important aspects of results present in the table that are worth noting. First, the estimated slope coefficients are around -0.05: considerably smaller than the estimates in the earlier part of the sample period. Second, the estimated coefficients do not vary with credit quality. In the early sample period, the slope coefficients for long-maturity portfolios are around -0.15 for AA-rated portfolios, between -0.15 and -0.36 for A-rated portfolios, and approximately -0.40 for BBB-rated portfolios.

In summary, the empirical analysis presented in this section shows that the relation between credit-spreads and interest-rate changes is much more negative during the early years of the sample period where dramatic spikes in spreads occur. In the later part of the period, there is very little evidence of a negative relation between credit-spread changes and interest-rate changes. In fact, AA, A, and BBB short-maturity corporate bond spreads tighten when Treasury bond yields fall in the later sample period. Further, where credit-spread changes are inversely related to interest-rate changes (long-maturity bond) the relation between credit-spreads and interest-rate changes is similar across credit

63 quality sectors. The theoretical models that predict a negative relation between credit-spreads and interest-rate changes predict a more negative relation for lower credit quality portfolios.

3.3 Stock Market Evidence of Interest Rates and Issuer Prospects

The findings in the previous section suggest that the relation between interest and credit-spreads changed during the sample period analyzed here. This obviously suggests that the relation between issuer prospects and interest-rates changed during the sample period. We find support for the idea that increases in interest-rates had a much more positive impact on issuer prospects by examining the relation between stock returns and interest-rate changes.

The Gordon Growth model (Gordon and Shapiro 1956) is a useful starting point for considering the relation between interest-rates and stock prices. The price of a share of stock viewed as a growing perpetuity is expressed as

Pt = Et/(rt – gt) where Pt is the price of share, Et is the current earnings per share, rt, is the nominal interest-rate and gt is the expected perpetual growth rate of earnings. A change in interest-rates increases the share price if and only if investors perceive that a larger increase in earnings growth will occur.

Whether or not investors perceive that earnings growth rates will match interest-rate increases is of limited interest for this analysis. We are interested in whether the relation between interest-rate changes and expected earnings growth changed during the sample period. If the finding that interest-rate increases were associated with credit-spread tightenings during the early part of the sample period and largely not associated with credit-spread tightenings during the latter part of the sample period, is

64 due to a fundamental change in the relation between interest-rates and earnings growth rates, then we would expect that the relation between stock returns and interest-rates to change during the sample period. Specifically, we would expect that the relation between interest-rate changes and stock returns would become more negative (or less positive) during the latter part of the sample period.

We examine the relation between the price return on two large capitalization stock indices, the Dow Jones Industrial Average and the Standard and Poor’s 500, and changes in the ten-year Treasury rate over different time periods within the sample period. We analyze the Dow Jones Industrial Average and Standard and Poor’s 500 because the firms in these indices are typically issuers of investment-grade public debt. Broader stock indices would include many firms that do not issue public debt.

Results of this analysis are presented in Table 3-10. For the entire sample period, there is a negative and significant relation between interest-rate changes and stock returns for both indices. However, the relation is much less negative during the early part of the sample period. For example, during the 1985:03 to 1990:12 period, the coefficient on the interest-rate variable is -0.031 for the Dow-Jones Industrial Average and the coefficient estimate is only marginally significant (p value of 5.99%) and -0.038 for the Standard and

Poor’s 500. During the 1985:03 to 1989:12 period, the negative relation between stock returns and interest-rate changes is not statistically significant at conventional levels.

Thus, interest-rate increases have a relative weak negative effect on stock returns during the time period when they have a positive effect on credit quality as measured by credit-spreads.

In contrast, in the latter part of the time period, when interest-rate increases have little, if any, positive effect on credit quality, they have a considerable negative effect on stock returns. Specifically, the coefficient on the change in ten-year Treasury bond yield variable is -0.048 in the 1991:12 to 1997:12 period and -0.057 in the 1993:12 to 1997:12 period. In both cases, the point estimates are statistically significant. The same pattern is observed with models run on returns to the Standard and Poor’s 500 Index.

3.4 Directionality of Agency Spreads

The observed relation between credit-spread and interest-rate changes on long-maturity portfolios during the later art of the sample period is difficult to reconcile with existing models that posit relations between interest-rates and credit-spread changes that are driven by changes in credit quality. First, short and long term portfolios exhibit the opposite relation between credit-spread and interest-rate changes. Second, the magnitude of the inverse relation between credit-spread and interest-rate changes are very similar across the four long-maturity portfolios.

One possible explanation for the patters observed in long-maturity portfolios is that the relation between corporate bond yield spreads and interest-rates is driven by changes in the value of the liquidity premium built into long-maturity Treasury bond prices. Liu,

Longstaff, and Mandell (Working Paper 1-2) found the changes in the liquidity premium built into Treasury bond prices (the “specialness” of Treasury bonds) explain much of the volatility of swap spreads. When investors are willing to pay a large liquidity premium on Treasury bonds, Treasury bond yields decline and credit-spreads widen. To the extent that this pattern drives the relation between interest-rate changes and credit-spreads on the long end of the term structure, the directionality of credit-spreads would be very similar across credit quality portfolios as observed.

We find evidence in support of this idea by examining the relation between yield spread changes and changes in interest-rates. Specifically, we find a negative relation between long-maturity agency bond yield spreads and changes in interest-rates during the pre-1991 period, but no significant relation in the post-1991 period. This result is important because agency securities have no meaningful credit risk. The directionality of agency spreads cannot be driven by changes in credit quality and is probably driven by changes in the liquidity value of Treasury bonds that are correlated with interest-rate changes. Further, there is no significant relation between agency spread changes and interest-rate changes for the medium and short-maturity agency portfolios.

Table 3-11 shows the relation between long-maturity agency spread changes and changes in interest-rates. Since there are no significant results for medium and short-maturity agency portfolios, these are not reported. Notice that coefficients on the rate change variable are approximately -0.04. The magnitude of the relation between agency spread changes and changes in rates in quite similar to what is observed with long-maturity corporate bonds during the latter part of the sample period.

3.5 Conclusions

In this chapter, we analyze monthly credit-spread data on noncallable and nonputable corporate bonds from 1985 through 1997. The analysis reveals that the relation between credit-spread changes and interest-rates has changed dramatically over time. Prior examinations of corporate bond yields (Longstaff and Schwartz 1995; Duffee

1998) found a negative relation between corporate bond yield spread changes and changes in Treasury bond yields: yield spreads tighten when interest-rates rise. Our analysis confirms the negative relation between credit-spreads and interest-rate changes.

We find this relation is very strong during the initial years of the sample period

(1985-1987). Further, the relation between credit-spread changes and interest-rate changes is stronger for lower credit quality portfolios.

In contrast, we find little evidence of a negative relation between credit-spread changes and interest-rate changes for the period from 1991-1997. There is a positive relation between interest-rate changes and credit-spread changes for AA, A, and BBB- rated short-maturity portfolios. There is no significant relation between interest-rate changes and spread changes for the medium-maturity portfolios. A negative relation between interest-rate changes and spread changes occurs for AAA-rated short-term portfolios and for all credit quality long-maturity portfolios.

These findings imply that the relation between interest and credit-spreads changed during the sample period, suggesting that the relation between issuer prospects and interest-rates changed during the sample period. To test this, we examine the relation between the return on two large capitalization stock indices, the Dow Jones Industrial

Average and the Standard and Poor’s 500 Index, and changes in the ten-year Treasury rate. Although we find a negative relation between interest-rate changes and stock returns for both indices, the relation is much less negative during the early part of the sample period.

Finally, we find evidence that the relation between corporate bond yield spreads and interest-rates is driven by changes in the value of the liquidity premium built into long-maturity Treasury bond prices. A negative relation between long-maturity agency bond yield spreads and changes in interest-rates is found during the pre-1991 period, but no significant relation exists after 1991. This result is important because agency securities have no meaningful credit risk.

Table 3-1. Credit-spread summary statistics for U.S. corporate debt. Summary statistics for the entire sample period are shown. Twelve portfolios are formed by credit quality and maturity: short-maturity (2-7 year maturity corporate bonds), medium-maturity (7-15 year maturity corporate bonds), and long- maturity (15-30 year maturity corporate bonds) and AAA, AA, A and BBB- rated. The source of the data is t The Fixed Income Database from the University of Houston from January 1985 through December 1997. Number of Mean number of bonds Mean years Mean Maturity Rating monthly obs. per monthly obs. to maturity SPREAD Long AAA 71 1.5 25.3 0.56 AA 122 1.3 27.1 0.82 A 131 6.1 21.5 1.07 BBB 97 5.4 23.9 1.69

Medium AAA 151 24.4 9.1 0.65 AA 151 24.7 9.6 0.68 A 78 1.6 5.3 0.90 BBB 155 15.9 4.4 1.36

Short AAA 156 18.1 4.0 0.69 AA 156 77.7 4.1 0.74 A 156 266.0 4.3 0.79 BBB 156 136.1 4.5 1.25

Table 3-2. Credit-spread summary statistics for U.S. agency debt. Summary statistics for U.S. agency debt is shown. Twelve portfolios are formed by credit quality and maturity: short-maturity (2-7 year maturity corporate bonds), medium- maturity (7-15 year maturity corporate bonds), and long-maturity (15-30 year maturity corporate bonds) and AAA, AA, A and BBB-rated. The source of the data is t The Fixed Income Database from the University of Houston from January 1985 through December 1997. Only AAA-rated debt is used in the study. Number of Mean number of bonds Mean years Mean Maturity Rating monthly obs. per monthly obs. to maturity SPREAD Long AAA 144 13.8 25.9 0.53 Medium AAA 156 21.8 8.5 0.50 Short AAA 156 111.8 3.8 0.29

Table 3-3. Directionality of credit-spreads for the entire sample period. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The twelve portfolios are grouped by credit quality and maturity: short-maturity (2-7 year maturity corporate bonds), medium-maturity (7-15 year maturity corporate bonds), and long-maturity (15-30 year maturity corporate bonds) and AAA, AA, A and BBB-rated. The change in Treasury bond yield variables are (1) the change in the 2-year Treasury bond yield for short-maturity portfolio models, (2) the change in the five-year Treasury bond yield for medium-maturity portfolio models, and (3) the change in the ten-year Treasury bond yield for long-maturity portfolio models. The regressions are run over the entire sample period (1985:03 through 1997:12). The first observation in some models occurs after 1985:03 because of missing data in the early parts of the sample period. Treasury Portfolio Sample period Intercept yield change R2 N Short-maturity 1985:3 – 1997:12 -0.003 -0.115** 12.45% 154 AAA (0.008) (0.023) Short-maturity 1985:3 – 1997:12 0.002 -0.082** 12.33% 154 AA (0.006) (0.017) Short-maturity 1985:3 – 1997:12 -0.000 -0.082** 8.91% 154 A (0.010) (0.028) Short-maturity 1985:3 – 1997:12 -0.010 -0.139** 7.88% 154 BBB (0.019) (0.038) Medium-maturity 1985:9 – 1997:12 0.001 -0.044** 3.04% 140 AAA (0.014) (0.021) Medium-maturity 1985:3 – 1997:12 -0.002 -0.105** 18.60% 148 AA (0.006) (0.018) Medium-maturity 1985:3 – 1997:12 0.000 -0.116** 14.49% 148 A (0.008) (0.023) Medium-maturity 1985:3 – 1997:12 0.000 -0.134** 10.87% 148 BBB (0.011) (0.032) Long-maturity 1985:3 – 1997:12 -0.002 -0.060** 18.27% 94 AAA (0.004) (0.013) Long-maturity 1985:10 -1997:12 -0.006 -0.104** 21.07% 129 AA (0.005) (0.017) Long-maturity 1985:3 – 1997:12 0.000 -0.212** 30.22% 147 A (0.008) (0.027) Long-maturity 1986:4 – 1997:12 -0.009 -0.263 * 16.31% 135 BBB (0.016) (0.052) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-4. Directionality of credit-spreads for the pre-1994 sample period, short-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the 2-year Treasury bond yield for short-maturity portfolio models. The regressions are run over the successively shorter sample periods between (1985:03 through 1993:12). Treasury Portfolio Sample period Intercept yield change R2 N AAA 1985:3 – 1993:12 0.000 -0.115** 12.24% 106 (0.011) (0.030) AA 1985:3 – 1993:12 0.000 -0.113** 18.15% 106 (0.009) (0.023) A 1985:3 – 1993:12 -0.003 -0.119** 14.70% 106 (0.010) (0.028) BBB 1985:3 – 1993:12 -0.010 -0.192 * 11.66% 106 (0.019) (0.052) AAA 1985:3 – 1992:12 0.000 -0.114** 11.79% 94 (0.014) (0.036) AA 1985:3 – 1992:12 0.002 -0.119** 19.33% 94 (0.009) (0.025) A 1985:3 – 1992:12 0.000 -0.125** 15.90% 94 (0.011) (0.030) BBB 1985:3 – 1992:12 -0.006 -0.201* 12.30% 94 (0.021) (0.056) AAA 1985:3 – 1991:12 -0.003 -0.107** 10.07% 82 (0.014) (0.036) AA 1985:3 – 1991:12 0.002 -0.125** 19.89% 82 (0.010) (0.028) A 1985:3 – 1991:12 0.002 -0.137** 17.96% 82 (0.011) (0.033) BBB 1985:3 – 1991:12 -0.003 -0.217 * 13.28% 82 (0.024) (0.062) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-4. Continued. Treasury Portfolio Sample period Intercept yield change R2 N AAA 1985:3 – 1990:12 0.007 -0.112** 11.34% 70 (0.015) (0.038) AA 1985:3 – 1990:12 0.016 -0.139** 28.17% 70 (0.011) (0.027) A 1985:3 – 1990:12 0.015 -0.145** 22.72% 70 (0.013) (0.032) BBB 1985:3 – 1990:12 0.023 -0.214** 26.54% 70 (0.017) (0.043) AAA 1985:3 – 1989:12 0.005 -0.121** 12.98% 58 (0.018) (0.042) AA 1985:3 – 1989:12 0.011 -0.140** 30.66% 58 (0.011) (0.028) A 1985:3 – 1989:12 0.007 -0.144** 27.34% 58 (0.013) (0.032) BBB 1985:3 – 1989:12 -0.002 -0.215** 44.51% 58 (0.013) (0.032) AAA 1985:3 – 1988:12 0.004 -0.157 * 16.93% 46 (0.021) (0.052) AA 1985:3 – 1988:12 0.013 -0.167** 38.36% 46 (0.013) (0.032) A 1985:3 – 1988:12 0.010 -0.171** 35.14% 46 (0.014) (0.035) BBB 1985:3 – 1988:12 -0.004 -0.247** 49.54% 46 (0.015) (0.037) AAA 1985:3 – 1987:12 0.002 -0.177 * 18.40% 32 (0.028) (0.065) AA 1985:3 – 1987:12 0.007 -0.150** 33.04% 32 (0.014) (0.036) A 1985:3 – 1987:12 0.009 -0.185** 41.93% 32 (0.016) (0.038) BBB 1985:3 – 1987:12 -0.004 -0.270** 53.74% 32 (0.015) (0.044) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-5. Directionality of credit-spreads for the pre-1994 sample period, medium-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the five-year Treasury bond yield for medium- maturity portfolio models. The regressions are run over the successively shorter sample periods between (1985:03 through 1993:12). Treasury Portfolio Sample period Intercept yield change R2 N AAA 1985:3 – 1993:12 -0.001 -0.059** 4.13% 92 (0.011) (0.030) AA 1985:3 – 1993:12 -0.005 -0.144** 26.95% 100 (0.009) (0.024) A 1985:3 – 1993:12 -0.004 -0.160** 21.36% 100 (0.011) (0.031) BBB 1985:3 – 1993:12 -0.003 -0.177** 14.71% 100 (0.016) (0.043) AAA 1985:3 – 1992:12 -0.001 -0.063** 4.52% 80 (0.012) (0.033) AA 1985:3 – 1992:12 -0.004 -0.153** 29.15% 88 (0.010) (0.026) A 1985:3 – 1992:12 -0.002 -0.170** 23.10% 88 (0.013) (0.033) BBB 1985:3 – 1992:12 0.001 -0.188** 15.86% 88 (0.018) (0.047) AAA 1985:3 – 1991:12 0.001 -0.071** 5.08% 68 (0.014) (0.038) AA 1985:3 – 1991:12 -0.005 -0.172** 32.96% 76 (0.011) (0.028) A 1985:3 – 1991:12 -0.002 -0.188** 25.78% 76 (0.015) (0.037) BBB 1985:3 – 1991:12 0.005 -0.203 * 17.23% 76 (0.024) (0.052) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-5. Continued. Treasury Portfolio Sample period Intercept yield change R2 N BBB 1985:3 – 1991:12 0.005 -0.203 * 17.23% 76 (0.024) (0.052) AAA 1985:3 – 1990:12 0.019 -0.072** 7.11% 56 (0.014) (0.036) AA 1985:3 – 1990:12 0.005 -0.177** 38.15% 64 (0.012) (0.028) A 1985:3 – 1990:12 0.012 -0.191** 27.66% 64 (0.016) (0.039) BBB 1985:3 – 1990:12 0.028 -0.204 * 20.05% 64 (0.021) (0.052) AAA 1985:3 – 1989:12 0.012 -0.075** 7.93% 46 (0.011) (0.038) AA 1985:3 – 1989:12 0.002 -0.180** 40.33% 52 (0.014) (0.031) A 1985:3 – 1989:12 0.009 -0.191** 29.68% 52 (0.018) (0.042) BBB 1985:3 – 1989:12 0.017 -0.250** 34.60% 52 (0.021) (0.049) AAA 1985:3 – 1988:12 0.008 -0.095** 12.84% 34 (0.019) (0.043) AA 1985:3 – 1988:12 0.005 -0.215** 51.30% 40 (0.015) (0.033) A 1985:3 – 1988:12 0.005 -0.222** 35.37% 40 (0.022) (0.049) BBB 1985:3 – 1988:12 0.006 -0.297 * 47.18% 40 (0.023) (0.051) AAA 1985:3 – 1987:12 0.003 -0.128 * 20.31% 22 (0.027) (0.057) AA 1985:3 – 1987:12 0.003 -0.219** 54.30% 28 (0.014) (0.040) A 1985:3 – 1987:12 0.004 -0.258 * 40.39% 28 (0.032) (0.061) BBB 1985:3 – 1987:12 0.014 -0.310 * 46.82% 28 (0.031) (0.065) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-6. Directionality of credit-spreads for the pre-1994 sample period, long-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the ten-year Treasury bond yield for long-maturity portfolio models. The regressions are run over the successively shorter sample periods between (1985:03 through 1993:12). Treasury Portfolio Sample period Intercept yield change R2 N AA 1985:3 – 1993:12 -0.010 -0.129** 23.95% 81 (0.008) (0.026) A 1985:5 – 1993:12 -0.002 -0.259** 14.70% 106 (0.010) (0.035) BBB 1986:4 – 1993:12 -0.013 -0.349 * 21.10% 87 (0.023) (0.073) AA 1985:3 – 1992:12 -0.011 -0.139** 26.21% 69 (0.008) (0.028) A 1985:3 – 1992:12 0.000 -0.125** 15.90% 94 (0.011) (0.030) BBB 1986:4 – 1992:12 -0.006 -0.366 * 21.19% 75 (0.027) (0.081) AA 1985:3 – 1991:12 -0.011 0.146** 25.82% 57 (0.011) (0.033) A 1985:3 – 1991:12 0.002 -0.137** 17.96% 82 (0.011) (0.033) BBB 1986:4 – 1991:12 -0.008 -0.403 * 23.58% 63 (0.031) (0.062) AA 1985:3 – 1990:12 0.003 -0.156** 33.84% 45 (0.011) (0.033) A 1985:3 – 1990:12 0.015 -0.145** 22.72% 70 (0.013) (0.032) BBB 1986:4 – 1990:12 0.031 -0.428 * 41.24% 51 (0.026) (0.073) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-6. Continued. Treasury Portfolio Sample period Intercept yield change R2 N AA 1985:5 – 1989:12 -0.009 -0.165** 38.89% 33 (0.013) (0.037) A 1985:3 – 1989:12 0.007 -0.144** 27.34% 58 (0.013) (0.032) BBB 1986:4 – 1989:12 0.009 -0.440 * 48.61% 39 (0.027) (0.074) AA 1985:5 – 1988:12 -0.019 -0.155** 38.04% 21 (0.017) (0.045) A 1985:5 – 1988:12 0.012 -0.350 * 49.09% 39 (0.026) (0.056) BBB 1986:4 – 1988:12 0.012 -0.483 * 56.91% 27 (0.033) (0.084) AA 1985:3 – 1987:12 -0.034 -0.140 * 33.29% 18 (0.032) (0.075) A 1985:5 – 1987:12 0.018 -0.362 * 48.38% 27 (0.037) (0.075) BBB 1986:4 – 1987:12 0.022 -0.413 51.43% 15 (0.050) (0.111) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-7. Directionality of credit-spreads for the post-1991 sample period, short-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the 2-year Treasury bond yield for short-maturity portfolio models. The regressions are run over the successively shorter sample periods between (1991:12 through 1997:12). Treasury Portfolio Sample period Intercept yield change R2 N AAA 1993:12 – 1997:12 -0.009 -0.066 ** 12.45% 48 (0.007) (0.022) AA 1993:12 – 1997:12 0.000 0.021 ** 6.69% 48 (0.003) (0.011) A 1993:12 – 1997:12 -0.002 0.040 ** 13.67% 48 (0.004) (0.014) BBB 1993:12 – 1997:12 -0.007 0.037 * 7.51% 48 (0.005) (0.052) AAA 1992:12-1997:12 -0.008 -0.078 ** 11.79% 60 (0.006) (0.022) AA 1992:12-1997:12 -0.003 0.023*** 19.33% 60 (0.003) (0.010) A 1992:12-1997:12 -0.008 0.044 ** 13.35% 60 (0.004) (0.015) BBB 1992:12-1997:12 -0.014 0.039 ** 7.34% 60 (0.005) (0.018) AAA 1991:12 – 1997:12 -0.005 -0.104 ** 26.10% 72 (0.006) (0.021) AA 1991:12 – 1997:12 -0.003 0.005 ** 2.56% 72 (0.003) (0.011) A 1991:12 – 1997:12 -0.007 0.022 ** 2.41% 72 (0.005) (0.016) BBB 1991:12 – 1997:12 -0.015 0.011** 13.28% 72 (0.007) (0.022) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-8. Directionality of credit-spreads for the post-1991 sample period, medium-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the five-year Treasury bond yield for medium- maturity portfolio models. The regressions are run over the successively shorter sample periods between (1991:12 through 1997:12). Treasury Portfolio Sample period Intercept yield change R2 N AAA 1993:12 – 1997:12 0.001 -0.005** 0.23% 48 (0.004) (0.015) AA 1993:12 – 1997:12 0.002 0.010 ** 1.22% 48 (0.004) (0.013) A 1993:12 – 1997:12 0.000 0.018 ** 2.54% 48 (0.005) (0.017) BBB 1993:12 – 1997:12 -0.003 0.000 ** 0.00% 48 (0.007) (0.023) AAA 1992:12-1997:12 0.002 -0.001 ** 0.01% 60 (0.004) (0.014) AA 1992:12-1997:12 0.002 0.015 ** 2.62% 60 (0.003) (0.012) A 1992:12-1997:12 -0.004 0.023 ** 4.33% 60 (0.004) (0.014) BBB 1992:12-1997:12 -0.006 0.007 ** 0.23% 60 (0.006) (0.020) AAA 1991:12 – 1997:12 0.000 -0.006 ** 0.29% 72 (0.004) (0.013) AA 1991:12 – 1997:12 -0.000 0.013*** 2.14% 72 (0.003) (0.010) A 1991:12 – 1997:12 -0.004 0.012 ** 0.88% 72 (0.004) (0.014) BBB 1991:12 – 1997:12 -0.010 -0.013 ** 0.38% 72 (0.006) (0.022) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-9. Directionality of credit-spreads for the post-1991 sample period, long-maturity. Estimated models of the monthly changes in credit-spreads for twelve corporate bond portfolios against changes in Treasury bond yields during the same month are shown. The four portfolios are grouped by credit quality: AAA, AA, A and BBB-rated. The change in Treasury bond yield variables is the change in the ten-year Treasury bond yield for long-maturity portfolio models. The regressions are run over the successively shorter sample periods between (1991:12 through 1997:12). Treasury Portfolio Sample period Intercept yield change R2 N AAA 1993:12 – 1997:12 0.000 -0.071** 26.17% 48 (0.005) (0.017) AA 1993:12 – 1997:12 -0.001 -0.057** 19.92% 48 (0.005) (0.017) A 1993:12 – 1997:12 -0.002 -0.061** 18.07% 48 (0.005) (0.019) BBB 1993:12 – 1997:12 -0.009 -0.059** 5.52% 48 (0.009) (0.036) AAA 1992:12-1997:12 0.002 -0.062** 19.75% 60 (0.004) (0.016) AA 1992:12-1997:12 0.000 -0.052** 16.63% 60 (0.003) (0.015) A 1992:12-1997:12 -0.001 -0.048** 11.07% 60 (0.004) (0.018) BBB 1992:12-1997:12 -0.010 -0.074** 7.07% 60 (0.009) (0.035) AAA 1991:12 – 1997:12 0.000 -0.062** 19.75% 72 (0.004) (0.015) AA 1991:12 – 1997:12 -0.003 -0.058** 19.05% 72 (0.004) (0.014) A 1991:12 – 1997:12 -0.003 -0.038** 6.55% 72 (0.004) (0.017) BBB 1991:12 – 1997:12 -0.009 -0.077** 8.58% 72 (0.008) (0.030) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-10. Relation between stock returns and interest-rate changes. Estimated models of the monthly changes in stock returns against changes in Treasury bond yields during the same month are shown. Changes in both the S&P 500 and the Dow Jones Industrial Average are used in the regressions. The regressions are run over the successively shorter sample periods between (1985:01 through 1997:12). 10-yr. Treasury Index Sample period Intercept yield change R2 N S&P 500 1985:01 - 1997:12 0.010 -0.045*** 11.73% 156 (0.002) (0.001) S&P 500 1985:01 - 1990:12 0.007 -0.038*** 6.63% 72 (0.194) (0.017) S&P 500 1985:01 - 1989:12 0.011 -0.025*** 1.99% 60 (0.102) (0.147) S&P 500 1990:01 - 1997:12 0.009 -0.070*** 29.14% 96 (0.002) (0.001) S&P 500 1991:01 - 1997:12 0.011 -0.057*** 22.85% 84 (0.001) (0.001) S&P 500 1992:01 - 1997:12 0.011 -0.053*** 24.17% 72 (0.001) (0.001) DJIA 1985:01 - 1997:12 0.011 -0.037*** 11.07% 216 (0.001) (0.001) DJIA 1985:01 - 1990:12 0.010 -0.031 * 7.07% 72 (0.113) (0.059) DJIA 1985:01 - 1989:12 0.013 -0.018*** 19.75% 60 (0.063) (0.302) DJIA 1990:01 - 1997:12 0.010 -0.060*** 19.05% 96 (0.002) (0.001) DJIA 1991:01 - 1997:12 0.012 -0.048*** 6.55% 84 (0.001) (0.001) DJIA 1992:01 - 1997:12 0.012 -0.045*** 8.58% 72 (0.001) (0.001) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

Table 3-11. Directionality of credit-spreads for long-maturity agency bonds. Estimated models of the monthly changes in credit-spreads for U.S. agency bond portfolios against changes in Treasury bond yields during the same month are shown. The change in Treasury bond yield variables is the change in the ten- year Treasury bond yield for long-maturity portfolio models. The regressions are run over the successively shorter sample periods between (1986:02 through 1997:12). 10-yr. Treasury Portfolio Sample period Intercept yield change R2 N US Agency 1986:02 - 1997:12 0.001 -0.019*** 0.30% 143 (0.966) (0.222) US Agency 1986:02 - 1990:12 0.003 -0.003*** 1.70% 59 (0.775) (0.902) US Agency 1986:02 - 1989:12 0.004 -0.004*** 2.10% 47 (0.785) (0.910) US Agency 1991:12 - 1997:12 -0.002 -0.040*** 21.50% 84 (0.412) (0.001) US Agency 1992:12 - 1997:12 -0.001 -0.040*** 18.80% 72 (0.522) (0.001) US Agency 1993:12 - 1997:12 -0.001 -0.043*** 20.80% 60 (0.647) (0.001) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

12.00

10.00

8.00

6.00 Rate (%) 4.00

2.00

0.00 1985 1985 1986 1986 1987 1987 1988 1989 1989 1990 1990 1991 1992 1992 1993 1993 1994 1994 1995 1996 1996 1997 1997 Yield Figure 3-1. Yield spreads on U.S. corporate bonds. The yield spreads on U.S. corporate bonds are shown from 1985 through 1997. Results are shown for four different rating categories: AAA, AA, A, and BBB. The Fixed Income Database from the University of Houston is the source of the data.

12.00

10.00

8.00

6.00 Rate (%) 4.00

2.00

0.00 1985 1985 1986 1986 1987 1987 1988 1989 1989 1990 1990 1991 1992 1992 1993 1993 1994 1994 1995 1996 1996 1997 1997 Yield Figure 3-2. Treasury bill yields. The rate on 2-year U.S. Treasury Bills is shown from 1985 through 1997. The Fixed Income Database from the University of Houston is the source of the data.

CHAPTER 4 SERIAL CORRELATION IN U.S. CORPORATE BOND EXCESS RETURNS

The difference between corporate bond and similar-maturity Treasury bond yields

(yield spreads) exhibit considerable variation over time. There are two potential sources of this variation: changes in credit quality and changes in risk or liquidity premiums.

Changes in credit quality represent changes in expected cash flows. Risk or liquidity premium changes are changes in the rate at which expected corporate bond cash flows are discounted (expected return premium) that result from changes in the market price of credit risk or changes in the liquidity premium in Treasury bond prices.

There is reason to believe that time variation in the expected return premium on corporate bonds is significant. For example, Liu, Longstaff, and Mandell (Working

Paper 1-2) show that most of the time variation in LIBOR swap spreads is due to changes in the liquidity of Treasury bonds rather than changes in default risk. Casual observation of the quality spread seems to suggest time variation in required corporate bond returns.

For example, Brown (2001) shows there is considerable variation in quality spreads over time. Elton, Gruber, Agraway, and Mann (2001) and Huang and Huang (“How Much of the Corporate-Treasury Yield Spread is Due to Credit Risk? A New Calibration

Approach,” Working Paper 4-1, Pennsylvania State University) argued that quality spreads are too volatile to be explained entirely by changes in credit quality.

This chapter shows that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. The intuition is straightforward. An increase in the expected return

84 85 premium reduces bond prices and results in a low holding-period return. However, after an increase in the expected return premium and a low realized holding-period return, the excess return is expected to be higher. In contrast, when excess returns are driven by changes in investor perceptions of default probabilities, excess returns are generally uncorrelated.

The empirical analysis examines the relation between excess corporate bond returns, the difference between the realized return on a corporate bond and the realized return on an equal duration Treasury bond, and lagged excess corporate bond returns over the 1990-1997 period using the Fixed Income Database constructed by the University of

Houston. The database provides month-end pricing data for bonds found in the Lehman

Brothers Bond Indexes. Strong evidence that corporate bond excess returns are negatively related to lagged excess returns is found. We find statistically significant negative relations between excess returns and up to eleven month lagged excess returns for bonds that enter the data set as investment-grade. Results suggest that much of the volatility in corporate bond excess returns is driven by time-varying risk or liquidity premiums.

We find limited evidence that below investment-grade (junk) bonds excess returns display negative serial correlation. This is not surprising since one would expect that innovations in expected default probabilities are a much more important determinant of junk bond holding-period returns.

Results of this analysis have important implications for the equilibrium pricing of credit risk. Since changes in discount factors appear to be an important determinant of excess returns in that excess returns are negatively serially correlated, the additional risk

86 of holding a corporate bond over a Treasury bond declines with the investor’s holding-period. In fact, the risk from shocks to the excess return premium on corporate bonds can be managed using strategies like immunization. Further, the analysis of Elton, et al. (2001) seems to over state price of corporate bond risk. Their analysis determines the required risk premium in corporate bond yields from estimates of the loadings of corporate bond excess returns on the Fama and French (1992) factors using monthly data.

This analysis indicates that this approach to estimating the market price of risk over states the risk of a corporate bond to an investor with a longer holding-period.

4.1 Sources of Serial Correlation in Excess Bond Returns

This section contrasts the relation between current and prior period excess returns, the holding-period return on corporate bond minus the holding-period return on an equal duration Treasury bond, in two cases. In the first case, excess returns are result of changes in investor perception about the probability that the bond will default. In the second case, excess returns are result of changes in the expected return premium on corporate bonds. The analysis in this section yields three results that motivate the empirical analysis. First, when excess returns are result of changes in investor perceptions about the probability that the bond will default, then excess returns are not serially correlated. Second, when excess returns are result of changes in expected return premia, then excess returns tend to be negatively serially correlated. Third, the relation between current and lagged excess returns is complex when excess returns are result of changes in the expected return premia.

The idea that excess corporate bond returns are negatively related to the prior period excess returns when excess returns are driven by expected return premium shocks while corporate bond excess returns are generally uncorrelated when excess returns are

87 driven by changes in default probabilities is shown using a simple zero-coupon bond example. However, the relation between excess returns and longer lagged excess returns is more complex in the case where excess returns are result of changes in expected return premiums. Anticipated relations in this case are generated from estimating regression models using simulated data.

4.1.1 Zero-coupon Bond Example

The basic intuition behind why excess returns are uncorrelated when excess returns are result of changes in default probabilities and negatively correlated when excess returns are result of changes in the expected return premia is seen in the following simple depiction of the price of noncallable zero-coupon corporate bond.

The following model shows the price of a $100 zero-coupon corporate bond at three dates: time 0, 1, and 2. The bond is issued at t=0 and matures in n periods, where n>2. For simplicity, it is assumed that the bond pays the investor in full with probability

ρ and defaults with probability 1-ρ. The market’s perception of the default probability can change through time, and is thus denoted ρt. When the bond defaults, the investor receives nothing, again for simplicity. The market price of the bond is the expected terminal cash flow discounted at a rate equal to the risk-free rate (rate on an equal maturity Treasury zero-coupon bond) plus an additional expected return premium that compensates investors for the risk characteristics of the cash flows from the corporate bond and/or the lack of liquidity of the corporate bond. Since we are concerned with excess returns, the risk-free rate is assumed to be zero throughout the model.

The expected return premium for a risky corporate bond that matures in n-i periods is denoted ri. That is, r0 is the n-period discount rate at time t=0, and r1 represents the

(n-1)-period discount rate at t=1. Using this, the price of the bond can be derived, using

88 the required discount rate and the expected default probability. The expected price of the bond is

P = ρ 100 . (4-1) i i n−i (1+ ri )

We first consider the case where all ri = r and all ρi = ρ. The excess returns in the first and second-periods, denoted EX1 and EX2, respectively, are

P1 EX1 = −1= r, and P0

P2 EX2 = −1 = r. (4-2) P1

The excess returns in both periods equal the initial excess return premium. Now, consider the case where investors change their perception about the probability of default at t=1, i.e. ρi ≠ ρj. The first-period excess return is

ρ1 EX1 = r . (4-3) ρ0

Likewise, the second-period excess return is

ρ 2 EX2 = r . (4-4) ρ1

The second-period excess return, EX2, is uncorrelated with the first-period excess return, EX1, to the extent that changes in investor perception about the default probability are uncorrelated over time. Changes in investor perceptions about default probabilities would be uncorrelated under rational expectations. Assuming that investor perceptions about the probability of default remains constant but the expected return premium changes over time, i.e. ri ≠ rj, the first-period excess returns is

(1+ r ) n EX = 0 −1. (4-5) 1 n−1 (1+ r1 )

Obviously, EX1 is greater than r0 when r1 < r0 and less than r0 when r1 > r0. The second-period excess return is

(1+ r ) n−1 EX = 1 −1 . (4-6) 2 n−2 (1+ r2 )

In this case, the second-period excess return is negatively correlated with the first-period excess return. When the expected return premium increases, the first-period excess returns is low as the end of period market price reflects expected cash flows discounted at a higher. However, the second-period excess returns will tend to be higher.

Unless changes in investor time-varying risk premium are highly positively correlated, excess returns will exhibit a negative serial correlation.

Since excess returns that are result of time varying required returns are negatively serially correlated, the risk from required return shocks declines with the investor’s holding-period up to the duration of the bond. In fact, risk from the required return shocks can be managed in the same manner as interest-rate risk is managed using an immunization strategy. Immunization manages interest-rate risk by offsetting the price and reinvestment risk consequences of changes in the rate at which bond cash flows are discounted. Shocks to the expected return premium have the same effect on the value of reinvested cash flows and liquidation values as a function of the investor’s holding-period as changes in the risk-free rate.

4.1.2 The Relation between Excess Returns and Past Excess Returns

The subsequent empirical analysis examines the relation between corporate bond excess returns and lagged excess returns. While the above analysis provides the basic

90 intuition as to why excess corporate bond returns will display negative serial correlation when excess returns are driven by shocks to the required rate of return, the relation between excess returns and longer lagged excess returns is complex. To see this, consider the case where changes in the excess return premium, dY, follow a process where each dYi is independent and identically distributed. The approximate first month excess return is the initial expected excess return premium (Y0) minus the change in the premium (dY1) times the duration of the bond (DT)

Y0 EX1 ≈ − dY × D . (4-7) 12 1 T

The second month excess return is

Y0 + dY1 EX2 ≈ − dY × D . (4-8) 12 2 T −1

This can be expressed in a more general form as

n−1 Y0 + ∑ dYi i=1 EXn ≈ − dY × D . (4-9) 12 n T −(n−1)

We are interested in the expected coefficients of the following simple linear regression assuming that excess corporate bond returns are driven by changes in required rates of return

EXn = α + β1 EXn-1 + β2 EX n-2 + … + βk EX n-k + ε. (4-10)

Eq. 4-7 and Eq. 4-8 clearly show that a negative relation is expected between excess returns and prior period excess returns: dY1 is negatively related to EX1 and positively related to EX2. However, an increase in the expected return premium should also have a positive effect on subsequent excess returns: dY1 should be positively related to EX3, EX4, and so on. Estimating the “long-run impact” of dY1 in a regression model

like Eq. 4-10 is problematic since dYi effects both the independent variable EXi+k and the other independent variables EXi+j, where j < k.

Since determining the expected coefficients from estimating the model shown in

Eq. 4-10 is analytically complex, we instead simulate an excess return process in a simple bond-pricing environment to develop an intuition of the actual coefficients. We simulate pricing for a 100 zero-coupon bonds with a $1,000 face value over 60 months, with all of the bonds maturing at month 60. We allow all of the bonds to pay the full $1,000 at maturity. There is no default risk. Each bond is then subjected to a different risk premium environment. All bonds start with an excess risk premium factor (Y0) of 10%.

Then, for each of the 100 price-paths, the change in the risk premium (dYi) follows a unique, random path. By not changing the default probability, but simply the excess risk premium, we focus specifically on results from (4-5) and (4-6). The expected serial correlation is negative, and this should be reflected in regressions of the model in Eq.

4-10. The price path for each bond is shown, in aggregation (Figure 4-1). For the data presented, dY is distributed normally, with a different mean and variance for each path.

The monthly average mean change in rates ranges from -0.00041 to 0.00037, and the monthly standard deviation in the excess return premium ranges from 0.004 to 0.015.

For each of the 100 bonds, we run a regression of excess returns against twelve lagged excess returns. Results for ten of the bonds are reported in Table 4-1. The ten bonds represent of the range of price paths. Results using different price paths are not materially different. Regression 1 represents a volatile excess return environment, with the remaining regressions representing more stable environments, moving from

92 regression 2 through regression 10. The distribution for dY used in each regression is reported in Table 4-1.

Results of the low volatility environment (Table 4-1, regression 10) show that almost all regression coefficients are negative, and the magnitude and significance of the coefficients fall with higher lags. In the more volatile discount factor environments, only the first three lagged coefficients are negative and significant. In fact, some of the coefficients on the longer lags are positive. We also ran regressions for several environments holding the mean change in rates, dY, to zero, but increasing the variance only (not reported). Although results for the higher variance regressions show a less consistent pattern, holding the mean change to zero improves results. Regressions with a similar variance as a regression in Table 4-1 exhibit a stronger pattern of negative coefficients on the lagged return variables.

The analysis in this section indicates that when the expected return premium on corporate bonds changes, empirical models excess corporate bond returns should reveal negative coefficient on prior excess returns. It is important to note that innovations in the excess return premium may be serially correlated. For example, one might expect that the risk premium tends to move towards a long-run mean value. This would lead to more complex relations between current and lagged excess returns. This will be considered in future work.

4.2 Data and Bond Excess Return Calculations

This section begins with a description of how the sample is constructed. Next, the methodology for calculating excess returns for a given bond is described. Finally, this section provides summary statistics for the sample.

4.2.1 Sample Selection Criteria

The data we examine come from the Fixed Income Database constructed by the

University of Houston. The database provides month-end pricing data for bonds found in the Lehman Brothers Bond Indexes. Warga (1995) provides a detailed description of the data. Specifically, month-end trader-quoted prices and yields, maturity, and Standard and

Poor’s (S&P) rating are obtained for corporate bond issues for March 1973 through

December 1997.

To eliminate the effect of changes in the value of imbedded options on bond yields, the sample excludes all callable and putable bonds and bonds with sinking fund provisions. Further, debt with structured payoffs (CMOs, convertibles, etc.) and debt structured as lease obligations are excluded. We also require that the debt include semi-annual coupon payments. Finally, we limit the sample to only trader quoted prices, excluding price data based on a matrix quote.

We limit the sample to bond-months starting in January 1990. Before 1986, the database includes a limited sample of bonds meeting the above criteria. Specifically, most of the bonds in the Lehman Indexes include a call option. We also want to compare the relation between excess returns and lagged excess returns for investment-grade and junk grade debt. However, there are limited junk bond observations in the database before 1990. From 1990 through the end of 1992, junk debt remains relatively sparse, so we also report separate results for the period starting January 1993.

Unlike other studies using this database (Flannery and Sorescu 1996, and Elton, et al. 2001), we include bond-months before a bond entering the Lehman Brothers Indexes, and bond-months after a bond exits the Indexes. Warga indicated that such data is less reliable, so previous studies typically avoid including these bond-months in their

94 samples. A bond enters the Indexes according to the criteria set forth by the Indexes. For most bonds, this involves (at least) a seasoning period. A bond exits the Indexes for a variety of reasons, including low remaining maturity and low outstanding balance. In these cases, the bond usually exits the Indexes, and then the database entirely shortly thereafter.

An investment-grade bond also exits the Indexes if its credit quality falls below investment-grade. 144 issues fall into this category for our sample period. The bond-months for these 144 bonds are of particular interest to this study, so we include them to the extent possible. The sample includes all bond-months for bonds that are downgraded to junk at any point in the sample years. For all other bonds in the sample, we include 24 bond-months before entering the Indexes and after exiting the Indexes, where available. The combined bond-months from these two groups account for roughly

5% of the final sample. It is important to maintain these observations in the analysis since they represent large changes in the perceived credit quality of the bond.

The data from each bond-month are grouped into one of four S&P rating categories (AA– or better, all A, all BBB, and BB+ or worse) according to the bond’s initial rating in the database. If a bond’s credit rating is upgraded or downgraded, it remains in the same initial category. With this methodology, we capture the full history of a bond within a single grouping. For the empirical analysis, bonds are then grouped by cohort year. For example, to establish the investment-grade cohort for 1990, we find all bonds in the database that are traded in 1990 with an investment-grade rating. These bonds are the sample of interest. We then select all bond-months for these bonds in years

1990 or later. Using this method, no new bonds enter the sample. Bonds exit the sample

95 by maturing, defaulting, or by being dropped from the database, for reasons previously described.

Table 4-2 provides summary statistics for the number of bond-months in each of the four S&P rating categories. A total of 131,302 bond-months appear in the sample, representing 3,355 individual bond issues. For the full sample, approximately 17% of the bonds are initially rated AA or better, and 11% are in the junk category. These bonds account for 17% and 7% of the bond-months for the highest rated and lowest rated bonds in the sample, respectively. In the subperiod starting in 1993, these groups account for

15% and 8% of the bond-months, respectively. Bond rating and maturity change little between the full sample and the sub-sample. The mean issue size is around $200 million, with the highest rating group issuing somewhat larger bonds in both the full sample and the period starting in 1993.

4.2.2 Excess Returns

For each bond in the sample, a time series of excess returns is constructed. A bond is first matched with a Treasury bond in the database with a similar duration, rather than maturity match. If the corporate bond and the matched Treasury have the same maturity, the corporate bond will have a shorter duration since it has a higher coupon rate. In this case, the corporate bond will tend to have positive (negative) excess returns when interest-rates rise (fall) introducing excess return volatility that is not a source of either changes in credit quality or the required return premium.

A duration match typically results in several possible matches. Among the possible matches, we then choose the Treasury with the closest maturity and issue date, in that order. Accordingly, at month-end t, the excess return for bond i, denoted EXCESSt,i, is constructed by subtracting the return to the matched Treasury from the return of bond i.

The return includes price changes and accrued interest. The matched pair is maintained throughout the study.

Table 4-3 summarizes the excess returns by rating group. It includes a separate statistics for the full 8-year sample, the 5-year subperiod starting in 1993, and by year. A number of interesting facts stand out. For the full sample, the mean excess return for all groups falls with 0.72% and 0.82%. This is a surprisingly narrow band considering the variation in credit quality among the issues. The real distinction among the rating groups is standard deviations. The highest rated bonds exhibit a standard deviation over the

8-year period of 1.54%, while the junk rated debt is higher at 2.56%. This relation is also true during the period starting in 1993.

Consistently across the groups, the variation in excess returns is lowest for the highest rated debt, and generally increases as the credit quality falls. For any given year, however, the mean excess return does not follow a distinct pattern. In 1992, for example, junk rated debt exhibits a mean excess return of 0.61%, the lowest among the four groups, yet exhibits the highest variation, nearly double that of the closest group.

4.3 Empirical Results

This section presents results of estimated models of the relation between excess returns and lag excess returns. First, the empirical model and different specifications are presented. Second, results of models estimated over the entire sample period of 1990 through 1997 are presented. Next, results from the 1993-1997 sub-period are shown. We further examine the sub-period by investment-grade.

4.3.1 Empirical Specification

This analysis regresses the monthly bond excess returns against lagged excess returns. For each month t and bond i, twelve separate regressions are estimated, using lag

97 excess returns from month one through month twelve. Since bond-specific characteristics may drive the formation of actual excess returns, a fixed-effect model is estimated. The standard fixed-effects model is

R EXCESSt,i = α + δi + ∑ β r ×lag r (EXCESSt−r,i ) + ε , R={1,2,…,12}. (4-11) r=1

Bond-specific effects are captured in the δi term for each of the 3,355 separate issues, leaving the actual structure of lag returns in the βs. The nature of the dataset makes the fixed-effect specification impractical. It requires estimating fixed-effect coefficients for each of the 3,355 separate bond issues as they appear in each regression.

Since the actual value of the fixed-effect coefficient is not of interest in this study, the fixed-effect regression is handled in a slightly different fashion. For each bond examined in the fixed-effect regression, the data are ordered sequentially from the oldest bond-month to youngest. Then, for each even month (February, April, etc.), the excess return (and lags) of the preceding bond-month is subtracted from the current month excess return (and respective lags). Under ordinary OLS, this has several results. First, the bond-effect is removed from the data, eliminating the need to estimate the 3,355 separate bond-effects. Unfortunately, this also eliminates the regression intercept. For this study, the intercept is not of interest. Further, the estimated coefficients on the lag excess returns remain consistent. Obviously, this also eliminates half of the possible data points. Given the size of the sample, however, this is not a concern. However, results from the junk group are viewed more cautiously since the sample size is smaller. In this spirit, the fixed-effect regression takes the form8

8 Other methods for differencing the data are tested (not reported). The primary results remain unchanged.

R EXCESSt,i – EXCESSt-1,i = ∑ β r lag r (EXCESSt−r,i − EXCESSt−r−1,i ) + ε. (4-12) r=1

This regression requires the use of a 2-stage least squares regression since, as constructed, the independent variable (EXCESSt,i – EXCESSt-1,i) is correlated with the first lagged excess return. The differenced 13th lagged excess return is used as an instrument variable in the first stage of this procedure.

4.3.2 Results of the Empirical Analysis

The estimated models of the excess return premia against the lagged excess return premia for investment-grade bonds over the entire sample are presented in Table 4-4.

The table reports results for six separate cohorts: bond portfolios formed at the start of each year from 1990 through 1995. Table 4-4 reports a large number of coefficients that are negative and significant. Further, as expected the lagged coefficients are less negative at longer lags. Finally, while clear evidence of negative serial correlation in excess returns is found in the 1990, 1991 and 1992 cohorts, the relations are not as strong as found in the latter cohorts.

Table 4-5 reports the analysis for below investment-grade bonds. With below investment-grade bonds, there is much weaker evidence of negative serial correlation in corporate bond excess returns. This is not surprising, as one would expect that changes in investor perceptions of credit quality should have a much stronger impact on below investment-grade excess returns.

Table 4-6 presents results from 1993 cohort, including bond-months from 1993 through 1997 for four credit quality sectors: bonds rated AA-rated or better; A-rated;

BBB-rated; and BB-rated. Results presented in Table 4-6 indicate that the negative serial correlation is strongest for the A and BBB-rated portfolios. It is important to note that

99 the lagged excess returns explain a large proportion of the variation in excess returns: the adjusted R2 values are over 30% for all of the investment-grade models.

The most puzzling results are found with the coefficients on the first lagged variable. For AA+ or better rated bonds and A-rated bonds the coefficients are positive and insignificant. This may be result of short run positive serial correlation in excess return premiums.

4.4 Implications for Risk Pricing

We presume, along with other authors (Elton, et al. 2001), that changes in excess returns are systematic because the price of risk changes over time. Results of the previous section offer evidence supporting this premise. A natural question arises then, asking what factors investors use to price risk. Two ways of thinking about this offer substantially different approaches to is selecting candidate factors.

One approach views the monthly excess return premia as independent, but identically distributed. Within this framework, excess returns are viewed as similar to monthly equity excess returns. Consequently, candidate factors used to price risk may be a set similar to factors used to price equity. One such example is the three-factor model proposed by Fama and French (1992). This approach assumes a short horizon in pricing risk. Holding-period returns are not considered since nothing dictates the “correct” holding-period to minimize risk.

This paper shows, however, that monthly excess returns are not always independent. Monthly excess returns exhibit a negative serial correlation through time9.

If only the price of risk is changing systematically, the bond investor can completely

9 This assertion appears less true for junk bonds based on the empirical results from the previous section.

100 immunize from changes in the price of risk by holding a bond for its duration. The monthly excess return deviation overstates the true risk of holding a bond for this length.

This has two implications for determining the factors of risk. Bond investors may have a holding-period differing from the duration of a portfolio of bonds. A holding-period differing significantly from the actual portfolio duration may result in substantial risk to the investor. In this case, the investor may indeed price risk in a fashion similar to the pricing of equities, and examining such factors empirically is wholly appropriate. On the other hand, a bond investor holding a portfolio to its duration avoids a substantial degree of risk. Such an investor has an objective function differing from equity investors. Appropriate factors need to account for the expected holding-period variation, which may be nonexistent.

4.5 Conclusions and Future Research

This analysis offers evidence that corporate bond excess returns are driven by shocks to corporate bond expected return premiums. Empirical results show that, in general, corporate bond excess returns display negative serial correlation. This result is strongest for investment-grade issues. Junk debt offers less support. In the latter part of the sample period (1993-1997), though, results show a stronger propensity for bond excess returns to exhibit negative serial correlation.

Results of this analysis have important implications for the equilibrium pricing of credit risk. The negative serial correlation suggests that an investor has the ability to eliminate much of the monthly variation in the price of risk. Any bond portfolio held to duration will (almost) guarantee a certain, predictable return. This leads to an interesting avenue for future research. Do actual bond returns exhibit return characteristics that allow considerable proportions of corporate bond risk to be immunized?

101

Table 4-1. Regression results from simulated price paths. Regression results of bond excess return premia against lagged excess return premia for simulated bond price paths are shown. Regression is of the form ri,t = b1ri,(t-1) + … + b12ri,(t-12) + ei,t. Columns delineate the standard deviation of the returns, with column (1) representing the highest return variation and column (10) representing the lowest return variations.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Intercept 0.001 0.002 0.005 0.007 0.011 0.010 0.013 0.021 0.025 0.019 (0.17) (0.64) (1.09) (1.67) (2.11) (2.62) (2.53) (3.5) (3.28) (2.73) 1st Lag -1.063 -0.768 -0.671 -0.666 -0.820 -0.158 -0.975 -0.875 -0.991 -0.952 (-6.5) (-4.58) (-4) (-4.13) (-4.96) (-0.96) (-5.8) (-5.38) (-6.56) (-6.24) 2nd Lag -1.027 -0.720 -0.588 -0.182 -0.614 -0.462 -0.614 -0.777 -0.751 -0.601 (-4.21) (-3.48) (-3.06) (-0.93) (-2.95) (-2.95) (-2.65) (-3.77) (-3.5) (-2.99) 3rd Lag -0.688 -0.491 -0.410 -0.289 -0.337 0.025 -0.468 -0.554 -0.761 -0.646 (-2.3) (-2.14) (-1.92) (-1.45) (-1.55) (0.14) (-2.11) (-2.52) (-3.16) (-2.93) 4th Lag -0.041 -0.276 -0.307 0.100 -0.084 -0.339 -0.406 -0.602 -0.803 -0.615 (-0.14) (-1.25) (-1.39) (0.49) (-0.38) (-2) (-2.03) (-2.69) (-3) (-2.53) 5th Lag 0.391 0.247 0.117 0.200 0.089 -0.148 -0.307 -0.453 -0.780 -0.302 (1.53) (1.19) (0.52) (1.03) (0.39) (-0.87) (-1.52) (-2.04) (-2.74) (-1.15) 6th Lag 0.671 0.189 0.004 -0.006 0.457 -0.268 0.103 -0.296 -0.312 -0.229 (3.08) (0.94) (0.01) (-0.04) (2.02) (-1.56) (0.5) (-1.36) (-1.04) (-0.87) 7th Lag 0.749 0.513 0.094 0.196 0.239 0.040 0.182 -0.417 -0.377 -0.262 (3.32) (2.49) (0.43) (1.05) (1.01) (0.25) (0.91) (-2.1) (-1.28) (-1.01) 8th Lag 0.736 0.505 0.357 0.126 -0.126 -0.231 0.100 -0.347 -0.408 -0.055 (2.84) (2.24) (1.73) (0.67) (-0.54) (-1.51) (0.5) (-1.84) (-1.5) (-0.23) 9th Lag 0.407 0.514 0.344 -0.224 -0.157 0.022 0.025 -0.219 -0.130 -0.043 (1.46) (2.3) (1.71) (-1.21) (-0.74) (0.14) (0.13) (-1.39) (-0.54) (-0.2) 10th Lag 0.243 0.244 0.241 -0.078 -0.325 -0.114 -0.156 -0.320 -0.292 -0.250 (0.95) (1.1) (1.36) (-0.45) (-1.85) (-0.83) (-0.9) (-2.26) (-1.45) (-1.28) 11th Lag 0.040 0.104 0.227 -0.042 -0.210 -0.167 -0.151 -0.153 -0.268 -0.164 (0.19) (0.57) (1.61) (-0.26) (-1.39) (-1.45) (-0.96) (-1.1) (-1.51) (-0.98) 12th Lag 0.026 -0.036 0.072 -0.027 -0.069 0.020 -0.048 -0.044 -0.190 0.033 (0.19) (-0.27) (0.56) (-0.2) (-0.62) (0.17) (-0.39) (-0.41) (-1.43) (0.27)

Adjusted R2 0.538 0.384 0.340 0.487 0.532 0.267 0.474 0.553 0.648 0.524 dY distribution mean (x 100) -0.041 0.037 -0.030 0.027 -0.021 0.017 -0.013 0.009 -0.004 0.000 std. dev. 0.015 0.012 0.010 0.011 0.010 0.008 0.007 0.006 0.005 0.005

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Table 4-2. Summary statistics for U.S. corporate debt issues, 1990-1997. Summary statistics are shown for U.S. corporate debt issues from 1990 though 1999. The Fixed Income Securities Database is the source of the data. Data are reported for both the full sample (1990-1997), as well as the subperiod 1993- 1997.

Year AA or better A BBB BB or worse Bond-months 90-97 22,228 63,393 36,853 8,828 93-97 15,351 49,135 30,638 8,151 Bonds 90-97 565 1,608 922 260 93-97 445 1,447 872 240 Rating 90-97 3.99 7.03 9.93 14.63 93-97 4.03 7.05 9.94 14.62 Size (000) 90-97 267,123 199,394 192,889 221,461 93-97 233,654 206,411 194,601 219,363 Maturity (years) 90-97 9.0 9.9 11.3 9.4 93-97 10.1 10.4 11.7 9.5

Table 4-3. Additional summary statistics for U.S. corporate debt issues, 1990-1997. Summary statistics for U.S. corporate debt issues from 1990 though 1997 are listed. The Fixed Income Securities Database is the source of the data.

AA or better A BBB BB or worse Year N Mean Median Std. Dev. N Mean Median Std. Dev. N Mean Median Std. Dev. N Mean Median Std. Dev. 90 - 97 22,228 0.721 0.749 1.514 63,393 0.730 0.767 1.738 36,853 0.765 0.799 2.113 8,828 0.808 0.818 2.656 93 - 97 15,351 0.643 0.596 1.548 49,135 0.664 0.670 1.613 30,638 0.724 0.739 1.882 8,151 0.810 0.814 2.358 1990 1,642 0.687 0.702 1.316 2,806 0.494 0.645 2.100 1,028 0.295 0.563 2.865 109 1.144 0.867 6.527 1991 2,282 1.335 1.169 1.126 4,783 1.519 1.285 2.248 1,804 1.594 1.302 3.694 133 1.006 1.187 4.367 1992 2,953 0.671 0.888 1.592 6,669 0.744 0.942 1.886 3,383 0.832 1.078 2.518 435 0.619 0.800 4.755 1993 3,303 0.925 0.556 1.316 8,394 0.941 0.584 1.359 5,026 1.025 0.663 1.573 1,112 1.140 0.788 3.434 1994 3,010 -0.297 -0.180 1.548 9,047 -0.314 -0.177 1.654 5,602 -0.241 -0.119 2.155 1,415 -0.069 0.233 2.321 1995 2,993 1.530 1.324 1.314 9,786 1.574 1.365 1.429 6,021 1.643 1.414 1.757 1,607 1.524 1.278 1.982 1996 3,055 0.263 0.133 1.524 10,668 0.315 0.121 1.593 6,745 0.337 0.146 1.803 1,908 0.666 0.655 1.863 1997 2,990 0.778 0.855 1.396 11,240 0.784 0.850 1.388 7,244 0.859 0.949 1.564 2,109 0.813 0.928 2.135 103

104

Table 4-4. Regression results for investment-grade debt, 1990-1997. Regression results of bond excess return premia against lag excess return premia in a 2-stage regression are shown. Regression is of the form ri,t = b1ri,(t-1) + … + b12ri,(t-12) + ei,t. Matching each bond with a duration-matched Treasury bond of similar- maturity, and finding the difference between the bond return calculate excess return premia and the Treasury return for a given month. Excess returns are in 100 basis point units. To eliminate any fixed effects, bond-months are differenced within a given bond. The 13th lag is used as an instrument variable in stage 1 regressions.

1990 1991 1992 1993 1994 1995 1st Lag 0.569613 0.063302 1.451602 -0.70568 -1.22073 -1.17963 (0.47) (0.28) (2.34) (-2.76) (-5.27) (-6.69) 2nd Lag -0.73406 -0.71152 -0.71763 -0.63422 -0.60728 -0.62964 (-3.83) (-13.88) (-21.58) (-21.48) (-17.25) (-26.64) 3rd Lag 0.375772 -0.13640 0.799544 -0.49256 -0.80549 -0.74008 (0.39) (-0.88) (2.13) (-3.27) (-5.85) (-7.62) 4th Lag -0.63664 -0.56330 -0.55107 -0.36897 -0.40667 -0.41764 (-6.28) (-15.77) (-13.04) (-33.71) (-20.37) (-28.14) 5th Lag 0.260440 -0.08465 0.583156 -0.46620 -0.71962 -0.67308 (0.41) (-1.05) (2.12) (-4.06) (-6.90) (-9.54) 6th Lag -0.34375 -0.26211 -0.19358 -0.20079 -0.24690 -0.24432 (-3.43) (-7.40) (-7.12) (-28.66) (-20.24) (-21.59) 7th Lag 0.108727 -0.12005 0.186795 -0.20791 -0.35075 -0.40811 (0.26) (-2.83) (2.68) (-3.43) (-6.24) (-8.54) 8th Lag -0.20576 -0.13274 -0.01286 -0.13018 -0.10002 -0.12180 (-2.42) (-9.36) (-0.73) (-15.18) (-7.54) (-12.20) 9th Lag 0.059623 -0.09266 0.055921 -0.12645 -0.22753 -0.31083 (0.21) (-3.93) (2.36) (-2.96) (-5.31) (-7.66) 10th Lag -0.11819 -0.08024 -0.03723 -0.06430 -0.00067 -0.01951 (-9.55) (-14.49) (-2.91) (-10.88) (-0.04) (-1.43) 11th Lag -0.01168 -0.03033 -0.01349 -0.05950 -0.12717 -0.20789 (-0.27) (-5.52) (-1.03) (-2.95) (-5.65) (-7.95) 12th Lag -0.00458 0.008798 -0.00121 0.032737 0.109589 0.116708 (-0.36) (1.49) (-0.09) (3.66) (5.92) (7.97) N 12,838 20,606 27,008 30,618 27,888 23,969 Adjusted R2 0.2800 0.4529 0.1573 0.3707 0.2998 0.3326 F p-value 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

105

Table 4-5. Regression results for junk debt, 1990-1997. Regression results of bond excess return premia against lag excess return premia in a 2-stage regression are shown. Regression is of the form ri,t = b1ri,(t-1) + … + b12ri,(t-12) + ei,t. Matching each bond with a duration-matched Treasury bond of similar- maturity, and finding the difference between the bond return calculate excess return premia and the Treasury return for a given month. Excess returns are in 100 basis point units. To eliminate any fixed effects, bond-months are differenced within a given bond. The 13th lag is used as a instrument variable in stage 1 regressions.

1990 1991 1992 1993 1994 1995 1st Lag 0.880153 -0.81427 -1.68652 0.789573 -1.83948 1.321045 (1.47) (-1.07) (-0.19) (0.60) (-1.19) (0.88) 2nd Lag -0.44319 -0.58367 -0.79716 -0.56794 -0.93129 -0.48074 (-1.81) (-1.72) (-0.48) (-3.75) (-4.74) (-3.12) 3rd Lag 0.721190 -0.72156 -1.32448 0.373496 -1.32712 0.828071 (1.55) (-1.24) (-0.24) (0.41) (-1.31) (0.80) 4th Lag -0.16464 -0.40944 -0.70195 -0.24479 -0.68228 -0.28977 (-0.44) (-1.72) (-0.38) (-1.37) (-3.44) (-2.36) 5th Lag 0.436139 -0.46616 -0.96471 0.125151 -0.94868 0.514067 (1.63) (-1.20) (-0.25) (0.23) (-1.34) (0.74) 6th Lag 0.130661 -0.31323 -0.70051 -0.09762 -0.57003 -0.11727 (0.37) (-1.48) (-0.31) (-0.47) (-2.22) (-1.11) 7th Lag 0.579106 -0.39822 -0.64923 -0.05656 -0.53828 0.209338 (1.75) (-1.15) (-0.37) (-0.20) (-1.61) (0.70) 8th Lag 0.497470 -0.26715 -0.48908 -0.06089 -0.35956 -0.03417 (1.29) (-1.24) (-0.27) (-0.51) (-2.31) (-0.28) 9th Lag 0.421804 -0.33604 -0.32935 -0.05753 -0.33873 0.044717 (1.95) (-1.02) (-0.38) (-0.31) (-1.59) (0.25) 10th Lag 0.342139 -0.23424 -0.22416 0.008944 -0.26903 0.023441 (2.37) (-1.49) (-0.33) (0.14) (-1.68) (0.19) 11th Lag 0.238011 -0.08866 -0.04237 0.003420 -0.11266 -0.00418 (2.22) (-0.48) (-0.42) (0.05) (-0.99) (-0.07) 12th Lag 0.061616 -0.16614 -0.09443 0.005046 -0.07941 0.064734 (0.60) (-1.76) (-0.74) (0.13) (-1.19) (0.78) N 116 343 1,152 2,102 2,247 2,082 Adjusted R2 0.2514 0.0486 0.0422 0.1121 0.1482 0.1576 F p-value 0.0001 0.0043 0.0001 0.0001 0.0001 0.0001

106

Table 4-6. Regression results by grade, 1990-1997. Regression results of bond excess return premia against lag excess return premia in a 2-stage regression are shown. Regression is of the form ri,t = b1ri,(t-1) + … + b12ri,(t-12) + ei,t. Matching each bond with a duration-matched Treasury bond of similar-maturity, and finding the difference between the bond return calculate excess return premia and the Treasury return for a given month. Excess returns are in 100 basis point units. To eliminate any fixed effects, bond-months are differenced within a given bond. The 13th lag is used as a instrument variable in stage 1 regressions.

AA or better A BBB BB or worse

1st Lag 0.136466 0.520903 -1.23168 0.789573 (0.05) (1.07) (-2.59) (0.60) 2nd Lag -0.66808 -0.71050 -0.65464 -0.56794 (-6.67) (-91.71) (-49.84) (-3.75) 3rd Lag 0.074586 -0.12775 -0.71491 0.373496 (0.04) (-12.77) (-2.62) (0.41) 4th Lag -0.43901 -0.63197 -0.30970 -0.24479 (-1.72) (-67.99) (-8.16) (-1.37) 5th Lag 0.072860 -0.07826 -0.66608 0.125151 (0.06) (-6.77) (-3.17) (0.23) 6th Lag -0.21923 -0.35584 -0.04454 -0.09762 (-1.06) (-37.50) (-2.63) (-0.47) 7th Lag 0.067565 -0.01605 -0.30715 -0.05656 (0.12) (-1.40) (-2.77) (-0.20) 8th Lag -0.14922 -0.24238 -0.01768 -0.06089 (-1.61) (-26.71) (-1.11) (-0.51) 9th Lag -0.00858 0.017873 -0.25496 -0.05753 (-0.03) (1.91) (-2.50) (-0.31) 10th Lag -0.01565 -0.11964 0.003099 0.008944 (-0.17) (-15.78) (0.14) (0.14) 11th Lag -0.00808 0.003357 -0.13925 0.003420 (-0.12) (0.62) (-2.60) (0.05) 12th Lag 0.039917 0.021667 0.047548 0.005046 (1.46) (3.48) (2.36) (0.13)

N 5,692 15,268 9,654 2,102 Adjusted R2 0.3514 0.3959 0.3177 0.1121 F p-value 0.0001 0.0001 0.0001 0.0001

107

Table 4-7. S&P ratings for initial bond issuance. The conversion from numerical to alpha ratings for bond ratings is shown. The ratings are S&P bond ratings as listed in the Fixed Income Securities Database. Numerical rating Alpha rating 1 AAA 2 AA+ 3AA 4 AA- 5A+ 6A 7A- 8 BBB+ 9 BBB 10 BBB- 11 BB+ 12 BB 13 BB- 14 B+ 15 B 16 B- 17 CCC+ 18 CCC 19 CCC- 20 CC 21 C 25 D 26 Suspended 27 NR

108

1200.00

1000.00

800.00

600.00 Price

400.00

200.00

0.00 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 Month

Figure 4-1. Simulated bond price paths. To develop a notion of bond returns, holding- period variance, and lag regression coefficients, the price path for 100 zero- coupon bonds is simulated. The bonds have five years to maturity, and each bond is subjected to a different excess return environment.

CHAPTER 5 CONCLUSION

In chapters 2, 3, and 4, I examined several areas in corporate bond design and valuation. In each case, both theory and empirical evidence is presented offering new insights. I now conclude by reviewing the main results from each chapter.

The equivalent security hypothesis developed in chapter 2 offers a new understanding of the role of embedded options in corporate debt. For over 2 decades, the call provision hypothesis has argued that a call option resolves several agency conflicts created through the use of debt-financing. Although empirical tests of the hypothesis offered limited support for the premise, the hypothesis is still promoted as strong support for the use of call options by many U.S. firms.

Chapter 2 concludes that the call provision hypothesis is incomplete and offers a theoretical justification why the call provision hypothesis may fail in empirical investigations. Examining asymmetric information, future investment opportunities, and risk-shifting, I develop what I term the equivalent security hypotheses. This hypothesis shows that these three agency conflicts arising from debt-financing are resolved using either a call option or a put option in the debt covenants. I further show that either option will result in identical ex ante expected outcomes and identical ex post state-dependent outcomes for both debt issuers and investors. I conjecture that other securities (perhaps convertible debt) may also have a role in understanding the limits of the equivalent security hypotheses. Empirical data on the combined use of straight debt as well as debt

109 110 including either a call or a put provision is also offered. The evidence suggests a number of important questions that will be the focus of future research.

Finally, chapter 4 shows that when corporate bond excess returns are driven by shocks to corporate bond expected return premiums, corporate bond excess returns display negative serial correlation. A simple model is presented demonstrating this.

Then, an extensive empirical analysis examines the relation between excess corporate bond returns and lagged excess corporate bond returns. We find statistically significant negative relations between excess returns and up to eleven month lagged excess returns for bonds that enter the data set as investment-grade. Results suggest that much of the volatility in corporate bond excess returns is driven by time-varying risk or liquidity premiums. These results are shown to have important implications for the equilibrium pricing of credit risk. They also suggest further research on the nature of holding-period returns in bond portfolios.

APPENDIX A PROOF OF PROPOSITION 1

I first establish the value of the firm with callable debt-financing in a pooling equilibrium assuming no call premium. With probability p, the firm value increases during the first-period. At this point, the firm rationally calls the debt, since the debt is riskless and RC ≥ 0. Then, at time t=2, the investor is repaid in full with interest, and the entrepreneur realizes the residual value of the project. Alternatively, with probability

(1-p), the firm value decreases during period one. The call option is not exercised. At time t=2, if the project value increases during the second-period, the debt is repaid with interest, and the entrepreneur retains the residual value. If the value decreases during the second-period, the entrepreneur defaults on the loan, leaving an amount less than the original loan for the investor and zero for the entrepreneur. Using the project values from

Figure 2-1, the risk-neutral entrepreneur’s valuation of the residual equity value of the project when financed with callable debt as

2 2 VP = p (M3 - D) + p(1-p)(M4 - D) + p(1-p)(M4 - DRC) + (1-p) (0). (A-1)

To establish the required rate on callable debt and to show that it results in a separating equilibrium, it is useful to rearrange the terms in Eq. A-1 as follows:

2 2 mis V P = [ p M 3 + 2 p (1 − p )M 4 + (1 − p ) M 5 − D ] + V C (A-2)

The first bracketed term in Eq. A-2 represents the intrinsic value of the firm, and is denoted Vi. This represents the value of the entrepreneur’s expected payoff after repaying the full value of the debt, and is constant across all financing choices. The

111 112 second term represents misinformation in firm value occurring in a pooling equilibrium,

mis mis and is denoted VC (G) for Good firms and VC (B) for Bad firms.

Flannery (1986) shows that a pooling equilibrium in short-term debt dominates other straight debt strategies when zero transaction costs exist. I only need consider whether issuers with favorable private information find that issuing callable debt dominates short-term debt in equilibrium. I also need to establish that this is a separating equilibrium. Using notation similar to Eq. A-2, the entrepreneur’s valuation under a

i mis short-term strategy is represented as V S = V + V S . Note that short-term and callable debt valuations differ only in the misinformation each creates.

To establish a separating equilibrium where Good firms issue callable debt and Bad firms issue short-term debt, Bad firms must have a dominant strategy in short-term debt.

Bad firms, in general, will follow the debt maturity choice of Good firms if they benefit from doing so. Good firms, then, attempt to use callable debt in such a way that Bad firms are hurt in a pooling equilibrium. Formally, this entails using callable debt such

i i that VS(B) > V (B) and V (B) > VC(B).

These conditions accomplish two requirements. First, Bad firms prefer short-term debt when Good firms issue short-term debt. Flannery found this to be true. Second,

Bad firms prefer short-term debt when Good firms issue callable debt. That is, when

Good firms issue callable debt, Bad firms will prefer a separating equilibrium. This

mis condition can be also be expressed as VC (B) < 0.

For short-term and long-term debt, Flannery found that misinformation for a Bad firm in a pooling equilibrium is always positive. Further, when the coupon rate equals

R the market’s required rate (a 2-period rate equivalent to RS ) and no call premium is offered,

113

mis it is easily shown that VC (B) > 0. However, when Good firms issue callable debt with the a call premium D RC such that

2 2 (1− pB ) M 5 + DR1 ( pB − pB ) − D RC = + ε . (A-3) − pB D

mis For some small, positive real numberε , VC (B) < 0 holds. Substituting Eq. A-3 into

Eq. A-2 and simplifying reveals that

mis VC (B) = -ε . (A-4)

R Further, it can be readily shown that RS > RC. This condition ensures that callable debt acts as described, validating the valuation in Eq. A-1. Firms will not call debt after the first-period, being forced to refinance the debt at the short-term rate R1 when the firm’s value decreases during the first-period. Further, a call premium will be offered to induce a separating equilibrium.

APPENDIX B PROOF OF EQUIVALENT SECURITY HYPOTHESIS 2

The proof retains the notation established in BT. The risk-free rate for both periods is ρ. The firm makes an initial investment at t=0 of I0, and then receives an payoff at t=2

’ ’’ of θR(I0), where θ is a random variable, R (I0) > 0, and R (I0) < 0. The state of nature at t=1 is indexed by µ, and θ is conditionally distributed on the realized µ. At t=0, µ, F(µ), and F(θ|µ) are public information. The state of µ at t=1 is also known. BT found that the all-equity firm will invest an amount that maximizes the expected wealth of the shareholders. This is given by

∞∞ e θR(I 0 )dF(θ | µ)dF(µ) N 0 = − I 0 . (B-1) ∫∫ (1+ ρ) 2 00

BT found that the expected wealth to shareholders falls when straight debt is used to fund part of the initial investment. Straight debt also results in a lower funding of future investment opportunities. However, Eq. B-1 attained with callable debt, and the full all-equity funding in future investment opportunities resulted.

Putable debt issued at t=0 gives the investor the option of redeeming the debt at t=1 for the full principal amount. I also allow putable debt investors to receive any accrued interest during the first period. The firm gets the cash needed to refund the debt by issuing new debt at the required refund rate, rr, based on the firm’s second-period prospects. Investors will find the put worthwhile when, once µ is revealed, prospects for

θ are less favorable then expected at t=0. With this, divide µ into two regions, where

114 115

(0,µ*) is the region where investors exercise the put option, and (µ*,∞) is the region where investors do not. The shareholders’ value from issuing putable debt is then written

∞∞(θR(I ) − (1+ r )2 D dF(θ | µ)dF(µ) N p = 0 p 0 − E 0 ∫∫ 2 0 ** (1+ ρ) µθpn

µ * ∞ (θR(I0 ) − (1 + rr )D0dF(θ | µ)dF(µ) + ∫∫ 2 * (1 + ρ) 0 θ pp

µ* ((1+ rp )D0 − D0 )dF(µ) + . (B-2) ∫ 1+ ρ 0

The bankruptcy points at t=2 are given by

* θ pp R(I 0 ) = (1+ rr ) (B-3) if the investor puts the bond at t=1, and

* 2 θ pn R(I 0 ) = (1 + rp ) (B-4) if the investors retain the debt for the second-period. With this setup, the investors will put the debt because they demand a one-period expected return of ρ, so the equilibrium value of the refund rate, rr, is determined by

* ∞ θ pp (1+ ρ)D0 = ∫ (1+ rr )D0dF(θ | µ) + ∫θR(I 0 )dF(θ | µ). (B-5) * θ pp 0

Similarly, the equilibrium value for the initial rate on putable debt, rp, is set such that investors expect a return of ρ over the 2 periods. This, of course, depends on the probability that they will put the issue at t=1. The following will hold with the equilibrium put rate rp:

116

µ* 2 (1+ ρ) D0 = ∫(1+ rp )D0 (1+ ρ)dF(µ) 0

∞∞ 2 + ∫∫(1+ rp ) D0dF(θ | µ)dF(µ) ** µθpn

* ∞θ pn + ∫∫θR(I0 )dF(θ | µ)dF(µ). (B-6) µ* 0

Substituting Eq. B-5 and Eq. B-6 into Eq. B-2 and simplifying results in

∞∞ e θR(I 0 )dF(θ | µ)dF(µ) N 0 = − I 0 , (B-7) ∫∫ (1+ ρ) 2 00 which is the same solution as Eq. B-1.

APPENDIX C REGRESSIONS USING DIFFERENT BENCHMARK TREASURIES

The empirical analysis of the relation between credit-spread and interest-rate changes use a single interest-rate to characterize changes in the term structure of Treasury bond yields. Specifically, for short-maturity portfolios, the 2-year Treasury bond yield is used, for medium-maturity portfolios, the 2-year Treasury bond yield is used, for medium-maturity portfolios, the five-year Treasury bond yield is used, and for long-maturity corporate bonds, the ten-year Treasury bond is used. These Treasury bond yields are used because they have the best fit in the credit-spread change models.

Further, we do not report results where the change in Treasury bond yields are characterized by more than one point along the Treasury bond yield curve.

Table C-1 reports regressions run on the four long-maturity corporate bond portfolios. The first model is the one reported in the text: the change in interest-rates is the change in the ten-year bond yield. The second, model uses the change in the one-year

Treasury bond yield and the change in the difference between the thirty-year and one- year Treasury bond yield. This approach is very similar to Duffee (1998) who used the

90-day Treasury bill yield and the change in the difference between the thirty-year

Treasury bond and 90 day Treasury bill yields to characterize the yield curve. The third specification uses the change in the one-year Treasury bond yield, the change in the difference between the ten-year Treasury bond yield and the one-year Treasury bond yield, and the change in the difference between the thirty-year Treasury bond yield and the ten-year Treasury bond yield.

117 118

In all four models, the specification using the 90-day Treasury bill yield and the change in the difference between the thirty-year Treasury bond and 90-day Treasury bill yields, the explanatory power is of the models is considerably lower than simple one factor model reported in the text. Changes in the ten-year Treasury bond yield better explain long-maturity corporate bond yield spreads than the 2-factor model that uses bond yields from the extremes of the term-structure.

The three-factor model, which uses the ten-year bond yield change information, has only slightly higher explanatory power than the single factor model. Further, the estimated coefficient on the change in the ten-year Treasury bond yield in the single factor model are remarkably similar to the estimated coefficient on the change in the difference between the ten and one-year Treasury bond yield for all four credit quality models.

119

Table C-1. Directionality of credit-spreads with different treasury yields. Estimated models of the monthly changes in credit-spreads for a corporate bond portfolio against changes in Treasury bond yields during the same month are shown. The change in Treasury bond yield variables are the change in the one- year Treasury bond yield; the change in the ten-year Treasury bond yield; the change in the ten-year minus one-year Treasury bond yield; the change in the thirty-year minus one-year Treasury bond yield; and the change in the thirty- year minus ten-year Treasury bond yield. The regressions are run over the sample period 1985:05 through 1997:12. 1-yr 10-yr 10-yr 30-yr 30-yr less Sample period Intercept 2 N yield yield less 1-yr less 1-yr 10-yr R 1990:03-1997:12 -0.001 -0.059*** 18.27% 94 (0.642) (0.001) 1990:03-1997:12 -0.001 -0.046** -0.055*** 27.34% 94 (0.749) (0.058) (0.010) 1990:03-1997:12 -0.001 -0.045** -0.069*** -0.005 48.61% 94 (0.742) (0.047) (0.001) (0.807) 1985:10-1997:12 -0.005 -0.103*** 38.04% 129 (0.291) (0.001) 1985:10-1997:12 -0.004 -0.088*** -0.059** 49.09% 129 (0.421) (0.006) (0.039) 1985:10-1997:12 -0.005 -0.097*** -0.090*** 0.021 56.91% 129 (0.340) (0.001) (0.001) (0.489) 1985:05-1997:12 -0.000 -0.212*** 33.29% 147 (0.993) (0.001) 1985:05-1997:12 0.001 -0.265*** -0.144*** 48.38% 147 (0.934) (0.001) (0.001) 1985:05-1997:12 -0.001 -0.263*** -0.195*** -0.000 51.43% 147 (0.954) (0.001) (0.001) (0.987) 1986:04-1997:12 -0.008 -0.262*** 33.29% 135 (0.582) (0.001) 1986:04-1997:12 -0.009 -0.364*** -0.204*** 48.38% 135 (0.555) (0.001) (0.011) 1986:04-1997:12 -0.009 -0.367*** -0.261*** -0.049 51.43% 135 (0.529) (0.001) (0.001) (0.589) ***, **, and * indicate significance at the 1, 5, and 10 percent levels, respectively.

LIST OF REFERENCES

Acharya, Viral and Jennifer Carpenter. “Corporate Bond Valuation and Hedging with Stochastic Interest-rates and Endogenous Bankruptcy,” Review of Financial Studies, Vol. 15 (2002), pp. 1355-1383.

Axel, Ralph and Prashant Vankudre. “Managing the Yield Curve with Principle Component Analysis,” Lehman Brothers Fixed Income Research, 1998.

Barnea, Amir, Robert A. Haugen, and Lemma W. Senbet. “A Rationale for Debt Maturity Structure and Call Provisions in the Agency Theoretic Framework,” Journal of Finance, Vol. 35, No. 5 (December 1980), pp. 1223-1234.

Barnea, Amir, Robert A. Haugen, and Lemma W. Senbet. Agency Problems and Financial Contracting. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1985, pp. 88-91.

Black, Fischer and Myron Scholes. “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3. (May-June, 1973), pp. 637-654.

Bodie, Zvi and Robert A. Taggart, Jr. “Future Investment Opportunities and the Value of the Call Provision on a Bond,” Journal of Finance, Vol. 33, No. 4 (September 1978), pp. 1187-1200.

Bowlin, Oswald D. “The Refunding Decision: Another Special Case in Capital Budgeting,” Journal of Finance, Vol. 21, No. 1. (March, 1966), pp. 55-68.

Boyce, William M. and Andrew J. Kalotay. “Tax Differentials and Callable Bonds,” Journal of Finance, Vol. 34, No. 4. (September, 1979), pp. 825-838.

Brick, Ivan E. and Oded Palmon. “The Tax Advantages of Refunding Debt by Calling, Repurchasing, and Putting.” Financial Management, Vol. 22, No. 4 (Winter 1993), pp. 96-105.

Brown, David T. “An Empirical Analysis of Credit Spread Innovations,” Journal of Fixed Income, Vol. 11, No. 2 (September 2001), pp. 9-27.

Collin-Dufresne, Pierre, Robert Goldstein and J. Spencer Martin. “The Determinants of Credit-spread Changes,” Journal of Finance, 2003, forthcoming.

Cook, Douglas O. and John C. Easterwood. “Poison Put Bonds: An Analysis of Their Economic Role,” Journal of Finance, Vol. 49, No. 5. (December 1994), pp. 1905- 1920.

120 121

Crabbe, Leland. “Event Risk: An Analysis of Losses to Bondholders and "Super Poison Put" Bond Covenants,” Journal of Finance, Vol. 46, No. 2. (June 1991), pp. 689- 706.

Crabbe, Leland E. and Jean Helwege. “Alternative Tests of Agency Theories of Callable Corporate Bonds,” Financial Management, Vol. 23, No. 4 (Winter 1994), pp. 3-20.

Crabbe, Leland E. and Panos Nikoulis. “The Putable Bond Market: Structure, Historical Experience, and Strategies,” Journal of Fixed Income, Vol. 7, No. 3 (December 1997), pp. 47-60.

Dichev, Ilia D. “Is the Risk of Bankruptcy a Systematic Risk?” Journal of Finance, Vol. 54, No. 3 (June 1998), pp. 1131-1147.

Duffee, Gregory. “The Relation between Treasury Yields and Corporate Bond Yield Spreads”, Journal of Finance, Vol. 53 (December 1998), pp. 2225-2241.

Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann. “Explaining the Rate Spread on Corporate Bonds,” Journal of Finance, Vol. 56, No. 1 (February 2001), pp. 247-277.

Fama, Eugene and Kenneth R. French. “The Cross-Section of Expected Stock Returns,” Journal of Finance, Vol. 47, No. 2 (June 1992), pp. 427-465.

Flannery, Mark J. “Asymmetric Information and Risky Debt Maturity Choice,” Journal of Finance, Vol. 16, No. 1 (March 1986), pp. 19-37.

Flannery, Mark J., Simon H. Kwan, and M. Nimalendran, “Market Evidence on the Opaqueness of Banking Firms’ Assets,” Journal of Financial Economics, 2003, forthcoming.

Flannery, Mark J. and Sorin M. Sorescu. “Evidence of Bank Market Discipline in Subordinated Debenture Yields: 1983-1991,” Journal of Finance, Vol. 51, No. 4. (September 1996), pp. 1347-1377.

Gordon, Myron J. and Eli Shapiro, “Capital Equipment Analysis: The Required Rate of Profit,” Management Science, Vol. 20 (October 1956), pp. 102-110.

Jen, Frank C. and James E. Wert. “The Effect of Call Risk on Corporate Bond Yields,” Journal of Finance, Vol. 22, No. 4. (December, 1967), pp. 637-651.

Jensen, Michael C. and William H. Meckling. “Theory of the firm: Managerial behavior, agency costs and ownership structure,” Journal of Financial Economics, Vol. 3, No. 4 (October 1976), pp. 305-360.

Kidwell, David S. “The Inclusion and Exercise of Call Provisions by State and Local Governments,” Journal of Money, Credit and Banking, Vol. 8, No. 3. (August, 1976), pp. 391-398.

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Kish, Richard J. and Miles Livingston. “Determinants of the Call Option on Corporate Bonds,” Journal of Banking and Finance, Vol. 16, No. 4 (August 1992), pp. 687- 703.

Longstaff, Francis and Eduardo Schwartz, “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,” Journal of Finance, Vol. 50 (July 1995), pp. 789-820.

Robbins, Edward H. and John D. Schatzberg, “Callable Bonds: A Risk-Reducing Signaling Mechanism,” Journal of Finance, Vol. 41, No. 4 (September 1986), pp. 935-949.

Thomas, Shawn. “Firm Diversification and Asymmetric Information: Evidence from Analysts’ Forecasts and Earnings Announcements,” Journal of Financial Economics, Vol. 64, No. 3 (June 2002), pp.373-396.

Warga, Arthur. “A fixed income database,” Fixed income research program, University of Wisconsin-Milwaukee, 1995.

BIOGRAPHICAL SKETCH

John C. Banko obtained his B.S.B.A. (high honors) in finance from the University of Florida in December 1990. He then held positions with Andersen Consulting and the

University of Florida for several years in computer systems development before pursuing his Ph.D. in Finance in August 1997. His research interests include security design, agency issues, and fixed-income asset pricing.

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