Capital Market Equilibria Edi ted by

Günter Bamberg and Klaus Spremami

With Contributions by G.Bamberg M.Brennan V.Firchau R.Geske B.Rudolph E.S.Schwartz K.Spremann S.Trautmann

With 4 Figures and 12 Tables

Springer-Verlag Berlin Heidelberg New York Tokyo

^ WsT" X fir

Prof. Dr. Günter Bamberg Institut für Statistik und Mathematische Wirtschaftstheorie Universität Augsburg Memminger Straße 14, D-8900 Augsburg, F R G

Prof. Dr. Klaus Spremann Abteilung Wirtschaftswissenschaften Universität Ulm Oberer Eselsberg, D-7900 Ulm, F R G

ISBN 3-540-16248-8 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-16248-8 Springer-Verlag New York Heidelberg Berlin Tokyo

Library of Congress Cataloging-in-Publication Data. Capital market equilibria. Includes bibliogra­phies and indexes. 1. Capital market-Mathematical models. 2. Equilibrium (Economics )-Mathe-matical models. 3. Efficient market theory-Mathematical models. I. Bamberg, Günter, 1940-. II. Spremann, Klaus. HG4523.C33 1986 332.6'0724 86-10104 ISBN 0-387-16248-8 (U.S.)

This work is subject to copyright. All rights are reserved, whether the whole or part of material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use a fee is payable to "Verwertungsgesellschaft Wort", Munich.

© Springer-Verlag Berlin Heidelberg 1986 Printed in Germany

The use of registered names, trademarks, etc. in the publication does not imply, even in the absence of a specific statement, that such names are excempt from the relevant protective laws and regulations and therefore free for general use.

Offsetprinting: Beltz Offsetdruck, Hemsbach/Bergstrasse Binding: J. Schäffer O H G , Grünstadt

2142/3140-543210

Univfcrsitats-Bibhö'hek München

Table of Contents

Prologue (G. Bamberg and K. Spremami) 1

1. Equilibrium versus Market Imperfections 1

2. Questions and Answers 2

The Hybrid Model and Related Approaches to Capital Market Equilibria (G. Bamberg) 7

1. Introduction 8

2. Portfolio Models Based on Different Sets of Parameters . . 10 2.1 One-Parameter Models 10 2.2 Two-Parameter Models: Mean-Semivariance Approach 11 2.3 Other Two-Parameter Approaches 14 2.4 Extensions to Three or More Parameters 16

3. Rationale of the Hybrid Model 17 3.1 Consistency of the Mean-Variance Approach with

Expected Utility and Stochastic Dominance 17 3.2 Explicit Solutions of the Portfolio Problem 21 3.3 Explicit Solutions of the Equilibrium Conditions . . . . 27 3.4 Which Mean-Variance Approaches Provide Explicit

Solutions? 30

4. Applications of the Hybrid Model 33 4.1 Consideration of Income Taxation 34 4.2 Heterogeneous Expectations 39 4.3 Restrictions on Short Sales 41 4.4 Some Other Market Imperfections 44

5. Appendix 46 | 5.1 Proof of Theorem 4 46 1

5.2 Solution of Partial Differential Equation (31) 48 I

References 49 j Portfolio Decisions and Capital Market Equilibria Under Incomplete Information (V. Firchau) 55

1. Introduction 55

Vili

2. Risk Situation with Regard to the Prior Parameters: A Two-Level Bayes Approach 59

3. Risk Situation with Regard to the Prior Parameters: Lin's Approach 62

4. Partial Uncertainty with Regard to the Prior Parameters . . 66

5. Asset Pricing under Uncertainty 72

References 77

Option Valuation: Theory and Empirical Evidence

(R. Geske and S. Trautmann) 79

1. Introduction 80

2. Option Valuation Theory 81 2.1 Preference and Distribution-Free Results 81

2.1.1 Call Options 81 2.1.2 Put Options 83 2.1.3 Relations Between Puts and Calls 85 2.1.4 Additional Arbitrage Restrictions 85

2.2 Distributional Assumptions and Hedging Models . . . . 86 2.2.1 Hedge Portfolios 86 2.2.2 The Classical Black-Scholes Model 89 2.2.3 A Brief Description of Other Option

Valuation Models : . 90 2.2.4 Analytic Models For American Calls and Puts . 93

2.3 Preference Assumptions and Non-Hedging Models . . . 94 2.4 New Option Instruments 95 2.5 Applications of Option Theory 97

3. Empirical Tests of Option Valuation 97 3.1 Test of Boundary Conditions Among an Individual

Equity Option and the Underlying Stock 100 3.2 Test of Boundary Conditions Among Different Equity

Options and the Underlying Stock 104 3.3 Tests of Equity Option Pricing Models 107

3.3.1 Results of Robustness Tests 109 3.3.2 Results of Predictability Tests I l l 3.3.3 Results of Unbiasedness Tests 113 3.3.4 Results of Hedge Return Behavior Tests . . . . 116

3.4 Tests of New Option Instruments 119 3.5 Estimation Problems 121

4. Appendix: Formulae for the Evaluation of European Calls . 123

References 127

IX

The Value of Security Agreements (B. Rudolph) 135

1. A Survey of Credit Support Decision Models 136 1.1 Credit Decisions in a Restricted Capital Market . . . . 136 1.2 Market Uncertainty 136 1.3 Credit Support Decisions with Event Uncertainty . . . . 138

2. Neoclassical Theory and Secured Debt 138 2.1 The Basic Approach 138 2.2 Secured Debt and Capital Market Equilibrium 139 2.3 Collateral Policy and Non-Market-Value Debt Claims . 141

3. The Theory of Credit Support Decisions in the Light of the Economics of Information 143 3.1 Collaterals as a Tool to Limit the Creditability Risk . . 143 3.2 Contemporaneous Examination of Credit Standing Risk

and Credit Reliability Risk 145 3.2.1 Changing the Dividend Policy 146 3.2.2 Changing the Credit Policy 147 3.2.3 Changing the Investment Policy 148

4. A Scheme of Credit Contract Covenants 149 4.1 Credit Contract Covenants 149 4.2 Covenants Referring Indirectly to Means of Payment . . 150

4.2.1 Special Obligations of the Debtors 150 4.2.2 Special Rights of the Creditors 151

4.3 Claims of Creditors which Refer to Means of Payment . 152

5. The Efficiency of Securing Debt 153

6. Appendix: Secured Debt and Uncertainty 154 6.1 The Firm's Position 154 6.2 Derivation of the Value of Secured Debt 156 6.3 Market Value of the Debt in Dependence of its

Collateral Policy 157 6.4 The Maximization of the Market Value with

Total Collateral Policy 158

References 160

Asset Pricing in a Small Economy: A Test of the Omitted Assets Model (E.S. Schwartz and M . Brennan) 163

1. Introduction 164

2. Portfolio Based Tests of Efficiency 167

3. Omitted Assets 169 3.1 The Model 169 3.2 Integrated and Segmented Capital Markets 171

X

4. The Data 173

5. Efficiency of the Canadian Market Index 174 5.1 Beta Estimation under Thin Trading 174 5.2 Preliminary Estimates 175 5.3 Maximum Likelihood Estimation 178

6. Tests of the Omitted Assets Hypothesis 181

Appendix: Iterative Maximum Likelihood Procedure 186

References 187

The Simple Analytics of Arbitrage (K. Spremami) 189

1. General Equilibrium, Modern Finance, and Arbitrage Theory 189 1.1 General Equilibrium 189 1.2 Modern Finance 190 1.3 Arbitrage 192

2. An Example, its Generalization, and the Question 193 2.1 A Portfolio of Savings Bonds and Term Deposits . . . . 193 2.2 Is a Free Lunch Possible? 194 2.3 Events and Futures 195 2.4 The Question:

Should the Original Portfolio be Revised? 198

3. Arbitrage versus Equilibrium 199 3.1 Some Borrowing from Production Theory 199 3.2 Either Arbitrage is Possible or Equilibrium Prices Exist 200 3.3 The Lemma of MINKOWSKI-FARKAS as

Mathematical Background 200 3.4 The Derivation of an Issue Price 201 3.5 Summing up the Results 203

4. Derivative Contracts in Complete Capital Markets 204 4.1 Complete Capital Market 204 4.2 One-Period Option Pricing 204

References 206

About Contributors 209

Author Index 213

Subject Index 219

The Value of Security Agreements

Bernd Rudolph

Summary : The purpo s e o f t h i s paper i s t o examine s e c u r i t y agreements i n t he l i g h t of some w e l l known models o f f i n a n c i a l t h e o r y . I n s e c t i o n 1 a s u r v e y of common c r e d i t s u p p o r t d e c i s i o n models i s g i v e n and t h e r o l e o f c o l l a t e r a l i z a t i o n i s examined i n the c o n t e x t o f t h e s e models. S e c t i o n 2 seeks t o p r o v e t h a t t he n e o c l a s s i c a l t h e o r y o f f i n a n c e f a i l s t o e x p l a i n the e m p i r i c a l e v i d e n c e o f s e c u r i t y agreements i n c r e d i t -c o n t r a c t s . S e c t i o n 3 examines a r a t h e r new a p p r o a c h and i t i s shown on the b a s i s o f t h i s a p p r o a c h t h a t s e c u r i t y agreements can be i n t e r ­p r e t e d i n a r a t h e r s a t i s f a c t o r i n g manner. C o l l a t e r a l s and c r e d i t c o v e n a n t s a r e r e a l i z e d as i n s t r u m e n t s o f i n f l u e n c i n g t h e t r u s t w o r t h i ­ness o f the b o r r o w e r . I n s e c t i o n s 4 and 5 f i n a l l y s e v e r a l t y p e s o f c r e d i t c o n t r a c t c o v e n a n t s a r e s t r u c t u r i z e d and d i s c u s s e d w i t h r e s p e c t t o t h e i r p r a c t i c a l e f f i c i e n c y . I n t h e a p p e n d i x some main r e s u l t s o f the n e o c l a s s i c a l a p p r o a c h a r e p r o v e d i n a more g e n e r a l way.

Table of Contentò:

1. A Survey of Credit Supponi Decision Model* 7 36 1.1 Credit Vecli>ions in a Restricted Capital Market 7 36 1.2 Market Uncertainly 7 36 J.3 Credit Support Decision* with Event Uncertainty 7 3$

2. Ueoclassical Theory and Secured Vebt 73$ 2.1 The Basic Approach 73S 2.2 Secured Vebt and Capital Market Equilibrium 7 39 2.3 Collateral Policy and Hon-Market-Value Veht Claim* 141

3. The Theory of Credit Support décidions in the Light of 743 the Economico of Information

3.1 Collaterals a* a Tool to Limit the Creditabillty RUk 743 3.2 Contemporaneous Examination of Credit Standing Risk 745

and Credit Reliability Risk 3.2.1 Changing the dividend Policy 746 3.2.2 Changing the Credi! Policy 747 3.2.3 Changing the Investment Policy 74$

4. A Scheme of Credit Contract Covenants 749 4.1 Credit Contract Covenants 149 4.2 Covenants Referring Indirectly to Means of Payment 150

4.2.1 Special Obligations of the Debtors 7 50 4.2.2 Special Rights of the Creditors 75/

4.3 Claim* of Creditors which Refer to Means of Payment 7 52 5. The Efficiency of Securing debt 153

6. Appendix.: Secured Vebt and Uncertainty 154

6.1 The Firm'* Poòillon 154 6.2 Derivation of the Value of Secured Vebt 156 6.3 Market Value of the Vebt in Dependence of its 7 57

Collateral Policy 6.4 The Maximization of the Market Value with Total 15%

Collateral Policy References 760

Capital Market Equilibria. Ed. by G. Bamberg and K. Spremann © Springer-Verlag Berlin Heidelberg New York Tokyo

136

1. A S u r v e y o f C r e d i t S u p p o r t D e c i s i o n M o d e l s

1.1 C r e d i t D e c i s i o n s i n a R e s t r i c t e d C a p i t a l M a r k e t

To d i s c u s s t h e com p r e h e n s i o n of s e c u r e d d e b t i n t h e s e v e r a l a p proaches of f i n a n c i a l t h e o r y i t i s u s e f u l t o c l a s s i f y t h e a s s u m p t i o n s a b o u t the e x p e c t a t i o n s o f t h e c r e d i t o r s i n t h e d i f f e r e n t models o f c r e d i t s u p p o r t d e c i s i o n , as shown i n f i g u r e 1.

F i r s t o f a l l one c a n d i s t i n g u i s h c r e d i t s u p p o r t d e c i s i o n s when l e n d e r s have s e c u r e e x p e c t a t i o n s from such d e c i s i o n s under r i s k o r u n c e r t a i n ­t y . C r e d i t s u p p o r t d e c i s i o n s w i t h s e c u r e e x p e c t a t i o n s a r e s t r i c t l y spoken t r i v i a l d e c i s i o n s , b u t o f t e n d i s c u s s e d i n c o n n e c t i o n w i t h im­p e r f e c t c a p i t a l m a r k e t s w i t h c r e d i t r e s t r i c t i o n s and t h e r e f o r e t h i s c a s e i s i n c l u d e d i n the scheme of f i g u r e 1. On r e s t r i c t e d c a p i t a l m a r k e t s c r e d i t r a t i o n i n g i s a c h a r a c t e r i s t i c f e a t u r e . C r e d i t r a t i o n i n g i t s e l f can be i n t e r p r e t e d as a r e a c t i o n o f t h e l e n d e r on t h e u n c e r ­t a i n t y a bout the f u t u r e f i n a n c i a l r e s u l t o f h i s i n v e s t m e n t s . T h i s un­c e r t a i n t y i s o n l y i m p l i c i t l y t r e a t e d i n t h e l e n d e r ' s c a l c u l a t i o n , above a l l i n t h e form o f f i x e d c r e d i t l i n e s . C o l l a t e r i z a t i o n i n such an a p p r o a c h i s t o be seen as a d i f f e r e n t t o o l t o l i m i t t h e c r e d i t o r ' s commitment.

1.2 M a r k e t U n c e r t a i n t y

As H i r s h l e i f e r and R i l e y (1979) made c l e a r i n t h e i r r e m a r k a b l e ex­p o s i t o r y s u r v e y on the economics o f u n c e r t a i n t y and i n f o r m a t i o n t h a t the a n a l y t i c a l d e c i s i o n t h e o r y has t o d e a l w i t h two k i n d s of u n c e r ­t a i n t y : t he market u n c e r t a i n t y and t h e t e c h n o l o g i c a l o r e v e n t u n c e r ­t a i n t y . A l t h o u g h the f i n a n c i a l l i t e r a t u r e c o n s i d e r s a l m o s t e x c l u s i v e ­l y e v e n t u n c e r t a i n t y , t h e r e i s the r e m a r k a b l e e x c e p t i o n o f M i l d e ' s (1980, 1981) a p p r o a c h w h i c h i s o f i n t e r e s t f o r our s u r v e y because o f comprehending the phenomenon o f s e c u r i n g d e b t e x p l i c i t y .

We d i s c u s s t h i s a p p r o a c h s e p a r a t e d from o t h e r a p p r o a c h e s o f i n d i v i ­d u a l c r e d i t s u p p o r t d e c i s i o n , because the a s s u m p t i o n s about the ex­p e c t a t i o n s o f the c r e d i t o r s a r e n o t u n i q u e . M i l d e wants t o e x p l a i n why t h e c r e d i t market i s c h a r a c t e r i z e d by a v a r i e t y o f d i f f e r e n t i n t e r e s t r a t e s , a phenomenon c a l l e d ' i n t e r e s t r a t e d i s p e r s i o n ' .

I n t e r e s t r a t e d i s p e r s i o n i s n o t o n l y evoked by d i f f e r e n t i n t e r e s t r a t e s w h i c h r e l a t e t o the d i f f e r e n t r a t i n g - c l a s s e s o f d e b t o r s , b u t f u r t h e r m o r e because d e b t o r s do not know the s p e c i f i c s e c u r i t y r e ­q u i r e m e n t s o f the banks. To p r e v e n t h i g h c o s t s o f s e a r c h i n g f o r the

137

Credit support decisions

with certain expectations with uncertain expectations _ — l

about terms of market t

about credit repayment _ T

û

with a probability d i s ­t r i b u t i o n of the states dependent on the debtors' actions

* ...

with an exogenously given probability d i s t r i ­bution of the states

Individual credit support decisions theory

Credit p o r t f o l i o decision theory

Capital market equilibrium theory

figure 1

d e b t o r ' s s p e c i f i c r i s k c l a s s s p e c i a l i z e d bank, t h e b o r r o w e r s a c c e p t i n t e r e s t r a t e s t o o h i g h i n r e l a t i o n t o t h e i r s t a n d i n g . The c o s t s o f s e a r c h i n g a r e d i f f i c u l t t o s p e c i f y and t h u s one h a r d l y e x p e c t p r e ­s c r i p t i v e s t a t e m e n t s of t h i s a p p r o a c h . B u t i t i s a c o n v i n c i n g i d e a to e x p l a i n i n t e r e s t d i s p e r s i o n w i t h the p r e v e n t i o n o f s e a r c h i n g c o s t s .

U n t i l now we d i d n o t s p e c i f y M i l d e ' s d e f i n i t i o n o f ' s e c u r e d d e b t ' . I n h i s model the d e b t o r pays h i s l o a n back w i t h t h e p r o c e e d s X ( s ) o f t h e i n v e s t m e n t p r o j e c t , and, under c e r t a i n c i r c u m s t a n c e s w i t h t h e l i q u i d a t i o n p r o c e e d s Y(s) o f t h e c o l l a t e r a l . X ( s ) and Y ( s ) a r e random numbers w h i c h a r e dependent on t h e s t a t e of the w o r l d s. I f K i s t h e amount of the c r e d i t , and r i s t h e l o a n ' s i n t e r e s t r a t e a t t h e end o f t h e p e r i o d , t h e bank w i l l g e t :

Z = mint (1 + r) K , X(s) + Y(s) ]

I f t h e r e i s no doubt about the b o r r o w e r ' s w i l l i n g t o r e p a y the c r e ­d i t , each a s s e t of the d e b t o r i s l i a b l e t o t h e bank even w i t h o u t a c l a i m on a c o l l a t e r a l s e c u r i t y , and t h e r e f o r e t h e bank w i l l n o t need a c o l l a t e r a l Y t o s e c u r e t h e d e b t c l a i m . S e c u r i t i e s i n M i l d e ' s a p p r o a c h d e f i n e the f i r m ' s l e v e l o f s o l v e n c y , w h i c h i s measured by the amount of n e t p r o p e r t y b e f o r e c r e d i t s u p p o r t .

T h e r e f o r e t h e r e s u l t s o f the model do n o t r e f e r t o the c o l l a t e r a l p o l i c y o f the bank, b u t t o the bank's s o l v e n c y p o l i c y s p e c i f y i n g t h e minimum s o l v e n c y r e q u i r e m e n t s f o r the c u s t o m e r . A s i m i l a r argumenta­t i o n can be shown to h o l d f o r the d e f i n i t i o n o f s e c u r e d d e b t i n t h e

138

c r e d i t r a t i o n i n g a p p r o a c h o f S t i g l i t z and Weiss (198 1 ) .

1.3 C r e d i t S u p p o r t D e c i s i o n s w i t h E v e n t U n c e r t a i n t y

We a l r e a d y m e n t i o n e d t h a t comprehending m a r k e t u n c e r t a i n t y i s the e x c e p t i o n o f the r u l e i n c r e d i t s u p p o r t t h e o r y . U s u a l l y one r e g a r d s e v e n t u n c e r t a i n t y , where an u n c e r t a i n t y a b o u t t h e f u t u r e s t a t e s i s assumed w h i c h d e t e r m i n e the repayment o f t h e c r e d i t . D e c i s i o n t h e o r y d i s t i n g u i s h e s between the r i s k s i t u a t i o n , where t h e f u t u r e s t a t e s o f the w o r l d w i l l o c c u r w i t h s p e c i f i e d g i v e n p r o b a b i l i t i e s , and t h e gam b l i n g s i t u a t i o n , where t h e s t a t e s a r e t h e v a r i o u s a c t i n g p o s s i b i ­l i t i e s o f the opponent.

I t t he s t a t e s o f the w o r l d o c c u r i n d e p e n d e n t l y o f t h e b o r r o w e r ' s be­h a v i o r , t h e n the r i s k o f the c r e d i t p o s i t i o n i s t o be seen as t h e r i s k on t h e l a c k i n g c r e d i t s t a n d i n g o f the d e b t o r . I f t h e s t a t e s depend on t h e a c t i n g p o s s i b i l i t i e s o f the d e b t o r , t h e n the c r e d i t r i s k i s a c r e d i t r e l i a b i l i t y r i s k . B u t one s h o u l d assume t h a t c r e d i t s t a n d i n g and c r e d i t r e l i a b i l i t y r i s k do n o t o c c u r i s o l a t e d b u t i n c o m b i n a t i o n .

The most e l a b o r a t e d n e o c l a s s i c a l a p p r o a c h o f the c r e d i t s u p p o r t t h e o r y c o n s i d e r s the r i s k o f a d e c r e a s i n g c r e d i t s t a n d i n g o f the bor r o w e r e x c l u s i v e l y . We w i l l d i s c u s s the main models o f the neo­c l a s s i c a l a p p r o a c h i n the n e x t s e c t i o n .

2. N e o c l a s s i c a l Theory and Se c u r e d Debt

2.1 The B a s i c A p p r o a c h

T h i s t h e o r y assumes t h a t a bank d e c i d e s about an i n d i v i d u a l c r e d i t s u p p o r t a t the time the customer a s k s f o r t h i s l o a n . Each c r e d i t d e c i s i o n i s made e x c l u s i v e l y w i t h o u t c o n s i d e r i n g t he t o t a l c r e d i t engagement o f the bank. The need o f an i n d i v i d u a l d e c i s i o n i s c a u s e d i n d e f a u l t o f i n f o r m a t i o n a b o u t the f u t u r e c r e d i t demand, and by t h e o r g a n i z a t i o n o f d e c e n t r a l i z e d bank d e c i s i o n s , w h i c h i s c h a r a c t e r i s t i c f o r b r a n c h bank systems (Rudolph 1974).

The bank's d e c i s i o n s about c r e d i t s u p p o r t s depend on t h e n e t p r o f i t o f t h e c r e d i t p o s i t i o n s . L e t us d e f i n e K as t h e demanded l o a n amount, and r as the i n t e r e s t r a t e . F u r t h e r o n i i s the i n t e r e s t r a t e t he bank has t o pay f o r t h e r e f i n a n c e m e n t o f i t s c r e d i t s u p p o r t . Thus the mean o f the i n t e r e s t e x c e s s G o f a c r e d i t p o s i t i o n w i l l be

139

E (G) = (l + r ) K a ( r , K ) - ( l + i ) K ,

where a i s t h e mean c r e d i t repayment q u o t a . F o r a =1 t h e bank e x p e c t s t h e repayment a t the end o f t h e p e r i o d w i t h c e r t a i n t y , f o r a <1 t h e bank e x p e c t s w i t h a c e r t a i n p r o b a b i l i t y w h i c h among o t h e r s depends on t h e i n t e r e s t r a t e r and on t h e c r e d i t amount K t h a t t h e c r e d i t w i l l n o t be p a i d back i n t h e whole amount.

G i v e n t h i s v e r y e a s y a p p r o a c h , one can s p e c i f y c o l l a t e r a l as an i n ­s t r u m e n t t o r a i s e the mean repayment q u o t a a . B u t n o t i c e t h a t s u c h a r e d u c t i o n of the c r e d i t f a i l m e n t i s o n l y i m a g i n a b l e i f s e v e r a l c r e ­d i t o r s s h a r e t h e chances and t h e r i s k o f the d e b t o r ' s a s s e t s . O n l y t h e n i t i s p o s s i b l e f o r one c r e d i t o r t o s h i f t r i s k t o t h e o t h e r s , i f h i s i n d i v i d u a l d e b t c o n t r a c t c o n t a i n s c o l l a t e r a l c o v e n a n t s . I f t h e bank i s t h e s o l e c r e d i t o r t he d e b t o r ' s t o t a l p r o p e r t y i s l i a b l e and an a d d i t i o n a l c o l l a t e r a l agreement c a n ' t improve the c r e d i t o r ' s p o s i t i o n .

C o n c e r n i n g c r e d i t c o l l a t e r a l p o l i c y we do n o t g e t new f u n d a m e n t a l r e s u l t s o f t h e t h e o r y o f c r e d i t p o r t f o l i o d e c i s i o n s e x c e p t t h e now n e c e s s a r y c o n s i d e r a t i o n o f the c o r r e l a t i o n o f e x p e c t e d f u t u r e v a l u e s o f the c o l l a t e r a l s e c u r i t y w i t h t h e e x p e c t e d f u t u r e v a l u e s o f t h e f i r m ' s t o t a l a s s e t s .

2 . 2 S e c u r e d Debt and C a p i t a l M a r k e t E q u i l i b r i u m

The t h e o r y o f c a p i t a l market e q u i l i b r i u m i n v e s t i g a t e s among o t h e r s whether a s h i f t o f d e f a u l t r i s k s f r o m one c r e d i t o r t o o t h e r c r e d i ­t o r s can cause any advantages f o r t h e d e b t o r . I n a c o r p o r a t i o n w i t h o u t s t a n d i n g d e b t t h e s e a d v a n t a g e s w o u l d r e s u l t i n a r i s e o f the market v a l u e o f the de b t and t h e r e f o r e i n an i n c r e a s e d m a rket v a l u e o f the f i r m .

I f t he c r e d i t o r s a c t r a t i o n a l l y and on t h e p r e s u m p t i o n s u s u a l l y summarized f o r the a s s u m p t i o n o f a p e r f e c t c a p i t a l market one can show t h a t t he c o l l a t e r a l p o l i c y o f a l e v e r e d f i r m i s i r r e l e v a n t f o r i t s market v a l u e . One c o u l d c a l l t h i s s t a t e m e n t a n a l o g o u s t o the i r r e l e v a n c e h y p o t h e s i s o f M o d i g l i a n i and M i l l e r (1958) the c o l l a t e r a l i r r e l e v a n c e h y p o t h e s i s : G i v e n p e r f e c t c a p i t a l m a r k e t s p o s s i b l e r i s k d i f f e r e n c e s between c r e d i t p o s i t i o n s a r e f u l l y r e f l e c t e d i n t h e i r market v a l u e s w i t h t he consequence t h a t r i s k t r a n s f e r s between c r e ­d i t o r s w i l l cause an a l t o g e t h e r e q u a l l y h i g h t o t a l m a r k e t v a l u e o f the o u t s t a n d i n g d e b t .

140

T h i s r e s u l t o f c a p i t a l market e q u i l i b r i u m t h e o r y (which w i l l be pr o v e d i n a more g e n e r a l way i n t h e a p p e n d i x ) c a n be e x p l a i n e d by a s i m p l e example. To t h a t end we i n s p e c t a company w i t h t he i n v e s t e d c a p i t a l c o n t a i n i n g o n l y two a s s e t s . A t the end o f t h e p e r i o d t h e l i ­q u i d a t i o n p r o c e e d s o f t h e two a s s e t s X and Y w i l l depend on t h r e e s t a t e s o f t h e w o r l d S i , s 2 and s 3 . The c o n t i n g e n t p r o c e e d s a r e shown i n t a b l e 1.

The f i r m i n c u r s d e b t from bank A and bank B and has t o redeem the amount o f T^=55 and T ß = 5 5 a t the end o f the p e r i o d . P r e ­sumed the d e f a u l t f r e e i n t e r e s t r a t e i s 10 % and t h e market i s r i s k n e u t r a l so t h a t t h e p r e s e n t market v a l u e o f f i n a n c i a l c l a i m s i s t h e d i s c o u n t e d mean, t h e d e b t c l a i m s o f bank A and B b o t h have t h e v a l u e :

F A = F B = 2 - Î . l [ 0 - 3 -88 + 0 . 7 • n o ] = 47

state S 3 mean liquidation ^ probability 0 .3 0 .4 0 . 3

proceeds

X 60 60 60 60

Y 28 105 72 72

X + Y 88 165 132 132

table 1

The v a l u e o f the e q u i t y o f the f i r m amounts t o

E [0 .4 • 55 + 0 . 3 • 22] = 26

and t h e t o t a l v a l u e o f the f i r m i s

W = F + F + E = 120 . A B

C o n s i d e r now bank A i n s i s t i n g on a c o l l a t e r a l t o s e c u r e i t s c r e d i t . The d e b t c o n t r a c t i s s e c u r e d i f the f i r m p l e d g e s t he a s s e t X o r Y or b o t h a s s e t s t o the bank w i t h the p r o v i s i o n t h a t s h o u l d t he f i r m d e f a u l t t h e bank has t h e r i g h t t o s e i z e and s e l l t h e c o l l a t e r a l i z e d a s s e t . S h o u l d t he p r o c e e d s from the s a l e e x c eed t h e o u t s t a n d i n g amount, t h e e x c e s s i s r e t u r n e d t o t h e f i r m . I f t h e p r o c e e d s a r e i n ­s u f f i c i e n t t o meet the o u t s t a n d i n g amount, the bank r e t a i n s a l l o f the p r o c e e d s and becomes an u n s e c u r e d c r e d i t o r f o r t h e r e m a i n i n g d e b t .

141

Assume the f i r m o f f e r s the a s s e t w i t h the l i q u i d a t i o n p r o c e e d s X as a s e c u r i t y t o the bank A . Because X = 60 f o r a l l s t a t e s t h e c r e d i t p o s i t i o n o f A i s r i s k l e s s and the v a l u e o f c l a i m A now i s

Because o f Bank A's e x p l o i t a t i o n r i g h t on t h e s e c u r i t y the p a y i n g s c h e d u l e f o r bank B changes i n t h e s t a t e S i and B's c l a i m now has a v a l u e o f

F = "7~~~7" (0 .3 • 33 + 0 . 7 • 55) = 44 . B 1.1

The v a l u e o f t h e t o t a l d e b t , w h i c h i s F = 47 + 47 = 94 w i t h o u t c o l l a ­t e r a l , does n o t change w i t h s e c u r i n g t h e d e b t p o s i t i o n o f bank A . The c l a i m A's v a l u e g a i n s 3 u n i t s , b u t t h i s r i s e i s e x a c t l y compen­s a t e d f o r by t h e 3 u n i t s d e c r e a s e o f t h e v a l u e o f c l a i m B .

2.3 C o l l a t e r a l P o l i c y and N o n - M a r k e t - V a l u e Debt C l a i m s

C o n t r a r y t o the j u s t d i s c u s s e d c o l l a t e r a l i r r e l e v a n c e h y p o t h e s i s S c o t t (1977) has shown t h a t a f i r m c an m aximize i t s v a l u e when i t uses a l l i t s a s s e t s as c o l l a t e r a l f o r t h e c r e d i t o r s . S c o t t i s a r g u ­i n g t h a t i n the c a s e o f the d e b t o r ' s d e f a u l t some d e b t has t o be p a i d b e f o r e d i s t r i b u t i n g the b a n k r u p t c y e s t a t e t o the c r e d i t o r s . These c o s t s a r e e s p e c i a l l y s a l e s t a x e s , p r o p e r t y t a x e s , e x c i s e t a x e s , the a d m i n i s t r a t i v e c o s t s o f b a n k r u p t c y and l e g a l damages c l a i m s . T y p i c a l l y , t h e s e c l a i m s have t o be p a i d o n l y under c e r t a i n c i r c u m ­s t a n c e s and t h e y a r e not c o n s i d e r e d i n t h e c a l c u l a t i o n o f the v a l u e o f the d e b t . T h e r e f o r e they do n o t i n c u r t h e v a l u e o f the f i r m . Thus, i f a l l the d e b t o r ' s a s s e t s a r e t r a n s f e r r e d as c o l l a t e r a l t o the c r e ­d i t o r s w i t h c l a i m s t r a d e d on t h e c a p i t a l m a r k e t , t h e y o u t r a n k t h e mentioned non-market v a l u e d c l a i m s i n c a s e o f d e f a u l t . The market v a l u e o f the f i r m r e a c h e s i t s maximum when t h e c l a i m s w i t h l a c k i n g market v a l u e s have the l o w e s t p r i o r i t y compared t o t h e c l a i m s o f the market p a r t i c i p a n t s .

One can e a s i l y c o n f i r m t h i s r e s u l t w i t h t h e h e l p o f t h e f o r m e r example. Look a g a i n a t t a b l e 1 t o see t h e d i s t r i b u t i o n o f the v a l u e o f the f i r m ' s s e c u r i t i e s . B e s i d e t h e p a y a b l e d e b t of T^=55 and T D = 55 c o n s i d e r now a l s o some t a x c o s t s o f U = 33 , w h i c h have t o be p a i d i n d e p e n d e n t of the s t a t e o f t h e w o r l d i n t = 1 . I t i s assumed t h a t i n a d e f a u l t o f the f i r m the t a x c o s t s o u t r a n k the c l a i m s T. and T 0 .

142

Presumed f u r t h e r o n a d e f a u l t f r e e i n t e r e s t r a t e o f 10 % and a r i s k n e u t r a l c a p i t a l m a r k e t , t h e v a l u e o f the d e b t c l a i m s i s

F r F B = 2 T T t o * 3 ( 8 S " 3 3 ) + 0 * 4 " 1 1 0 + 0 - 3 ( 1 3 2 - 3 3 ) J = 4 1

and t h e market v a l u e o f e q u i t y i s

E = T T 4 ( 1 6 5 " 1 1 0 ~ 3 3 )] = 8 • Thus t h e market v a l u e o f the f i r m amounts t o

w = F + F +E = 90 . A B

In a f i r s t s t e p we w i l l now s e c u r e the d e b t o f bank A w i t h the l i q u i d a t i o n p r o c e e d s X , t h e n i n a d d i t i o n we w i l l a l s o s e c u r e t h e de b t o f bank B w i t h t h e l i q u i d a t i o n p r o c e e d s o f Y t o o b s e r v e the a l t e r i n g o f the f i r m v a l u e when d i f f e r e n t s e c u r i n g s t r a t e g i e s a r e a p p l i e d .

I f bank A g e t s t i t l e on the a s s e t w i t h the l i q u i d a t i o n p r o c e e d s X , i t s c r e d i t p o s i t i o n i s r i s k l e s s and t h e m a r k e t v a l u e has the amount o f

F = - 50 . A 1.1

Bank B has t o c o n s i d e r t h a t i n s t a t e s s i and S 3 t a x c o s t s have a h i g h e r p r i o r i t y and the v a l u e o f i t s c l a i m t h u s w i l l be o n l y

F = — [ 0 . 4 • 55 + 0.3 • 44] = 32 . B 1.1

The c o l l a t e r i z a t i o n o f bank A does n o t change t h e t o t a l m a r k e t v a l u e of t h e d e b t F - 8 2 because the r i s k t r a n s f e r f u l l y d i m i n i s h e s the c l a i m of bank B : the t a x c o s t s 'J = 33 o u t r a n k c l a i m B i n the c a s e o f d e f a u l t .

But i f the c l a i m of bank B i s s e c u r e d by e x p l o i t a t i o n r i g h t s o f the l i q u i d a t i o n s p r o c e e d s Y ( w h i l e bank A keeps i t s c o l l a t e r a l ) , the market v a l u e o f d e b t F w i l l r i s e . I n t h i s c a s e =50 a g a i n , b u t bank B r e c e i v e s t h e l i q u i d a t i o n p r o c e e d s Y i n the s t a t e s s i and s 3 b e f o r e t h e t a x c o s t s a r e p a i d and t h i s w i l l i n c r e a s e t h e v a l u e o f i t s c l a i m t o

F =7^-r [0.3 • 28 + 0.7 • 55] = 42.64 . B 1.1

I f bank B would have a l s o a s u b o r d i n a t e e x p l o i t a t i o n r i g h t on t h e c o l l a t e r a l o f bank A , i t c o u l d o b t a i n a 5 u n i t r a i s e d l i q u i d a t i o n p r o f i t i n t h e s t a t e s i , and t h e d e b t v a l u e w o u ld be:

F o = - i — [0.3 • 33 + 0.7 • 55] = 44 . B 1.1

143

The j u s t d e s c r i b e d c o l l a t e r a l p o l i c y can c r e a t e t h e maximum v a l u e o f the d e b t F =94 because t h e c r e d i t o r s A and B a r e a b l e t o s h i f t t h e utmost r i s k on the c l a i m U w h i c h does n o t p o s s e s s a market v a l u e .

3. The Theory o f C r e d i t S u p p o r t D e c i s i o n s i n t h e L i g h t of the Economics o f I n f o r m a t i o n

3.1 C o l l a t e r a l s as a T o o l t o L i m i t t h e C r e d i t a b i l i t y R i s k

Our p r e v i o u s c o n s i d e r a t i o n s about c o l l a t e r a l p o l i c y i n the scope of the n e o c l a s s i c a l t h e o r y o f c r e d i t s u p p o r t d e c i s i o n s f o c u s i n -the f o l l o w i n g r e s u l t s o f the t h e o r y o f t h e c r e d i t market e q u i l i b r i u m :

• On a p e r f e c t and co m p l e t e c a p i t a l m arket the c o l l a t e r a l p o l i c y o f a f i r m i s i r r e l e v a n t f o r i t s m a r k e t v a l u e ( c o l l a t e r a l i r r e ­l e v a n c e h y p o t h e s i s ) .

• C o n s i d e r i n g i n s u f f i c i e n c i e s o f t h e c a p i t a l m a r ket, i . e . market exogenous c l a i m s on the c o r p o r a t e ' s s e c u r i t i e s , a c o l l a t e r a l p o l i c y s h i f t i n g t he utmost r i s k from the market c r e d i t o r s t o the non-market c r e d i t o r s w i l l c a u s e the maximum market v a l u e o f the f i r m ( f u l l y c o l l a t e r a l p o l i c y ) .

We a r e not s a t i s f i e d w i t h t h e s e r e s u l t s o f t h e n e o c l a s s i c a l t h e o r y : A l t h o u g h s e c u r i n g d e b t c a u s e s h i g h p r i v a t e and p u b l i c c o s t s (moni­t o r i n g c o s t s , c o n t r a c t c o s t s , a d m i n i s t r a t i v e c o s t s , law c o s t s e t c . ) t h i s i n s t r u m e n t i s s t i l l o f g r e a t i m p o r t a n c e on r e a l f i n a n c i a l mar­k e t s . The n e o c l a s s i c a l t h e o r y can e x p l a i n t h i s d i s c r e p a n c y o n l y w i t h the t o t a l c o l l a t e r a l p o l i c y . B u t on r e a l c a p i t a l markets f u l l c o l l a -t e r i z a t i o n i s r a t h e r t h e e x c e p t i o n t h a n t h e r u l e .

On the o t h e r hand i t i s n o t u n u s u a l t h a t d e b t c o n t r a c t s i m p l y c o l l a ­t e r a l - a g r e e m e n t s even i f the c o v e n a n t e e p r e s u m p t i v e l y i s and remains the s o l e c r e d i t o r , so t h a t i n t h i s c a s e a r i s k t r a n s f e r t o o t h e r c r e d i t o r s i s o f no i m p o r t a n c e b e c a u s e s e c u r e d and u n s e c u r e d c r e d i t p o s i t i o n s a r e e q u i v a l e n t .

I n c l u d i n g t h e r e a s o n i n g o f the economics o f i n f o r m a t i o n i n the neo­c l a s s i c a l t h e o r y o f c r e d i t s u p p o r t d e c i s i o n s w i l l d i s c l o s e us a t h e o r e t i c a l base t o e x p l a i n t h e p r a c t i c e of c o l l a t e r a l i z a t i o n i n c r e d i t o r / d e b t o r r e l a t i o n s . B u t n o t i c e t h a t t h e i d e a s o f the econo­mics o f i n f o r m a t i o n a r e t o c o m p l e t e o u r p r e v i o u s t h o u g h t s i n such a way t h a t d e c i d i n g about c r e d i t s u p p o r t the bank has t o c o n s i d e r

144

the r i s k o f c r e d i t s t a n d i n g and o f c r e d i t r e l i a b i l i t y combined.

To c o n c r e t e t h e i d e a o f t h e economics o f i n f o r m a t i o n i n t h i s c o n t e x t i t i s u s e f u l t o i n v e s t i g a t e i n the f i r s t s t a g e t h e i s o l a t e d r i s k o f c r e d i t r e l i a b i l i t y . I t w i l l be shown t h a t c o l l a t e r a l can bound o r even e l i m i n a t e t h a t r i s k . I n the n e x t s e c t i o n we w i l l examine the s i t u a t i o n where b o t h r i s k s have t o be c o n s i d e r e d c o n j o i n t l y .

The w e l l known model o f J a f f e e and R u s s e l l (1976) i s a f i r s t a p p r o a c h t o i n v e s t i g a t e t h e i s o l a t e d r i s k o f c r e d i t r e l i a b i l i t y . The t o p i c o f t h e model i s the phenomenon o f c r e d i t r a t i o n i n g : " C r e d i t r a t i o n i n g o c c u r s when l e n d e r s q u o t e an i n t e r e s t r a t e on l o a n s and t h e n p r o c e e d t o s u p p l y a s m a l l e r l o a n s i z e t h a n t h a t demanded by th e b o r r o w e r s " .

The n e o c l a s s i c a l s o l u t i o n of t h i s gap p r o p o s e s t h a t t h e u n s a t i s f i e d b o r r o w e r s w i l l o f f e r a h i g h e r i n t e r e s t r a t e , w h i c h w i l l m o t i v a t e the bank t o r i s e t h e l o a n s u p p l y f o r an i n c r e a s e d r i s k premium; t h i s p r o c e s s f i n a l l y w i l l end when c r e d i t s u p p l y and demand a r e i n e q u i ­l i b r i u m a t a c e r t a i n i n t e r e s t r a t e .

C r e d i t r a t i o n i n g i s an i n s t r u m e n t o f t h e banks t o i n f l u e n c e the a v e r a g e s o l i d i t y o f t h e i r c u s t o m e r s h i p . A d e c r e a s e o f t h e mean c r e ­d i t s u p p l y can r e d u c e the number o f " d i s h o n e s t " d e b t o r s , because the i n c e n t i v e t o b r e a c h the c o n t r a c t i s s m a l l e r i f i t i s â p a l t r y c r e d i t amount. T h e r e f o r e c r e d i t r e l i a b i l i t y i s n o t a permanent ( f i x e d ) un­c h a n g e a b l e c o n d i t i o n o f the b o r r o w e r , b u t a consequence of an econo­m i c a l r e a s o n i n g .

The b o r r o w e r w i l l f u l f i l l the c o n t r a c t ( i . e . r e p a y the l o a n ) i f i t i s e c o n o m i c a l advantageous and on the o t h e r s i d e he w i l l b r e a c h the c o n t r a c t i f t h i s b e h a v i o r i s p r o f i t a b l e . Through i t s d e b t - p o l i c y t h e bank can i n f l u e n c e the l u c r a t i v e n e s s o f repayment f o r t h e d e b t o r . I f n o t p a y i n g i n v o l v e s c e r t a i n c o s t s f o r the b o r r o w e r ( c o s t t o d e f a u l t ) t h e bank ca n r e d u c e the numbers o f b o r r o w e r s w h i c h have an a d v a n t a g e i f t h e y f a i l t o r e p a y . These c o s t s a r e g i v e n e x o g e n o u s l y i n t h e J a f f e e and R u s s e l l model, whereas the e x o g e n o u s l y g i v e n amount can be d i f f e r e n t f o r each b o r r o w e r .

I n c o n t r a s t t o t h i s a s s u m p t i o n o f an exogenous c o s t f a c t o r R u d o l p h (1982) showed the a b i l i t y o f the banks to i n f l u e n c e t h e c o s t o f de­f a u l t . Banks c o u l d e s p e c i a l l y i n c r e a s e t h e s e c o s t s i f t h e y e n c l o s e c o l l a t e r a l c o n v e n a n t s i n l o a n c o n t r a c t s so t h a t i n c a s e o f t h e

145

b o r r o w e r ' s nonpayment he w i l l l o s e p a r t o f h i s s e c u r i t i e s t o the bank. C o l l a t e r a l s t h e r e f o r e can i n c r e a s e the p r o b a b i l i t y o f r e p a y ­ment.

W i t h t h e i n c l u s i o n o f c o l l a t e r a l i n t h e model o f J a f f e e and R u s s e l l one g e t s a common p r i c e e q u i l i b r i u m i n s t e a d o f t h e r a t i o n i n g e q u i l i ­b r i u m , because w i t h a g i v e n c r e d i t s t a n d i n g o f the b o r r o w e r the r e ­payment o f th e l o a n i s o n l y a q u e s t i o n of t h e d e b t o r ' s w i l l .

S i n c e the a s s u m p t i o n of a g i v e n c r e d i t s t a n d i n g i s n o t r e a l i s t i c , we have t o examine i n t h e n e x t s e c t i o n t h e d e c i s i o n s o f a bank i n th e f a c e o f a c r e d i t s t a n d i n g r i s k and a c r e d i t r e l i a b i l i t y r i s k . We w i l l d i s c u s s the p roblems of t h i s s i t u a t i o n w i t h t h e h e l p o f o u r f o r m e r n u m e r i c a l example.

3.2 Contemporaneous E x a m i n a t i o n o f C r e d i t S t a n d i n g R i s k and C r e d i t R e l i a b i l i t y R i s k

L e t us t a k e a g a i n t h e p r o b a b i l i t y d i s t r i b u t i o n s o f X and Y , as shown i n t a b l e 1 t o d e m o n s t r a t e the s i m u l t a n e o u s a n a l y s i s o f t h e c r e d i t - s t a n d i n g and c r e d i t - r e l i a b i l i t y r i s k o f a f i r m . The d i s t r i ­b u t i o n s d e t e r m i n e the d e b t o r ' s c r e d i t s t a n d i n g f o r g i v e n l o a n quan­t i t i e s .

The c r e d i t r e l i a b i l i t y r i s k on t h e o t h e r hand i s t o be s een i n t h e f a c t t h a t the c r e d i t o r does n o t know whether the f i r m w i l l keep the a s s e t s w i t h the l i q u i d a t i o n p r o c e e d s X and Y u n t i l the end o f the p e r i o d t o s e r v e the bank's r e c e i v a b l e s o r i f t h e f i r m s e l l s t h e a s s e t s and d i s p o s e s o f the p r o c e e d s i n a n o t h e r way. C r e d i t o r s a r e f a c e d w i t h u n c e r t a i n e x p e c t a t i o n s w h i c h o f t h e a l t e r n a t i v e l y p o s s i b l e p l a n s o f the f i r m w i l l be r e a l i z e d a f t e r the c r e d i t i s p l a c e d a t t h e f i r m ' s d i s p o s i t i o n .

Swoboda (1975) c a l l s t h e s e r i s k s as d i s t r i b u t i o n r i s k s : " W e ' l l c a l l t he r i s k t h a t a p o s i t i o n o f a c r e d i t o r a l t e r s c a u s e d by s u b s e q u e n t d e c i s i o n s o f the f i r m d i s t r i b u t i o n r i s k " (as e.g. i s s u i n g a d d i t i o n a l d ebt w h i c h w i l l d i l u t e the c l a i m o f t h e o r i g i n a l c r e d i t o r ) . L a t e r on s e v e r a l a r t i c l e s o f the f i n a n c i a l l i t e r a t u r e f o c u s e d on t h i s p r o b l e m and summarized the main p o s t - c r e d i t s t r a t e g i e s o f d e b t o r s (Smith and Warner 1979b,Smith 1980). We w i l l d i s c u s s t h e s e s t r a t e g i e s b a s e d on t h e n u m e r i c a l example of t a b l e 1 and examine whether c r e d i t o r s c o u l d d i m i n i s h the d i s t r i b u t i o n r i s k w i t h the h e l p o f c o l l a t e r a l .

146

3.2.1 Changing the D i v i d e n d P o l i c y

A f t e r t h e i s s u e o f the c r e d i t , the f i r m can r a i s e i t s d i v i d e n d r a t e , i n s p i t e o f a f o r m e r d e c l a r e d l o w e r r a t e , and t h u s i n c r e a s e t h e de­f a u l t r i s k f o r t h e c r e d i t o r s . The d i v i d e n d payments ca n be f i n a n c e d by r e d u c e d i n v e s t m e n t ( b a l a n c e s h e e t c u t ) o r f i n a n c e d by i s s u i n g a d d i t i o n a l d e b t (change o f l i a b i l i t i e s ) .

D i v i d e n d payments evoke a h i g h e r r i s k f o r t h e i n i t i a l c r e d i t o r , be­c a u s e l i a b l e c a p i t a l ( e q u i t y ) i s s u b s t i t u t e d by u n l i a b l e c a p i t a l ( d e b t ) .

L e t us c o n s i d e r t h e f i r m o f our example a d d i n g a new l o a n w i t h a r e c e i v a b l e of T c = 22 i n t = 1 t o i t s s e n i o r d e b t ( w i t h r e c e i v a b l e s o f T A = 5 5 and T ß = 55 ) .

A f t e r the a d d i t i o n a l l o a n i s i s s u e d , the m a rket v a l u e o f t h e whole d e b t w i l l be

F = (0 .3 • 88 + 0 . 7 . 132) = 108

compared t o 9 4 b e f o r e t h e j u n i o r d e b t . The c o r r e s p o n d i n g e q u i t y v a l u e s a r e 1 20 - 108 = 1 2 ( w i t h new debt) and 26 ( b e f o r e new d e b t ) . The d e b t v a l u e g a i n e d 14 u n i t i e s , w h i l e the e q u i t y v a l u e l o s t t h e s e 14 u n i t i e s . S i n c e t h e market v a l u e o f Bank C's c l a i m i s :

F c = i l r 1 0 8 = 1 8 ' t h e f i r m d i d n o t g e t 14 b u t 18 u n i t i e s by r a i s i n g t h e a d d i t i o n a l l o a n .

S i n c e the t r a n s a c t i o n changed the v a l u e s o f bank A 1 s and bank B's c l a i m s from 47 t o 45, the l o a n q u a n t i t y s h o u l d be d i v i d e d i n such a manner, t h a t the c a p i t a l owner would g e t 14 u n i t i e s and each o f the banks A and B would g e t 2 u n i t i e s . T h i s d i s t r i b u t i o n would keep t h e o l d market v a l u e r e l a t i o n o f the d e b t / e q u i t y c l a i m s . B u t d i s t r i ­b u t i n g the whole l o a n amount o f 18 t o the c a p i t a l owners, the s t o c k ­h o l d e r ' s w e a l t h i s i n c r e a s e d t o the d e t r i m e n t o f t h e o r i g i n a l c r e ­d i t o r s .

A w e a l t h - s h i f t i n g on a c c o u n t o f the c r e d i t o r s c a u s e d by a c r e d i t f i n a n c e d d i v i d e n d payment can be l i m i t e d ( i n s p e c i a l c a s e s even e l i m i n a t e d ) i f t h e d e b t o f t h e i n i t i a l c r e d i t o r s i s s e c u r e d .

L e t us c o n s i d e r t h e c a s e t h a t c r e d i t o r s A and B have p r o p e r t y r i g h t s ( c l a i m s ) o f the f i r m ' s a s s e t s , w h i c h a r e u n i t e d i n a s e -

147

c u r i t y p o o l and c o n s i s t o f the l i q u i d a t i o n p r o c e e d s X and Y . Under t h e s e a s s u m p t i o n s the market v a l u e o f t h e t o t a l d e b t and t h e v a l u e o f the u n s e c u r e d d e b t a r e c o r r e s p o n d i n g as d e m o n s t r a t e d i n s e c t i o n 2.2, and F = 47 + 47 = 94 .

I f the s e n i o r d e b t i s f u l l y s e c u r e d and the f i r m i s s u e s j u n i o r d e b t w i t h the p r i n c i p a l o f T c = 22 , i t s v a l u e w i l l be:

I f t h e f i r m g e t s t h e d i s p o s a l o f t h i s l o a n q u a n t i t y and pays i t i n s t a n t l y t o the e q u i t y owners, t h e c l a i m s o f t h e c r e d i t o r s A and B a r e n o t d i l u t e d . S i n c e t h e i r d e b t i s s e c u r e d , t h e y a r e p r o t e c t e d a g a i n s t d i s t r i b u t i o n r i s k s c a used by c r e d i t f i n a n c e d d i v i d e n d pay­ments t o t h e e q u i t y owners.

As f a r as i t concerns d i v i d e n d payments by d e s i n v e s t m e n t ( b a l a n c e s h e e t c u t ) , t h e y too can be p r e v e n t e d by s e c u r i n g the d e b t . S e c u r e d d e b t g i v e s the c r e d i t o r the e x p l o i t a t i o n r i g h t on the s e c u r i t y such t h a t the management o f t h e f i r m c a n n o t a r b i t r a r i l y d i s p o s e of t h e a s s e t . T h e r e f o r e t h e p o s s i b i l i t y o f a d i v i d e n d payment, f i n a n c e d w i t h p r o c e e d s o f s o l d a s s e t s , i s r e d u c e d .

However, a t o t a l p r e v e n t i o n of d e s i n v e s t m e n t f i n a n c e d payments i s r a t h e r i m p o s s i b l e . C r e d i t o r s would have t o use a l l t h e f i r m ' s a s s e t s as c o l l a t e r a l t o t r a n s f e r the r i g h t t o d i s p o s e o v e r t h e f i r m ' s e s t a t e t o t a l l y f r o m t h e management t o t h e l e n d e r s . S t i l l , by s e c u r ­i n g d e b t , one can i n s t a l l upper bounds f o r d i v i d e n d payments and p r o t e c t t h o s e a s s e t s w h i c h may n o t be s o l d i n o r d e r t o use the p r o ­ceeds f o r d i v i d e n d payments ( r e a l e s t a t e , n o t w o r k i n g a s s e t s ) .

3.2.2 Changing the C r e d i t P o l i c y

The l e v e r e d f i r m c a n r e p a y i t s d e b t t o some c r e d i t o r s p r e mature o r i t can s e c u r e some c r e d i t o r ' s d e b t . B o t h p o l i c i e s a r e d i s a d v a n ­tageous f o r the o t h e r c r e d i t o r s b ecause t h e i r c l a i m s ' v a l u e de­c r e a s e s . I n t h e c a s e o f a pr e m a t u r e repayment a l l t h e r i s k i s t r a n s ­f e r r e d t o t h e r e s i d u a l d e b t , w h i l e i n t h e c a s e of s e c u r e d debt t h e amount o f s h i f t e d r i s k from s e c u r e d t o u n s e c u r e d d e b t depends on the q u a l i t y o f the c o l l a t e r a l . C r e d i t o r s w i t h c o n t r a c t s i n c l u d i n g c o l l a t e r a l c o v e n a n t s u s u a l l y do n o t have t o f e a r t h e s e forms o f the d i s t r i b u t i o n r i s k .

148

3.2.3 C h a n g i n g the I n v e s t m e n t P o l i c y

F i n a l l y the f i r m has a t h i r d o p p o r t u n i t y t o t r a n s f e r r i s k i n v e s t i n g i n p r o j e c t s w i t h h i g h e r r i s k t h a n d e c l a r e d t o the c r e d i t o r s . Such an a l t e r e d i n v e s t m e n t p o l i c y can i n c r e a s e the v a l u e o f e q u i t y , because a l t h o u g h t h e d e f a u l t r i s k r i s e s , the f i r m r e a l i z e s h i g h e r y i e l d s f o r the b e n e f i t o f the s h a r e h o l d e r s i n d e f a u l t - f r e e s t a t e s (Swoboda 1982).

L e t us assume a g a i n a f i r m w i t h two a s s e t s w i t h t h e l i q u i d a t i o n p r o ­ceeds X and Y and i n a d d i t i o n the o p p o r t u n i t y o f t h e f i r m t o keep two o t h e r a s s e t s w i t h t h e l i q u i d a t i o n p r o c e e d s Z and Y i n i t s e s t a t e w i t h o u t any t e c h n i c a l d i f f i c u l t i e s . T a b l e 2 d e s c r i b e s t h e y i e l d s o f t h e a l t e r n a t i v e p l a n s x and z .

Though the mean of the r e c e i p t s d i s t r i b u t i o n i s s i m i l a r f o r p l a n x and z c r e d i t o r s A and B w i t h r e c e i v a b l e s o f T^ = 55 and T ß = 55 have e v e r y r e a s o n t o f e a r the r e a l i z a t i o n o f p l a n z i n s t e a d o f p l a n x . W h i l e t h e v a l u e o f d e b t i s F = 94 and t h e v a l u e o f e q u i t y i s E = 26 i f p l a n x i s c h osen, p l a n z w i l l p r o d u ce an e q u i t y v a l u e o f E** 42,4 and a d e b t v a l u e of o n l y F «77,6 . Thus the f i r m ' s management c a n cause an e s s e n t i a l i n c r e a s e o f the v a l u e o f e q u i t y by p r e f e r r i n g p r o j e c t s w i t h h i g h e r r i s k .

C o l l a t e r a l c a n be seen as a t o o l t o p r e v e n t (or l i m i t ) d i s t r i b u t i o n r i s k , c aused by a change o f i n v e s t m e n t p o l i c y , b e cause the i n v e s t ­ment p o l i c y o f the f i r m would be d e t e r m i n e d i f bank A o r B p u t the s e c u r i t y w i t h t h e y i e l d X i n p l e d g e .

To p r e v e n t an i n v e s t m e n t p o l i c y change, i t would even be s u f f i c i e n t i n t h i s c a s e , t h a t one o f the c r e d i t o r s p u t p l e d g e on a s s e t X . C o n d i t i o n a l o f the g i v e n c r e d i t r e l i a b i l i t y r i s k , s e c u r i n g one bank's d e b t w i l l a l s o improve the u n s e c u r e d c l a i m , because the r a i s e d de­f a u l t r i s k , w h i c h the u n s e c u r e d c r e d i t o r has t o f a c e a f t e r the o t h e r c r e d i t o r s c l a i m , can be more t h a n compensated by t h e r e d u c t i o n o f the c r e d i t r e l i a b i l i t y r i s k .

To p r o v e t h e s e market v a l u e r i s i n g e f f e c t s o f c o l l a t e r a l , we w i l l presume t h a t banks A and B e x p e c t w i t h an a p r i o r i p r o b a b i l i t y o f 5 0 % the r e a l i z a t i o n o f p l a n x o r z . I n t h i s c a s e the d e b t ' s v a l u e w i l l be

F = 0 . 5 . 9 4 + 0 . 5 - 7 7 . 6 = 85 .8

and the v a l u e s o f the c l a i m s A and B are 42.9 f o r each o f the c l a i m s .

149

state Si S2 s 3 mean ^ - ^ ^ probability 0,3 0,4 0,3

li q u i d a t i o n proceeds

X 60 60 60 60 plan x Y 28 105 72 72

X + Y 88 165 132 132

Z 0 105 60 60 plan z Y 28 105 72 72

Z + y 28 210 132 132

table 2

Now A g e t s t h e s e c u r i t y w i t h t h e l i q u i d a t i o n p r o c e e d s X as c o l l a t e r a l w i t h the r e s u l t of a r a i s e d v a l u e o f F =94 c a u s e d by t h e dropped c r e d i t r e l i a b i l i t y r i s k . The c o l l a t e r a l o f A p r o d u c e s a r i s k s h i f t i n g on a c c o u n t o f B and f a v o u r i n g A .

The v a l u e o f the s e c u r e d c l a i m A i s 50 and the v a l u e o f t h e un­s e c u r e d d e b t B i s o n l y 44, t h u s i n s p i t e o f t h e r i s k t r a n s f e r on a c c o u n t o f B the c o l l a t e r a l i z a t i o n i n c r e a s e s B's c l a i m f r o m 42.9 t o 44 .

4. A Scheme o f C r e d i t C o n t r a c t C ovenants

4.1 C r e d i t C o n t r a c t Covenants

The p r e v i o u s s e c t i o n s s h o u l d have made c l e a r t h a t c o l l a t e r a l i z a t i o n c a n cause a r i s k t r a n s f e r between t h e c r e d i t o r s , and c o l l a t e r a l i z a ­t i o n can i n f l u e n c e the b e h a v i o r o f t h e d e b t o r s d u r i n g t h e p e r i o d o f c r e d i t . E s p e c i a l l y , c o l l a t e r a l c a n i n d u c e l e v e r a g e d f i r m s o r o t h e r economic s u b j e c t s t o r u n a d e c e n t d i v i d e n d , c r e d i t , and i n v e s t m e n t p o l i c y .

One can a s c e r t a i n t h a t s e c u r i n g d e b t w i t h p l e d g e d a s s e t s i s a r a t h e r s t r o n g p o l i c y t o i n f l u e n c e the b e h a v i o r o f the e q u i t y owners. C r e d i t m a r k e t s have d e v e l o p e d a l s o o t h e r and weaker i n s t r u m e n t s t o l o w e r the r i s k - s h i f t i n g p o s s i b i l i t i e s o f t h e c o r p o r a t i o n . These s t r a t e ­g i e s a r e documented i n t h e s e v e r a l t y p e s o f c r e d i t c o n t r a c t c o ­v e n a n t s i n f i g u r e 2.

150

C r e d i t c o n t r a c t c o v e n a n t s t o l ower c r e d i t r i s k

r e f e r r i n g t o means o f payment

G u a r a n t e e s S e c u r e d d e b t

G e n e r a l l i e n on o b ­g u a r a n t e e s j e c t s and ( p r i v a t e r i g h t s ( c r e ­

p r o p e r t y d i t on s e ­o f u n ­ c u r i t i e s , l i m i t e d pawnbrok ing) p a r t n e r s , government g u a r a n t e e s )

r e g i s t e r e d mortgage and l a n d c h a r g e

S p e c i a l g u a r a n t e e s ( s u r e t y , c r e d i t -i n s u r a n c e )

p a w n - l i k e r i g h t s ( t r a n s f e r

o f t i t l e s , c e s s i o n , l e a s i n g )

n o t d i r e c t l y r e f e r r i n g t o means o f payment

S p e c i a l d u t i e s o f the d e b t o r

i n f o r m a t i o n d u t i e s

f i n a n c e - p o l i c y d e c l a r a t i o n s (obta inment o f

b a l a n c e s h e e t r a t i o s , me f i r s t r u l e s )

r e a l - p o l i c y d e c l a r a t i o n s (maintenance o b l i g a t i o n s , i n s u r a n c e -o b l i g a t i o n s )

S p e c i a l r i g h t s o f t h e c r e d i t o r

i n f o r m a t i o n r i g h t s

c a l l a b i l i t y -r i g h t s ( c r o s s - d e f a u l t -c l a u s e )

l e g a l a c t i o n r i g h t s ( b i l l o f

e x c h a n g e , r e c e i v a b l e )

f i g u r e 2

C r e d i t c o n t r a c t c o v e n a n t s a r e p r o v i s i o n s i n c l u d e d i n d e b t c o n t r a c t s which e i t h e r endow the c r e d i t o r s w i t h s p e c i a l r i g h t s o r b i n d t h e d e b t o r s t o s p e c i a l o b l i g a t i o n s . These c o v e n a n t s i n c o n t r a s t t o g u a r a n t e e - o r c o l l a t e r a l - a g r e e m e n t s , r e f e r o n l y i n d i r e c t l y t o means o f payment by i n f l u e n c i n g the p r o b a b i l i t y d i s t r i b u t i o n s w h i c h d e t e r ­mine the amount o f repayment o f the d e b t o r .

B e f o r e d i s c u s s i n g t h e c a s e s i n w h i c h the l e n d e r s s h o u l d use the s t r o n g e r o r the weaker p o l i c y t o c o n t r o l the d e b t o r ' s b e h a v i o r , we w i l l g i v e a s h o r t s u r v e y o f the d i f f e r e n t t y p e s o f c o v e n a n t s .

4.2 Covenants R e f e r r i n g I n d i r e c t l y t o Means o f Payment

4.2.1 S p e c i a l O b l i g a t i o n s of the D e b t o r s

S p e c i a l o b l i g a t i o n s a r e d u t i e s w h i c h a r e n o t g e n e r a l l y r e q u e s t e d by the codes o f c i v i l law. A f i r m , f o r example, can be o b l i g e d t o s u p p l y f i n a n c i a l and o t h e r i n f o r m a t i o n f o r t h e c r e d i t p e r i o d . The i n f o r m a -

t i o n a b o u t t h e economic s t a t u s of t h e f i r m can be g e n e r a l ( b a l a n c e s h e e t s , f i n a n c i a l s t a t e m e n t s , r e p o r t s e t c . ) o r r e f e r t o s p e c i a l s i ­t u a t i o n s as changes i n mortgage r i g h t s o r i n management. A d d i t i o n a l ­l y / t h e b o r r o w e r can b i n d h i m s e l f t o o b t a i n c e r t a i n b a l a n c e s h e e t r e l a t i o n s , l i q u i d i t y r a t i o s o r c a p i t a l s t r u c t u r e r e l a t i o n s as l o n g as t h e d e b t i s o u t s t a n d i n g .

Of g r e a t i m p o r t a n c e a r e the so c a l l e d 'me f i r s t ' r u l e s . By i n c l u d i n g a me f i r s t r u l e i n h i s d e b t c o n t r a c t a c r e d i t o r wants t o p r o t e c t h i s p o s i t i o n a g a i n s t d i l u t i o n , w h i c h c a n be evoked i f the f i r m i s s u e s a d d i t i o n a l d e b t . We can d i f f e r between t h r e e t y p e s o f me f i r s t r u l e s

• The d e b t o r can a s s u r e t h a t he w i l l n o t i s s u e d e b t w i t h a h i g h e r p r i o r i t y o r d o i n g so the e x i s t i n g d e b t w i l l be upgraded ( d e p t -p r i o r i t y - e q u a l i t y ) .

• S e c u r e d d e b t i s o f t e n endowed w i t h t h e o b l i g a t i o n of the d e b t o r t h a t the w i l l n o t s e l l , l e a s e o r pawn the s e c u r i t y , w i t h o t h e r words, t h e d e b t o r ' r e s e r v e s ' t h e p l e d g e d a s s e t t o t h e c r e d i t o r .

• The most r e s t r i c t i v e t y p e o f me f i r s t r u l e s b i n d s the d e b t o r n o t t o s e l l , l e a s e o r pawn h i s a s s e t s , n o t t o s e c u r e any o t h e r d e b t , o r i n the extreme ca s e even n o t t o i s s u e any a d d i t i o n a l d e b t a t a l l .

T h i s l a s t t y p e l e a d s us t o a group o f r e s t r i c t i o n s w h i c h b i n d s the d e b t o r t o a s p e c i f i c m a i n t e n a n c e o f t h i s a s s e t s . These o b l i g a t i o n s i n c l u d e f o r example the d u t y t o t r e a t r e a l e s t a t e , machines o r raw m a t e r i a l i n an o r d e r l y manner, o r t o i n s u r e t h e s e i t e m s . A l l t h e s e p r o v i s i o n s i n t e r f e r e w i t h the r e a l - s p h e r e o f t h e f i r m and u s u a l l y g e n e r a t e c o s t s .

4.2.2 S p e c i a l R i g h t s o f the C r e d i t o r s

A c c o r d i n g t o the s p e c i a l d u t i e s o f t h e d e b t o r s we w i l l f i r s t r e f e r t o t he i n f o r m a t i o n r i g h t s of t h e l e n d e r s w h i c h a r e n o t i n s t a l l e d i n c i v i l law. Banks o f t e n i n c l u d e i n t h e i r g e n e r a l c r e d i t r e q u i r e m e n t s t h e r i g h t o f an i n s i g h t i n the economic s i t u a t i o n of the b o r r o w e r a t any time wanted. A n o t h e r r i g h t o f t h e g e n e r a l r e q u i r e m e n t i s t h e c a l l a b i l i t y c l a u s e : the c r e d i t o r can r e q u e s t t h e immediate r e p a y ­ment o f the c r e d i t , i f the d e b t o r does n o t f u l f i l l h i s s p e c i a l ob­l i g a t i o n s .

152

E u r o Bond c o n t r a c t s f o r example o f t e n i n c l u d e t h e so c a l l e d ' c r o s s d e f a u l t c l a u s e ' w h i c h g i v e s t h e c r e d i t o r t h e r i g h t t o c a l l t h e c r e ­d i t i f the d e b t o r f a i l s t o f u l f i l l h i s p a y m e n t - o b l i g a t i o n s punc­t u a l l y t o any o t h e r c r e d i t o r .

The c r e d i t o r s can a l s o be endowed w i t h s p e c i a l r i g h t s t o c a l l i n t h e i r due r e c e i v a b l e s . The c r e d i t o r , whose c l a i m i s b a s e d on a b i l l o f exchange does n o t need t o r e m i n d t h e d e b t o r and has t o t a k e no a c c o u n t o f any terms i f t h e d e b t o r does n o t r e p a y p u n c t u a l l y . The b i l l c r e d i t endows the c r e d i t o r w i t h t h e r i g h t o f t h e b i l l p r o t e s t : t h e c r e d i t o r g e t s a day o f c o u r t h e a r i n g a t an e a r l y d a t e and he g e t s i n t h e d e c l a r a t o r y s u i t an e n f o r c e a b l e t i t l e a g a i n s t t h e b i l l d e b t o r . Thus the b i l l o f exchange f a c i l i t a t e s t h e a c t i o n f o r payment, and t h e r e f o r e endows the b i l l c r e d i t o r w i t h e x t r a r i g h t s compared t o t h e u s u a l c i v i l law r e g u l a t i o n s o f c r e d i t c o n t r a c t s .

4.3 C l a i m s o f C r e d i t o r s w h i c h R e f e r t o Means o f Payment

W h i l e the j u s t d e s c r i b e d c o v e n a n t s r e f e r o n l y i n d i r e c t l y t o means o f payment by i n f l u e n c i n g the p r o b a b i l i t y d i s t r i b u t i o n , we now d i s ­c u s s the c l a i m o f c r e d i t o r s w h i c h do r e f e r t o means o f payment d i ­r e c t l y . T h i s t y p e o f c o v e n a n t s can be d i v i d e d i n c o l l a t e r a l - a g r e e ­ments ( s e c u r e d debt) and i n g u a r a n t e e - a g r e e m e n t s .

S e c u r e d d e b t endows t h e l e n d e r w i t h t h e r i g h t t o s e i z e a p l e d g e d a s s e t o f t h e f i r m ' s e s t a t e i n c a s e o f d e f a u l t and t o s e l l i t . I f a bank f o r example s e c u r e s a c o r p o r a t i o n c r e d i t w i t h t h e s e i z e d depo­s i t o f s e c u r i t i e s o f the f i r m and the c o r p o r a t i o n d e f a u l t s , t h e bank c a n s e l l the s e c u r i t i e s . S h o u l d the p r o c e e d s from the s a l e exceed t h e r e c e i v a b l e s o f the bank, the e x c e s s i s r e t u r n e d t o the d e b t o r o r h i s e s t a t e ; i f the p r o c e e d s a r e i n s u f f i c i e n t , t h e bank r e t a i n s a l l o f the p r o c e e d s and becomes an u n s e c u r e d c r e d i t o r f o r t h e r e ­m a inder due t o him.

Depending on t h e l e g a l c l a s s i f i c a t i o n o f s e c u r e d d e b t one c a n d i s t i n g u i s h between l i e n on o b j e c t s and r i g h t s , r e g i s t e r e d mortgage and l a n d c h a r g e and p a w n - l i k e r i g h t s l i k e c e s s i o n and the t r a n s f e r o f t i t l e s f o r t h e purpose o f s e c u r i n g d e b t .

G u a r a n t e e s a r e c l a i m s o f the l e n d e r s on means o f payment o f a t h i r d p a r t y . I f t h e o r i g i n a l b o r r o w e r c a n n o t r e p a y the c r e d i t , the g u a r a n ­t o r i s o b l i g e d t o f u l f i l l t he d e b t o r ' s l i a b i l i t i e s .

153

I f g u a r a n t e e s s e r v e t o improve the p o s i t i o n of a l l c r e d i t o r s , t h ey a r e s a i d t o be g e n e r a l g u a r a n t e e s . G e n e r a l g u a r a n t e e s i n c r e a s e the l i a b l e p r o p e r t y o f the company. Examples a r e government g u a r a n t e e s or t h e p r i v a t e p r o p e r t y o f u n l i m i t e d p a r t n e r s . I f g u a r a n t e e s r e f e r t o an i n d i v i d u a l d e b t c o n t r a c t (which i s t o a c e r t a i n c r e d i t o r o r a g r o u p o f c r e d i t o r s ) t h ey a r e s a i d t o be s p e c i a l g u a r a n t e e s .

5. The E f f i c i e n c y o f S e c u r i n g Debt

One c a n n o t answer g e n e r a l l y the q u e s t i o n i f c r e d i t o r s s h o u l d use a s t r o n g i n s t r u m e n t as c o l l a t e r a l i z a t i o n t o i n f l u e n c e the owner's p o l i c y , o r i f a weaker p o l i c y ( c o v e n a n t s ) i s s u f f i c i e n t , because i t depends on t h e s p e c i f i c c r e d i t s i t u a t i o n . The i n t e r b a n k market f o r example can do w i t h o u t c o l l a t e r a l i z a t i o n , because the m a r k e t p a r t i ­c i p a n t s know each o t h e r w e l l , and t h e market p a r t i c i p a n t s a r e i n s t e a d y c o m m e r c i a l i n t e r c o u r s e . I f a b o r r o w i n g bank u n d e r t o o k a b u s i n e s s p o l i c y on the c r e d i t o r ' s d e t r i m e n t , i t c o u l d v e r y e a s i l y l o s e i t s s t a n d i n g and c o u l d be e x c l u d e d from the market. T h e r e f o r e i t seems t o be d i s p e n s a b l e on such a m a r k e t t o i n f l u e n c e t h e deb­t o r ' s p o l i c y e x p l i c i t l y .

On t h e c o m m e r c i a l c r e d i t m arket, where longterm c r e d i t o r / d e b t o r r e ­l a t i o n s a r e a s c e r t a i n a b l e , one can o b s e r v e c o l l a t e r a l i z a t i o n and n o n p e c u n i a r y c o v e n a n t s t o r e g u l a t e t h e b e h a v i o r o f t h e d e b t o r . A c t u a l l y t h e s e n o n p e c u n i a r y c o v e n a n t s a r e e x t r e m e l y i m p o r t a n t (as me f i r s t r u l e s ) . C o n c e r n i n g s m a l l e r f i r m s , c o l l a t e r a l i z a t i o n i s r e g u l a r , whereas the c r e d i t i n g banks r e q u e s t e s p e c i a l l y r e a l e s t a t e as s e c u r i t i e s .

I f f i r m s i s s u e o n l y s m a l l l o a n q u a n t i t i e s and a r e r e l a t i v e l y unknown to t h e c r e d i t i n g bank (because the c r e d i t c o n t r a c t i s the s o l e r e ­l a t i o n between customer and bank) the bank w i l l s e c u r e i t s d e b t w i t h c o l l a t e r a l - a g r e e m e n t s t o i n f l u e n c e ( a l t h o u g h i n d i r e c t l y ) the f i r m ' s b u s i n e s s p o l i c y d u r i n g the p e r i o d o f c r e d i t . I n t h i s c a s e , c o l l a ­t e r a l i s an e f f i c i e n t and cheap i n s t r u m e n t o f d e b t o r ' s s e l f b i n d i n g , w h i c h c a n save the c r e d i t o r / d e b t o r r e l a t i o n c o s t l y p l a n n i n g - and m o n i t o r i n g c o s t s ( D r u k a r c z y k 1983, 1984).

154

6. Appendix: Secured Debt and Uncertainty

6.1 The Firm's P o s i t i o n

The f i n a n c i a l e f f e c t s of securing debt s h a l l be derived i n a s i n g l e period model of a stock company. The firm's estate contains two assets, each of which can be values independently of the other asset value. The market valued of the s e c u r i t i e s at the end of the period are given by X(s) >0 and Y(s) >0 , where s (s = 1 , 2, . . . , s) i s the occuring state i n t=1 . If q(s) i s the present value of a f i n a n ­c i a l claim which w i l l pay i t s owner one unity of money i f state s occurs, the market value V of the firm i n t = 0 i s given by:

s V = I q(s) [X(s) + Y(s) ] . (1 )

s=l The firm has issued c r e d i t from bank A and B with the q u a n t i t i e s K A and K ß . The debt has to be repaid i n t = 1 i n the amount of T and T ß (the repayment includes the i n t e r e s t ) .

Furtheron we assume that during the period l i a b i l i t i e s i n the amount of U w i l l evoke which are not priced on the c a p i t a l market, and which i n case of d e f a u l t outrank the receivables T^ and T ß . To keep the anal y s i s simple, l e t us assume U<X(s) +Y(s) holds for a l l s such that the market value of the firm's s e c u r i t i e s i n t = 1 i s i n no case lower than the amount of the l i a b i l i t y U . Given the t o t a l claim of the c r e d i t o r s on the firm i s T = T A + T ß i n t = 1 , debt's value i n t = 0 w i l l be:

s F= I q(s) min[T,X(s) + Y(s) - u] , (2)

s = l because the banks w i l l get t h e i r receivable T or i n case of defaul the r e s i d u a l of the firm's value minus the amount of U , since U has the higher p r i o r i t y . This r e s i d u a l amount w i l l be smaller than the value of T , but since we assumed U<X(s) +Y(s) , the repay­ment to the banks cannot be negative.

Given X + Y >U + T holds for each state s , where s = 1 , 2 , . . . , k-1 and X + Y<U + T holds for each state s , where s = k,k+1,...,s , we d e l i v e r a rule of d i s t r i b u t i o n of the firm's estate to the c r e d i ­tors which corresponds to the Act of Bankruptcy. If the states of the world are divided i n the described way, the value of the debt w i l l be:

155

k-1 s F = T I q(s) + I q(s) [X(s) +Y(s) -U] . (3)

s=l s=k

I n t h e case o f d e f a u l t t h e r e s i d u a l amount o f t h e f i r m ' s e s t a t e minus U w i l l be s h a r e d between c r e d i t o r s p r o p o r t i o n a l t o t h e i r o r i g i n a l r e c e i v a b l e s T A and T ß . Thus t h e m a r k e t v a l u e o f bank A's p a r t o f t he debt w i l l be (on a c c o u n t o f a c l e a r e r p r e s e n t a t i o n we w i l l s t o p i n d i c a t i n g X and Y f u r t h e r o n ) :

s r T A F a = Z q(s) min|T A , — (X + <

s=l L

U) (4)

s I q(s) min[T,X + Y - U]

T s=l

T ' and t he market v a l u e o f bank B's r e c e i v a b l e i s :

(5) s r tB

F = X q(s) minj T , — (X + Y - U) B 8=1 L B T

ip S

= -2- I q(s) min[T,X+Y-U] s=l

- F .

T S i n c e the s h a r e h o l d e r s have c l a i m on t h e f i r m ' s a s s e t s minus t h e sum of l i a b i l i t i e s i n t = 1 , and be c a u s e of t h e l i m i t e d l i a b i l i t y o f common s t o c k , t h e v a l u e o f t h e e q u i t y w i l l be:

s E= I q(s) max[X+Y-U-T , 0 ] (6)

s=l k-1

= I q(s) [X+Y-U-T] s=l

S i n c e the market v a l u e o f the f i r m i s t h e sum o f the v a l u e s o f e q u i t y and debt and a t t h e same ti m e t h e m a r k e t v a l u e V o f t h e a s s e t minus t h e p r e s e n t v a l u e s o f t h e non mar k e t v a l u e d l i a b i l i t i e s , one can w r i t e :

W = E + F s

= I q(s) [X+Y-U] s=l

s = V - U I q (s) .

s=l

(7)

156

6.2 D e r i v a t i o n o f the V a l u e o f S e c u r e d Debt

L e t us assume now t h a t bank A g e t s t h e a s s e t w i t h t h e mar k e t v a l u e X as a c o l l a t e r a l f o r i t s c r e d i t . I n t h e c a s e o f d e f a u l t A has a c l a i m on t h e a s s e t w i t h v a l u e X ; t h u s t h e mar k e t v a l u e o f bank A's r e c e i v a b l e i s :

The f i r s t sum o f (8) c o n s i d e r s t h a t i f t h e f i r m does n o t d e f a u l t A w i l l g e t t h e e n t i r e amount o f i t s r e c e i v a b l e T^ , w h i l e t h e second sum o f (8) d e s c r i b e s t h e p a y o f f t o A i n c a s e o f d e f a u l t ( a l l s t a t e s where U +T > X + Y h o l d s ) , where A makes use o f t h e c o l l a t e r a l and r e c e i v e s i t s market v a l u e X ( s ) . I f t h e p r o c e e d s X ( s ) exceed T A , t h e s u r p l u s i s g i v e n back t o t h e b a n k r u p t ' s e s t a t e , b e c a u s e t h e r e ­payment t o A may n o t e x c e s s i t s r e c e i v a b l e T A . B u t i f t h e r e ­c e i v a b l e T A exceeds t h e p r o c e e d s o f X (T^ > X) , bank A has a r e s i d u a l c l a i m on t h e b a n k r u p t ' s e s t a t e i n t h e amount o f t h e e x c e s s T A - X , w h i c h i s o u t r a n k e d by the t a x c o s t s U , b u t i s on e q u a l p r i o r i t y w i t h t h e r e c e i v a b l e s o f bank B . I n t h e c a s e o f Y > U , t h e r e s i d u a l c l a i m o f bank A w i l l y i e l d t h e p o s i t i v e r a t i o ( T A - X) / (T - X) , whereas o t h e r w i s e t h e r a t i o w i l l be z e r o , b e c a u s e t h e r e s i d u a l a s s e t s a r e used t o pay t h e l i a b i l i t y U .

L e t us a d d i t i o n a l l y d i v i d e t h e s t a t e s o f t h e w o r l d (k,k+1 , . . . , s) i n t h e s t a t e s (k,k+1,...,1-1) , where x - T

A h o l d s , and i n t h e s t a t e s (1,1+1,...,s) , where X < T A h o l d s , and we can change (8) t o :

1-1 'x + max^—-(Y-U),o|» . (9) F = T I q(s) + I q (s)

A A S=l S=l { ^ < Y - U > , o }

The f i r s t sum of e q u a t i o n (9) shows t h a t A w i l l g e t t h e whole amount o f i t s r e c e i v a b l e i f t h e f i r m does n o t d e f a u l t ( s = 1 , 2 , . . . , k-1) , o r i f d e f a u l t does o c c u r , t h e l i q u i d a t i o n p r o c e e d s o f t h e c o l l a t e r a l a r e s u f f i c i e n t t o pay T A c o m p l e t e l y (s=k,k+1,...,1-1) . The second sum i n c l u d e s t h e p r e s e n t v a l u e o f b a n k r u p t ' s e s t a t e i f t h e r e c e i v a b l e T A exceeds t h e y i e l d s o f t h e c o l l a t e r a l . I n t h i s c a s e t h e bank w i l l g e t t h e v a l u e X o f the c o l l a t e r a l and i t s p a r t o f t h e redundancy Y - U , i f t h i s m a r g i n i s p o s i t i v e .

157

Comparing e q u a t i o n (9) t o ( 4 ) , whereas e q u a t i o n (4) v a l u e s t h e un­s e c u r e d c r e d i t o f A , and (9) t h e s e c u r e d c l a i m , one can see t h a t c o l l a t e r a l i z a t i o n

• has r a i s e d t h e p r o b a b i l i t y o f a t o t a l repayment t o bank A , un­l e s s none o f t h e s t a t e s s = (k,k+1 , . . . , 1-1 ) o c c u r s .

• has d i m i n i s h e d t h e amount o f an e v e n t u a l l a c k o f payment t o bank A , u n l e s s X = 0 h o l d s f o r s = ( 1,1+1 , . . . , s) .

I f one e x c l u d e s t h e extreme c a s e where X = 0 h o l d s f o r s = (k,k+1, ....,s) , t h e m a rket v a l u e o f t h e s e c u r e d d e b t q u a n t i f i e d by (9) i s h i g h e r t h a n t h e one o f t h e u n s e c u r e d d e b t i n e q u a t i o n ( 4 ) . And f i n a l l y i t i s p o s s i b l e t h a t , a l t h o u g h a p o s i t i v e d e f a u l t r i s k o c c u r s , bank A can c o n s t r u c t a r i s k l e s s c r e d i t p o s i t i o n by c o l l a ­t e r a l i z a t i o n . I f X > T A h o l d s f o r a l l s t a t e s s = (k,k+1,...,s) bank A's c l a i m i s f r e e o f any c r e d i t r i s k and i t s v a l u e i s :

F =T ! q(s) s=l

6.3 M a r k e t V a l u e o f t h e Debt i n Dependence o f i t s C o l l a t e r a l P o l i c y

Now we have t o examine t h e i n f l u e n c e o f c o l l a t e r a l i z a t i o n on t h e v a l u e o f t h e d e b t and o f t h e f i r m . I f s e c u r i n g bank A's d e b t r a i s e s n o t o n l y t h e v a l u e of i t s r e c e i v a b l e b u t a l s o t h e market v a l u e o f t h e d e b t , t h e m a rket v a l u e o f t h e f i r m c an a l s o be i n c r e a s e d . To p r o v e t h e s e r e l a t i o n s , we w i l l f i r s t i n s p e c t t h e i n t e r d e p e n d e n c y o f t h e v a l u e o f bank A's r e c e i v a b l e w i t h t h e c o l l a t e r a l i z a t i o n o f i t s d e b t .

We can e x p r e s s the v a l u e o f t h e u n s e c u r e d d e b t by: k - l 1-1

F =T I q(s) + I q (s) max {(X - T ) + (Y - U) ,0} (10) B B „ , " s=l s=k

+ X q(s) m a x | ^ (Y-U) ,oj

The f i r s t sum s t a n d s f o r the m a rket v a l u e o f t h e r e c e i v a b l e i n t h o s e s t a t e s where d e f a u l t does n o t o c c u r . The second sum i n d i c a t e s t h e market v a l u e i n t h e c a s e t h a t t h e p r o c e e d s o f s e c u r i t y X i n e x c e s s of the r e c e i v a b l e T^ o f bank A a l o n g w i t h t h e p r o c e e d s o f s e ­c u r i t y Y s e r v e t o pay t h e l i a b i l i t y U . A f t e r t h i s l i a b i l i t y i s p a i d t o o , bank B can d i s p o s e o v e r t h e r e s i d u a l b a n k r u p t ' s e s t a t e .

158

The t h i r d sum r e f e r s t o the s i t u a t i o n , where t he c o l l a t e r a l - p r o c e e d s c a n n o t s a t i s f y bank A's r e c e i v a b l e e n t i r e l y , such t h a t A and B have t o s h a r e o u t Y - U p r o p o r t i o n a l t o the q u a n t i t y o f t h e i r c l a i m a f t e r the l i a b i l i t y U i s p a i d .

I f you add the market v a l u e s of (9) and (10) you w i l l g e t t h e market v a l u e F 0 o f the d e b t under t h e as s u m p t i o n t h a t c r e d i t o r A g e t s t h e a s s e t w i t h t h e v a l u e X as a c o l l a t e r a l f o r i t s c r e d i t .

k-1 1-1 F 0 = T I q(s) + X q(s) max{X + Y-U,T} (11)

s=l s=k s

+ X q(s) max {X + Y - U , X } . s=l

We w i l l now compare t h i s market v a l u e F 0 w i t h t h e market v a l u e g i v e n i n (3) which i n d i c a t e s the v a l u e of the u n s e c u r e d d e b t . F o r an e a s i e r d e m o n s t r a t i o n e q u a t i o n (3) i s r e w r i t t e n a s :

k-l 1-1 s F = T X q(s) + X q(s ) [ X + Y - u ] + X q(s ) [ x + Y - u ] . (31)

s=l s=k s=l

Formulas (3') and (11) y i e l d

1-1 s F 0 = F+ X q(s) max {0, (TA-X) + (U-Y)} + X q (s ) max {0, (U-Y)} > F (12)

s=k s=l

whereby the i n e q u a l i t y F 0 >F can be s t r i c t s i n c e some s t a t e s c o u l d o c c u r where c r e d i t o r s w i l l r e c e i v e l i q u i d a t i o n p r o c e e d s on a c c o u n t o f t h e r e c e i v a b l e s U . From (12) we see t h a t t h i s i s t h e c a s e i f

T >X+Y-U holds for at least one of the states s = k , . . . , l - l or i f Y<U A holds for at least one of the states s = 1,.. . ,s .

The s i z e o f the i n c r e a s e o f F 0 depends on the amount o f the de­f a u l t r i s k which i s t r a n s f e r r e d to the c r e d i t o r w i t h r e c e i v a b l e U , caus e d by s e c u r i n g the de b t o f A .

6.4 The M a x i m i z a t i o n o f the Market V a l u e w i t h T o t a l C o l l a t e r a l P o l i c y

I f bank A would not g e t o n l y p r o c e e d s X , b u t a l s o Y as a c o l l a t e r a l , the market v a l u e o f i t s c l a i m would be:

m-1 s F = T X q(s)+ Z q ( s ) [ X + Y] , (13)

A A s=l m

159

i f s t a t e s ( 1,1+1 , . . . , s) a r e d i v i d e d i n (1,1+1,...,m-1) , where X +Y > T A h o l d s , and i n (m,m+1,...,s) , where X + Y < T A h o l d s .

The market v a l u e of bank B's c l a i m w o u l d t h e n be: k -1 m-1

F =T Z q(s) + Z q(s) max (X + Y -T - U , 0} . (14) D D A s=l s=k

Ad d i n g t h e market v a l u e s o f (13) und (14) t o t h e market v a l u e F o o

o f t h e d e b t , i f A i s t o t a l l y s e c u r e d , one r e c e i v e s :

k-1 m-1 s Foo=T Z q(s) + Z q(s) max {X + Y - U,TA) + Z q(s)[x + Y] . (15)

s=l s=k s=m

Comparing (15) w i t h t h e market v a l u e F o f t h e d e b t g i v e n i n ( 3 ) , whic h r e f e r s t o t h e u n s e c u r e d d e b t , one c a n see t h a t t h e market v a l u e o f t h e d e b t i s :

m-1 s Foo=F+ Z q(s) max (0,T A+U - (X+Y)} + U Z q ( s ) > F 0 > F , (16)

s=k s=m

i f the c l a i m o f bank A i s t o t a l l y s e c u r e d . C o r r e s p o n d i n g t o t h i s d e r i v a t i o n i t c o u l d be e a s i l y c o n f i r m e d t h a t t h e market v a l u e o f t h e de b t c o u l d be r a i s e d , i f bank B's d e b t would be a l s o s e c u r e d . The r i s k t r a n s f e r t o U i s o b t a i n e d i n d e p e n d e n t l y o f t h e chosen form of c o l l a t e r a l i z a t i o n . Whether the s e c u r i t i e s w h i c h s e r v e as c o l l a t e r a l a r e o r d e r e d i n a r a n k i n g ( f i r s t and second mortgage e.g.) o r a s e ­c u r i t i e s p o o l i s o f no i m p o r t a n c e .

I f no r e c e i v a b l e s U have t o be c o n s i d e r e d , (16) shows t h a t s i n c e U = 0 and X > T A h o l d s f o r s = k, k+1 , . . , 1-1 , r e s p . X + Y > T A h o l d s f o r s=1,1+1,...,m-1 , t h e market v a l u e o f t h e d e b t , i f d e b t A i s t o t a l l y s e c u r e d , e q u a l s t h e v a l u e o f t h e d e b t w i t h o u t c o l l a t e r a l i z a ­t i o n . Thus, i f t h e chosen c o l l a t e r a l i s o n l y t h e l i q u i d a t i o n p r o c e e d s X , as d e s c r i b e d i n s e c t i o n 2.2, a market v a l u e r i s e can n e i t h e r be a c h i e v e d , s i n c e i f U = 0 i n ( 1 1 ) , one g e t s :

max{x+Y,T} = (X + Y) i n s = k , . . . , l - l and A

max{x + Y, x] = (X + Y) i n s = l , . . . , s

and t h u s k-1 s

F 0 = T Z q(s)+ Z q(s)(X + Y) , ( 1 7 ) s=l s=k

160

and t h e r e f o r e

Fo = F . (18)

W i t h F from (3') and U = 0 one g e t s t h e r e s u l t t h a t a l t h o u g h the c o l l a t e r a l c a u s e s a c r e d i t o r ' s r i s k t r a n s f e r from bank A t o bank B , th e d e b t p o l i c y i s i r r e l e v a n t f o r t h e amount o f t h e ma r k e t v a l u e o f t h e t o t a l d e b t and t h e r e f o r e a l s o i r r e l e v a n t f o r the ma r k e t v a l u e of t h e f i r m , i f a l l c l a i m s on t h e f i r m a r e v a l u e d on t h e market.

R e f e r e n c e s

Adams, M. (1980): Ökonomische A n a l y s e d e r S i c h e r u n g s r e c h t e , König­s t e i n

B a l t e n s p e r g e r , E. (1976): The B o r r o w e r - L e n d e r R e l a t i o n s h i p , Com­p e t i t i v e E q u i l i b r i u m and t h e Theory o f He d o n i c P r i c e s , A merican Economic Review 66, 401-405

B a r r o , R.J. (1976): The Loan M a r k e t , C o l l a t e r a l and R a t e s o f I n ­t e r e s t , J o u r n a l o f Money, C r e d i t and B a n k i n g 8, 439-456

Ben j a m i n , D.K. (1978): The Use o f C o l l a t e r a l t o I n f o r c e Debt Con­t r a c t , Economic I n q u i r y 16, 333-359

D r o b n i g , U. (1980): S i c h e r u n g s r e c h t e im De u t s c h e n K o n k u r s v e r f a h r e n , i n : R a b e i s Z e i t s c h r i f t für ausländisches und i n t e r n a t i o n a l e s P r i v a t r e c h t , Bd. 44, 784-807

D r u k a r c z y k , J . (1983): Kreditverträge, M o b i l i a r s i c h e r h e i t e n und Vorschläge zu i h r e r Reform im I n s o l v e n z r e c h t , i n : Z e i t s c h r i f t für B e t r i e b s w i r t s c h a f t , v o l . 53, 328-349

D r u k a r c z y k , J . (1984): C r e d i t C o n t r a c t s , C o l l a t e r a l - B a s e d S e c u r i t y Agreements, and B a n k r u p t c y , i n : G. Bamberg, K. Spremann ( e d . ) , R i s k and C a p i t a l , B e r l i n , 139-159

G e r t h , A. (1980): A t y p i s c h e K r e d i t s i c h e r h e i t e n , 2nd.ed., F r a n k f u r t

H i r s h l e i f e r , J . ; R i l e y , J.G. (1979): The A n a l y t i c s o f U n c e r t a i n t y and I n f o r m a t i o n , i n : J o u r n a l o f Economic L i t e r a t u r e , v o l . 17, 1375-1421

J a f f e e , D.M.; R u s s e l l , Th. (1976): I m p e r f e c t I n f o r m a t i o n , U n c e r t a i n ­t y and C r e d i t R a t i o n i n g , i n : Q u a r t e r l y J o u r n a l o f Economics, v o l . 90, 651-666

K a l a y , A. (1982): S t o c k h o l d e r - B o n d h o l d e r C o n f l i c t and D i v i d e n d C o n t r a i n t s , i n : J o u r n a l o f F i n a n c i a l E c o n o m i c s , v o l . 10, 211 f f .

M e c k l i n g , W.H. (1977 ) : F i n a n c i a l M a r k e t s , D e f a u l t and B a n k r u p t c y : The R o l e of the S t a t e , i n : Law and Contemporary P r o b l e m s , v o l . 41, 13-38

161

M i l d e , H. ( 1 9 8 0 ) : K r e d i t r a t i o n i e r u n g , Z i n s d i s p e r s i o n und S e g m e n t i a l -suche, i n : Z e i t s c h r i f t für d i e Gesamte S t a a t s w i s s e n s c h a f t , v o l . 136, 266-285

M i l d e , H. (1981): A d v e r s e S e l e k t i o n und K r e d i t s i c h e r h e i t e n , i n : H. Göppl; R. Henn ( e d . ) , G e l d , Banken und V e r s i c h e r u n g e n I I , 1089 f f .

M o d i g l i a n i , F.; M i l l e r , M.H. (1958): The C o s t o f C a p i t a l , C o r p o r a t i o n F i n a n c e , and t h e Theory o f I n v e s t m e n t , i n : A m e r i c a n Economic Re­v i e w , v o l . 48, 261-297

Myers, St . C . (1977): D e t e r m i n a n t s o f C o r p o r a t e B o r r o w i n g , i n : J o u r ­n a l o f F i n a n c i a l E c onomics, v o l . 4, 147-175

P l a u t , J.E. (1985): The Theory o f C o l l a t e r a l , J o u r n a l o f B a n k i n g and F i n a n c e 9, 401-419

Rudolph, B. (1974): D i e K r e d i t v e r g a b e e n t s c h e i d u n g d e r Banken, Opladen

Rudolph, B. (1982): Können d i e Banken i h r e K r e d i t s i c h e r h e i t e n " v e r ­g e s s e n " , i n : K r e d i t und K a p i t a l , v o l . 15, 317 f f .

Rudolph, B. (1984): K r e d i t s i c h e r h e i t e n a l s I n s t r u m e n t e z u r U m v e r t e i ­l u n g und Begrenzung von K r e d i t r i s i k e n , i n : Z e i t s c h r i f t für be­t r i e b s w i r t s c h a f t l i c h e F o r s c h u n g , v o l . 36, 16-43

S c h i l d b a c h , Th. (1983): S i c h e r h e i t e n v e r s u s p a r c o n d i t i o c r e d i t o r u m , i n : B e t r i e b s - B e r a t e r 34, 2129-2136

Schmidt, R.H. (1981): E i n n e o - i n s t i t u t i o n a l i s t i s c h e r A n s a t z der F i ­n a n z i e r u n g s t h e o r i e , i n : E. Rühli, J.-P. Thommen ( e d . ) , U n t e r n e h ­mensführung aus f i n a n z - und b a n k w i r t s c h a f t l i c h e r S i c h t , 135-154

S c o t t , J . (1977): B a n k r u p t c y , S e c u r e d Debt, and O p t i m a l C a p i t a l S t r u c ­t u r e , i n : J o u r n a l o f F i n a n c e , v o l . 32, 1-19

S m i t h , C.W. (1980): On the Theory o f F i n a n c i a l C o n t r a c t i n g - The P e r s o n a l Loan M a r k e t , J o u r n a l o f M o n e t a r y Economic s , v o l . 6, 333 f f .

S m i t h , C.W.; Warner, J.B. (1979a): B a n k r u p t c y , S e c u r e d Debt, and O p t i m a l S t r u c t u r e : Comment, i n : J o u r n a l o f F i n a n c e , v o l . 34, 247 f f .

S m i t h , C.W.; Warner, J.B. (1979b): On F i n a n c i a l C o n t r a c t i n g - An A n a l y s i s o f Bond C o v e n a n t s , i n : J o u r n a l o f F i n a n c i a l E conomics, v o l . 7, 118 f f .

S t a h l s c h m i d t , D. (1982): Schutzbestimmungen i n Kreditverträgen, Wiesbaden

S t i g l i t z , J.E.; W e i s s , A. ( 1 9 8 1 ) : C r e d i t R a t i o n i n g i n M a r k e t s w i t h I m p e r f e c t I n f o r m a t i o n , i n : A m e r i c a n Economic Review, v o l . 71, 402 f f .

162

Swoboda, P. (1975 ) : B e t r i e b s w i r t s c h a f t l i c h e K a p i t a l t h e o r i e , i n : Handwörterbuch d e r B e t r i e b s w i r t s c h a f t , 4 t h . e d . , S t u t t g a r t , 2129 f f .

Swoboda, P. (1982): The R e l e v a n c e o f S e c u r i n g D e b t s , m a n u s c r i p t G r a z .

Author Index

Adams, M. 160 Agnew, R.A. 16,49 A l l a i s , M. 20,49 A l l i n g h a m , M.G. 35,49 A n a n t h a n a r a y a n a n , A,C. 110,122,128 A r d i t t i , F.D. 17,49 Arrow, K . J . 26,49,190,206

B a l l , C.A. 94,96,109,110,127 B a l t e n s p e r g e r , E. 160 Bamberg, G. 1 f f , 3 , I f f , 4 5 , 4 6, 4 9,50, 51 , 53,55,7 7 , 1 29 , 209 B a r o n , D.P. 8,49 B a r r o , R .J. 160 B a r t t e r , B . J . 207 Bawa, V.S. 11,50,59,61,77 B e c k e r s , S. 122,127 B e e d l e s , W.L. 17,53 B e n j a m i n , D.K. 160 B e r g e s , A. 166,187 Bey, R.P. 11,14,52 B h a t t a c h a r y a , M. 100-102,107,109,110,127 B i e r l e i n , D. 66,77 B i e r w a g , G.O. 8,50 B l a c k , F. 3,80,88,89,95-97,108-110,1 14,1 16,117,1 19,1 27,164,166,157,137,

193,206 Bl o m e y e r , E.C. 110,113,119,127 B o d u r t h a , J . 93,120,128 B o o k s t a b e r , R.M. 118,128 Bo o t , J.C.G. 62,78 B o r c h , K. 8,18,50 B o y l e , P.P. 110,111,122,128 B r a n s , J.P. 77 B r e e d e n , D.T. 206 Brennan, M.J. 4,34,36,50,95,96,97,113,128,163ff,206,209 B r e n n e r , M. 50,94,127,128,129,130,206 Brown, S . J . 59,61,77 Bühler, W. 66,77 B u r g e r , E. 70,77 B u t t l e r , J . S . 122,128

C a r r , R. 18 5,188 C h a m b e r l a i n , G. 17,18,5C Chipman, J.S. 8,20,50 C h i r a s , D.P. 110,113,128 Cohen, F . J . 58,77 C o o l e y , P.L. 130 C o p e l a n d , T.E. 8,50 C o u r t a d o n , G. 9 3,94,96,120,128 Cox, J.C. 89 , 90-92, 94,96,97, 1 1 3, 1 27 , 1 28, 1 29, 1 93 , 206

Debreu, G. 190,196,206 DeGroot, M.H. 59,77 Denneberg, D. 15,50 D i e t r i c h - C a m p b e l l , B. 120,129

214

Dimson, E. 17 4,177,180,182,187 Dothan, U.L. 129 Drèze, J.H. 206 D r o b n i g , U. 160 D r u k a r c z y k , J . 8,50,153,150 Dyer, J.S. 50

E g l e , K. 95,129 E f f r o n , E. 115,129 E l t o n , E . J . 204,206 Emanuel, D.C. 97,110-112,114,129 Epps, T.W. 3,21,23,24,50

F a h r i o n , R. 66,78 Fama, E.F. 2,15,16,50,167,174,175,187 F a r k a s , J . 200 F a r k a s , K.L. 113,129 F e l d s t e i n , M.S. 8,50 F i n n e r t y , J.E. 110,129 F i r c h a u , V. 3,40,49,50,55ff,209 F i s c h e r , E.O. 129 F o w l e r , D.J. 174,175,187 F u l l e r , R.J. 129

G a l a i , D. 9 7,100-102,104,107,110,117,118,128-130 Garman, M.B. 122,130 G e r t h , A. 160 Geske, R. 4 , 5 1 , 7 9 f f , 8 5, 39,91,9 3,9 6,9 7, 103, 1 10-1 1 5 , 1 22 , 1 30, 206 , 209 G i b b o n s , M. 167,174,180,188 G l a d s t e i n , M.L. 131 G o e l , P.K. 59,77 Gombola, M.J. 130 G o n z a l e s , IT. 8,51 Göppl, H. 49,50,129,133,161 G o u l d , J . 104,130 G r u b e r , M.J. 204,206 G u l t e k i n , N.B. 130

Hakansson, IT. H . 8,51 H a r r i s o n , J.M. 94,130,206 Hawawini, G.A. 58,77 Kenn, R. 4 9,50,54,129,133,161 H i r s h l e i f e r , J . 136,160 Hogan, W.W. 11 ,12,51 H o s k i n , R.E. 113,129 H s i a , C. 207 Hsu, D.A. 58,77 Hubermann, G. 207 Huschens, S. 66,78

I b b o t s o n , R. 185,188 I n g e r s o l l , J.E. 96,97,128,131

J a h a n k h a n i , A. 11,51 J a f f e e , D.M. 144,160 J a r r o w , R. 40-44,51 J e a n , W. 51 J e n n i n g s , R.H. 59,77 J e n s e n , M.C. 167,187,188 J e v o n s , W.S. 192 J o b s o n , J.D. 58,77

215

J o g , V. 174,187 John, F. 23,48,51 Johnson, U. 110,113,127 Johnson, H.E. 85,93,130

K a l a y , A. 160 K a l l b e r g , J.G. 19,51 Kalymon, B.A. 59,78 K a n d e l , S. 165,188 Keynes, J.M. 193 K l a s s , M.J. 122,130 K l e i n , R.W. 59,61,77 Klemkosky, R.C. 104-106,110,119,127,131 K n i g h t , F. 191,207 K o f l e r , E. 66,67,78 K o r k i e , B. 58,77 K r a u s , A. 17,51 K r e p s , D.M. 94,130,131,206 K r o l l , Y. 58,78 Kuhn, T. 190,207 Kuss, U. 66,78

Latanê, H.A. 108,110,122,131 L a V a l l e , I.H. 60,78 L e l a n d , H.E. 97,131 Levy, H. 8,17,49,51,58,78,132 L e w i s , D.C. 11,14,52 L i n , W.T. 3,62,63,65,78 L i n d e n b e r g , E.B. 11,50 L i n t n e r , J . 21,27,28,40,51,72,78 L i t z e n b e r g e r , R. 8,17,51,167,183,206

MacBeth, J.D. 110,11 2,1 14,1 16,1 29,131 ,167,174,175,137 Madansky, A. 131 M a i e r , S.F . 58,77,78 M a l i n v a u d , E. 179,187,188 M a n a s t e r , S. 110,118,128 Mao, J.C.T. 11,51,59,78 M a r k o w i t z , K.M. 8,11,51,190,191,207 Massé, P. 10,51 M a s u l i s , R.W. 97,130 Mayers, D. 165,188 M e c k l i n g , W.H. 160 Menges, G. 66,67,78 M e r v i l l e , L . J . 110,112,114,116,131 Me r t o n , R.C. 81,83,84,89,92,97,104,109,110,131,182,18 8,207 M i l d e , H. 136,137,161 M i l l e r , M.H. 1,2,15,16,42,50,52,139,161,190,193 M i n k o w s k i , H. 200 M o d i g l i a n i , F. 1,139,161,190,193 Morgan, I . 173,188 M o r r i s , C. 129 M o r r i s , J.R. 59,78,116 Möschlin, 0. 54 M o s l e r , K.C. 52 M o s s i n , J . 31,32,35,52,95,131 Müller, S. 52,207 Myers, S.C. 161

N a n t e l l , T.J. 11,52 N i k a i d o , H. 201,207

216

Owen, J . 16,52

P a r e t o , V. 190 P a r k i n s o n , M. 113,122,132 P a t e l l , J.M. 132 P e t e r s o n , D. 40,52 P e t e r s o n , D.W. 53,78 P e t e r s o n , P. 40,52 P h i l l i p s , S.M. 99,106,118,132 P l a u t , J.E. 161 P o r t e r , R.E. 11,14,52 P r a t t , J.W. 47,52,57,78 P r i c e , B. 11,52 P r i c e , K. 11,52

R a b i n o v i c h , R. 16,52 R a i f f a , H. 78 Ramaswamy, K. 94,132,167,138 Rendleman, R.J. 108,110,122,131,207 R e s n i c k , B.G. 104-106,127,131 R i c h t e r , H. 66,78 R i l e y , J.G. 136,160 R o b i n s o n , A. 18 5,188 R o c k a f e l l a r , R.T. 69,73 R o e n f e l d t , R.L. 130 R o g a l s k i , R.J. 110,130 R o l f o , J . 8 R o l l , R. 4,15,52,93,103,110-116,118,122,1 30,1 32,153,164,167,1^8, 207 Rorke, K. 174,175,187 Ross, S.A. 52,89,90-92,94,96,97,113,128,129,165,188,193,206,207 R u b i n s t e i n , M. 89,90,92,94,95,110,11 2-115,127,1 29,1 3 2, 19 3, 206 , 207 Rud o l p h , B. 4,3,45,52,135ff,138,144,161,210 R u s s e l l , T. 144,160

S a e l z l e , R. 36,39,52 Samüelson, P.A. 52 S a r i n , R.K. 50 S a r n a t , M. 19,53,132 Särndel, C.E. 59,78 S c h a c h t e r , B. 122,128 S c h i l d b a c h , T. 161 S c h l a i f e r , R. 57,78 Schmalensee, R. 110,132 Schm i d t , R.K. 161 S c h m i t z , N. 54 Schneeweiß, K. 8,10,14,20,53 S c h n e l l e r , M.I. 97,130 S c h n e i d e r , D. 53 S c h o l e s , M.S. 3,80,88,89,95,97,108-110,114,116,117,119,127,131,157,

175-177,187,188,193,206 S c h w a r t z , E.S. 4,96,97,113,120,128,129,163ff,210 S c h w a r t z , R.A. 58,77 S c o t t , J . 4,141,161 Sengupta, J.K. 53 S h a s t r i , K. 93,94,103,110,120,130,132 Sharpe, W.F. 12,41,53 S i m k o w i t z , M.A. 17,53 S m i t h , A. 189 S m i t h , C.W. 97,99,106,118,132,145,161,207 S o l n i k , B. 165,188 Spremann, K. 1 f f , 4, 4 5, 4 6, 4 9-51,5 3,55, 57, 7 7, 1 29,1 60, 1 8 9 f f , 2 0 7 , 2 1 O S t a h l s c h m i d t , D. 161

Stambaugh, R. 167,179,188 S t e h l e , R. 4,163,166,185,188 S t e i n , C. 116 S t i g l i t z , J . E. 35,53,136,161 S t o l l , H.R. 104,132 S t u l z , R. 165,166,13? Subrahmanyan, M. 94,128 S u n d a r e s a n , S.II. 94,132 Swoboda, P. 53,145,148,152

Takayama, A. 201,207 Tandon, K. 9 3,94,120,132 Thorpe, E. 122,132 T i n i c , S.M. 110,130 T o b i n , J . 8,19,21,53 T o r o u s , W.N. 94,96,109,1 10,1 27 Trautmann, S. 4,79ff,95,1C2,1 OS,1 10,1 1 2, 1 1 5,1 29,1 33, 21 1 T r i p p i , R.R. 110,132,133 T s i a n g , S.C. 8,53 Turgeon, G. 173,188

Van d e r Weide, J.H. 58,78 V a s i c e k , 0. 133 V i c k s o n , R.G. 53

Wald, A. 190 W a l r a s , L. 190 Warner, J.E. 14 5,161 Warren, J.K. 11,12,51 W e i s s , A. 138,161 Weston, J . F . 8,50 Whaley, R.E. 9 3,94,108,110,111,114,116,118,120,133 Whitcorab, D.K. 58,77 W h i l h e l m , J.E.W. 53,54,59,78,207,208 W i l l i a m s , J . 175-177,188 W i l s o n , R. 94,133 W i n k l e r , R.L. 59,78 W o l f s o n , M.A. 132

Zachow, E.W. 5 4 Ze c h n e r , R. 129 Ziemba, W.T. 19,51 Zimmerman, j . 97,132

Subject Index

A b o v e - n o r m a l 97,98,99,100,102,104,108,118 A b s o l u t e r i s k a v e r s i o n 21,23,24,95 A c t o f B a n k r u p t c y 154 A d d i t i v e s e p a r a b l e 31 A g g r e g a t i o n 27,28,30,32,36,39,40,42,45,94 A m e r i c a n c a l l 8 3,96,103,113,114,204

p u t 84,85,96,104,105,113 o p t i o n 4,80,83,94,104,111

A m p l i t u d e f a c t o r 126 A n a l y t i c f o r m u l a 93

model 9 3 APM ( A r b i t r a g e P r i c i n g Model) 81,98,166 A r b i t r a g e 2,3,4,5,81,82,86,189,192,195,198, 203

b o u n d a r i e s 79 c o n d i t i o n 79,80,85 o p p o r t u n i t i e s 104 p o r t f o l i o 92 p r i c i n g model 81,94 p r o f i t 98 r e l a t i o n 89 r e s t r i c t i o n s 84,85

A s s e t 91,92,97,98 , o m i t t e d 163,165,170,171,181,182,183 , r i s k l e s s ( r i s k - f r e e ) 11,17,18,22,24,92,125,164 , r i s k y 22,28,39,81,92,125,164

v a l u a t i o n 81 A s s e t p r i c i n g model 153,167,171,174,177

, g e n e r a l i z e d 164,168,169,171,175,178,179,180 , g l o b a l 163 , i n t e r n a t i o n a l 165 / n a t i o n a l 163 , N o r t h A m e r i c a n 163 , Zero B e t a 164,175,180,181

A s y n c h r o n o u s market 105 At-the-money o p t i o n 110 Av e r a g e d e v i a t i o n 1 5 Av e r a g e p r o f i t 101

B a l a n c e s h e e t 92,150,151 Bank o f Canada Review 173 B a n k r u p t c y 4,142 Bayes 3,57,58,65,67 B e l i e f 9,39,44,94,191 B e r k e l e y O p t i o n s T r a n s a c t i o n s Data Base 115,116 B e r n o u l l i d i s t r i b u t i o n 18 B e t a ( f a c t o r ) .4 , 30,168,1 69,1 70,1 73,174,175,176,178,1 82 B i a s 4,108,112,113,114,116,122,175 B i d - a s k - s p r e a d 99,101,102,106,118,119,120,121 B i l l o f exchange 152 B i l l p r o t e s t 152 B i n o m i a l model 89,90,93,123 B i v a r i a t e n o r m a l 125 B l a c k - S c h o l e s Model 89,90,91 ,96,109,11 2,113,114,115,119,1 22,1 23

e q u a t i o n 89,92 f o r m u l a 3,4,91,109,111,115

220

B l a c k - S c h o l e s v a l u e 115,118,126 Bond 89,96,97,165,181,182,193

, d i s c o u n t 91 , Government 181,183

Boundary c o n d i t i o n 80,99,100,104,107 v i o l a t i o n 101,104

Borrow 22,32,90,121,144 Box s p r e a d e r 85 B r a n c h bank system 138 B r o k e r a g e f e e 99 Br o w n i a n 97 B u t t e r f l y s p r e a d 82,84

C a l l ( o p t i o n ) 3,34,81,8 2,85,89,9 3,100,102,104,107,114,116,119,120,123, 204,205,206

C a l l v a l u e 8 2,86,123,125,126 C a l l a b i l i t y c l a u s e 151 C a n a d i a n 163,165,166,167,171,172,173,174,180,181,182,183,184,185,186 C a p i t a l

g a i n 34 market l i n e 12 s t r u c t u r e 1,34,91,190

CAPM ( C a p i t a l A s s e t P r i c i n g Model) 2,7,9,14,17,33,81,98,186,191 Cash f l o w 94 CBOE (C h i c a g o B oard O p t i o n s Exchange) 100,101,102,104,107,113,114,

115,117,118,119 C e r t a i n t y e q u i v a l e n t 30,35,57,63,68,69 C e s s i o n 150,152 CEV ( C o n s t a n t E l a s t i c i t y o f V a r i a n c e Model) 89,91,112,113,124 CMS ( C h i c a g o M e r c a n t i l e Exchange) 120 C o e f f i c i e n t o f d e t e r m i n a t i o n 111,112,114 C o l l a t e r a l 135,137,139,140,144,145,148,149,158

agreement 152,153 c o v e n a n t 147 i r r e l e v a n c e h y p o t h e s i s 2,139,141,143 p o l i c y 4,137,139,141,143,157 s e c u r i t y 137

C o l l a t e r a l i z a t i o n 2,136,153 Commissions c o s t s 99 Commodities 119 C o m p a r a t i v e s t a t i c 9,45 Complementary

b i n o m i a l d i s t r i b u t i o n f u n c t i o n 124 P o i s s o n 92,126 s t a n d a r d gamma d e n s i t y f u n c t i o n 124

Complete c a p i t a l market 204,205 Compound O p t i o n Model 89,91,92,93,111,124 Concave 35,46 C o n s o l 173 C o n s t a n t r i s k a v e r s i o n 7,21,23,55 C o n s t a n t s t o c h a s t i c r e t u r n t o s c a l e 26 C o n v e r t e r 8 5 Convex 22,64,66,67,69,70,75,82,84,86,164 C o r n e r 56,58 C o r p o r a t e d e b t 91

t a x e s 34 C o - s e m i v a r i a n c e 12,13,14 c o v a r i a n c e 12,14,18,38

m a t r i x 18,22,26,44,61 CPRA 95

221

C r e d i t c o v e n a n t 135,149 l i n e 136 r a t i o n i n g 144 r e l i a b i l i t y r i s k 130,143,145,140,149 repayment q u o t a 1 39 s t a n d i n g 138,145 s u p p o r t d e c i s i o n (model) 135,136,138

C r e d i t a b i l i t y r i s k 143 C r o s s - s e c t i o n a l r e g r e s s i o n 112,114 CRSP ( C h i c a g o R e cord o f S t o c k P r i c e s ) 173 C u r r e n c y 93,94,95,96,119,120,121

Data s y n c h r o n i z a t i o n 98 Debt 4,9 6,139,146,147,151,155,159

, c o n v e r t i b l e 97 - e q u i t y r a t i o 125,146,191

, j u n i o r 97,147 , o p t i o n 119,120,121 , p o l i c y 160 , s e c u r e d 152,154,157 , s e n i o r 146,147 , t o t a l l y s e c u r e d 159 , u n s e c u r e d 157,159

D e f a u l t r i s k 146,148,157,158 Demand 27,39,94,144,191 D e r i v a t i v e c o n t r a c t 202,203,204 D i f f u s i o n 86,89,92

-jump 89,126 -jump model 92,126 model 109

Dimson's b e t a e s t i m a t i o n 4,174,175,176,177,178,179,181,182,186 D i s c o u n t bond 91 D i s c r e t e p r o c e s s 90 D i s p l a c e d 89

d i f f u s i o n model 92,125 D i s t r i b u t i o n - f r e e 79,80,81 D i s t r i b u t i o n r i s k 145,147,148 D i v e r s i f i a b l e 93,126 D i v e r s i f i c a t i o n 17,27,87,165 D i v i d e n d 34,82,83,85,93,96,1 01,103,104,105,11 4,1 15,116,1 19,1 21 ,1 25,

147,191 p o l i c y 146 p r o t e c t e d 106,112 u n c e r t a i n t y 115 u n p r o t e c t e d 8 2,104,113

Down jump 1 24 Down movement 90 D y o p o l i s t i c 14,45

E a r l y e x e r c i s e 9 3,96,103,111,112,114,119,120 E f f i c i e n t f r o n t i e r 171

p o r t f o l i o 164 s e t 11 ,16,168

E l a s t i c i t y 91 E l l i p t i c a l d i s t r i b u t i o n 16 E m p i r i c a l t e s t 97,99 Employee s t o c k 97 E n d - o f - p e r i o d

- v a l u e 8,9,13,22,26,55,56 - w e a l t h 8,17,19,21,22,24,25,56

222

E q u i l i b r i u m 1,8,27,28,89,94,9 6,139,189,190,19 9 c o n d i t i o n 7,13,27,73,76,201,203,204,205 p o i n t 70 p r i c e 3,7,35,36,43,73,76 s t r a t e g y 70 v a l u e 28,38

E q u i t y 146,148,155,166 d e b t r a t i o 1 o p t i o n 107,121

E s t i m a t i o n r i s k 61 Euro Bond 152 European O p t i o n 4,80,85,89,93,96,111

c a l l 82,83,96,123,204 l o w e r bound 101,102,103 p u t 84

E v e n t 196,197,200 u n c e r t a i n t y 136,138

E x ^ a n t e p r o f i t 100 t e s t 98,99,101,104,105,117

Exchange membership 107 E x - d i v i d e n d 83,102 E x e r c i s e p r i c e 81,82,83,84,89,103,104,113,116,121,123

v a l u e 82,90,102 E x p e c t a t i o n s

, h e t e r o g e n e o u s 7,39,41,42 , homogeneous 27,39,41,7 2

E x p e c t e d r a t e o f r e t u r n 8 r e t u r n 95,98 u t i l i t y 9,10,13,14,15,16,17,18,23,33,47,81,94 v a l u e 10,94

E x p i r a t i o n 81,82,83,89,90,93,103,123,124,126 d a t e 80,82,104,116,121,204

E x p l i c i t r e p r e s e n t a t i o n 9 s o l u t i o n 7,21,23,25,27,30 v a l u a t i o n f o r m u l a 3,13,28,45

E x p l o i t a t i o n r i g h t 142,147 E x p o n e n t i a l u t i l i t y 3,21 E x - p o s t p r o f i t 100

t e s t 98,99,117

Face v a l u e 96 F i n a n c i a l i n t e r m e d i a t i o n 1 F i r m v a l u e 9,29,30,38,140 FOE ( F r a n k f u r t O p t i o n Exchange) 102,106,112,115 F r a c t i l e 15 F r a n k f u r t S t o c k Exchange 106 F r e e l u n c h 194,198,203 F u t u r e s 4,81,82,93,94,95,96,119,120,121,190,192,196,197,198,200

Game t h e o r y 4 5 Gamma d e n s i t y 1 24 Germany 36,93,99,103 Geske-Johnson A m e r i c a n model 113,120 G i b b o n s ' maximum l i k e l i h o o d a p proach 4,175,178 Government bond 9 8

s e c u r i t y 96 G r a d i e n t 35,42 Grand mean 122 Gr o s s d e f a u l t c l a u s e 152 Guarantee-agreement 152

223

G u a r a n t e e s , g e n e r a l 153 , s p e c i a l 153

Hedge 86,87,88,89,106,107,121 p o r t f o l i o 87 p o s i t i o n 104,105,106,108,117,118 r a t i o 87,93,109,117,118 r e t u r n 110,111,116,117,118

Hedging 80 model 90,92,94

, p e r f e c t 94 p r o b a b i l i t y 123

, r i s k l e s s 95 H i e r a r c h i c a l 59 H i s t o r i c a l v o l a t i l i t y 112,118 H y b r i d model 3,7,9,17,23,31,33,35,42,45,46,55,60,67,72 Hyperparameter 59

I m p e r f e c t c a p i t a l m arket 7 I m p l i c i t ( c h a r a c t e r i z a t i o n , r e p r e s e n t a t i o n ) 3,9,28,30 I m p l i e d v a r i a n c e 122 I n c e n t i v e 1,46 Income t a x 34

smoothing 4 5 Index 66,95,117,164,165,169,170,171,173,183,185 I n f o r m a t i o n 9 2,98,122,150

h e t e r o g e n e o u s 2 i n c o m p l e t e 2,3

I n f o r m a t i o n a l asymmetrie 1 I n i t i a l w e a l t h 4,22,23,25,55 I n s u r a n c e 97,197 I n t e g r a t e d c a p i t a l m a r k e t 167 I n t e r b a n k m a rket 153 I n t e r c e p t 104 I n t e r e s t ( r a t e ) 36,96,121 I n t e r e s t - r a t e d i s p e r s i o n 136,137 I n t e r e s t - r a t e - p a r i t y t h e o r y 193 I n t e r - s t o c k c o m p a r i s o n 122 In-the-money o p t i o n 102,112,114,115 I n v e n t o r y 81 I n v e s t m e n t 97,148 I r r e l e v a n c e theorem 1,190 ISD ( i m p l i e d s t a n d a r d d e v i a t i o n ) 108,111,112,114,115,118 I s s u e p r i c e 201,202 I s s u i n g s t r a t e g y 46,146

J a f f e e and R u s s e l model 144,145 J o i n t h y p o t h e s i s 80,99,100

t e s t 98,99 Jump 89,90,92,94,109,123,125,126

a m p l i t u d e 126 f r e q u e n c y 125,126 model 92,125 p r o c e s s 92,125 s i z e 123

Lag t erm 17 4,184 Lagrangean m u l t i p l i e r 42 L a v a l S e c u r i t i e s Tape 173 Lead term 174,184 L e a s i n g 97,150,151

224

L e a s t - s q u a r e s 104 Lend 22,32,85,103,121,136,144 L e v e r a g e 91

r a t i o 91 L e v e r e d p o s i t i o n 90 L i a b i l i t y 92 L i m i t e d l i a b i l i t y 34,82,84,155 L i n ' s a p p r o a c h 62,63,65 L i n t n e r ' s i n v e r s e a d d i t i v i t y r u l e 27,28 L i q u i d a t i o n p r o c e e d s 140,141,142,147,159 Lognormal 81,86,95,109,111,125 Long hedge p o s i t i o n 105,106 Long p o s i t i o n 105 Long term T r e a s u r y B i l l 119 L o s s - f u n c t i o n 63 L o s s - o f f s e t 34,35 Lower bound

, European 101,102,103 , pseudo-American 101,102,103 , v i o l a t i o n 101

Lowest c o s t t r a d e r 99,106

Macroeconomic v a r i a b l e 116 M a i n t e n a n c e 150,151 M a r g i n a l t a x r a t e 35,36,37 M a r k e t

c l e a r i n g ( c o n d i t i o n ) 28,32,33,43,94 e f f i c i e n c y 80,97,98,99,100,101,106,107,108,120 f a c t o r 1 6 i m p e r f e c t i o n 1,7,22,44,99 i n d e x 174,181,182,183,184,185 i n e f f i c i e n c y 104,108 i n t e g r a t i o n 171,186 model 16 p o r t f o l i o 7,12,163,164,169,171,191 p o r t f o l i o p r o x y 165,167 p r i c e 97,103 p r i c e o f r i s k 7,8,9,14,28,29

, s e c o n d a r y 112,117 s y n c h r o n i z a t i o n 98,100,108 v a l u e 102,124

M a t u r i t y 102,108,109,112,115,120,124 M a x E m i n ( - c r i t e r i o n ) 67,68,69,70,71 Maximum l i k e l i h o o d 4,178,179,184,185,186,187 Mean a b s o l u t d e v i a t i o n 15 M e a n - s e m i v a r i a n c e 7,11,13 M e a n - v a r i a n c e 4,7, 8,1 1 ,1 7,21 , 24, 30,47,1 91

e f f i c i e n c y 164,165,166 Median 10,15 Me f i r s t r u l e s 150,151,153 M i l d e ' s a p p r o a c h 136,137 Minkowski-Farkas-Lemma 200 Minmax 3,59,6 7,70 M i s p r i c i n g ( s i g n a l ) 9 8,101,102,104,106,110 Mode 15 M o d i g l i a n i - M i l l e r theorem 1,139,193 Moment 15,17

g e n e r a t i n g f u n c t i o n 48 M o n i t o r i n g c o s t s 143,153 M o n o p o l i s t i c 9,14,27 Mortgage 150,152 M o t i o n e q u a t i o n 89,123,124

225

M u l t i p l i c a t i v e s e p a r a b l e 31 M u l t i v a r i a t e n o rmal 7,23,25,55,178

N e o c l a s s i c a l a p p r o a c h 138,143 Net income 34 N o - a r b i t r a g e 95 Non-hedging model 94 N o n p a r a m e t r i c t e s t 115 N o n - s a t u r a t e d 192,195 Normal ( d i s t r i b u t i o n ) 3,7,15,19,20,21,24,25,34,48,56,60,67,81,86,89,

92,95,115,125 NYSE (New Yo r k S t o c k Exchange) 101,109,165

O d d - l o t p r i c e 106 O l i g o p o l i s t i c 9,14 OLS ( O r d i n a r y L e a s t Squares) 187 O m i t t e d a s s e t 4,163,165,170,181,182 One f a c t o r market model 16 0PM ( O p t i o n P r i c i n g Model) 81,107 O p t i o n v a l u a t i o n 79,81,90,94

, A m e r i c a n 80 , European 80

i n s t r u m e n t s 80 , l i s t e d 93,111

p r i c i n g 2,79 O r d i n a l p a r a m e t e r 10,15 OTC ( O v e r - t h e - C o u n t e r ) 103,104,117 Out-of-the-money 9 9,109,112,113,114,115,120 O v e r p r i c e d 9 7,108,112,116,118 O v e r v a l u e d 89,114,116,120,121

P a r t i a l d i f f e r e n t i a l e q u a t i o n 7, 20, 23, 31 , 48 ,93 e q u i l i b r i u m 3,89 i n f o r m a t i o n 66,67,72 moment 11 u n c e r t a i n t y 72

P a y o u t - p r o t e c t e d 85,103 P e r f e c t ( c a p i t a l ) m a r k e t 81,105,139 P e r f e c t l y d i v i s i b l e 23 P h i l a d e l p h i a S t o c k Exchange 104 P h i l a d e l p h i a S t o c k Exchange F o r e i g n C u r r e n c y O p t i o n M a r k e t 120 P o i s s o n 67 P o l y h e d r o n 67 P o r t f o l i o 3,4, 21,25,27,28,31 ,56,63,64,92,93,95,111 ,168

c o m p o s i t i o n 25,92,165 s e l e c t i o n 2,3,10,190 s t r a t e g y 9 8

P r e d i c t a b i l i t y t e s t 107,108,111 P r e d i c t i o n e r r o r 108,111,114,115 P r e f e r e n c e a s s u m p t i o n s 94

-based 94,95 - f r e e 79,80,81,94,95 f u n c t i o n a l 10,13,15,19,20,23,31

P r e f e r r e d s t o c k 97 Preknowledge 3,56,65,68,75 Premature e x e r c i s e 84,85,93,96,105 P r e s e n t v a l u e 82,85,90,91,103,154 P r i c e t a k e r 22,44 P r i n c i p a l 147 P r i o r d i s t r i b u t i o n 3,56,59,60,61,63,66,67,68,72,75 P r o d u c t i o n 192,199 P r o f i t 103,104,105,106,107

226

, paper 105,118 P r o g r e s s i v e t a x a t i o n 35 P r o p e r t y r i g h t s 146 P r o p o r t i o n a l r i s k a v e r s i o n 95

t a x s c h e d u l e 34,35 Pseudo-American l o w e r bound 101,102,103 P u t ( o p t i o n ) 81,83,85,93,96,100,104,107,119,120 P u t - c a l l p a r i t y 85,104,120 P u t v a l u e 84

Q u a d r a t i c u t i l i t y 9,18,19,31,81

Rate o f r e t u r n 89,91,108,125 r e q u i r e d 9

, r i s k - f r e e 8,22,98 R a t i o n a l i t y 9,20,47,81,86 R a t i o n a l p o r t f o l i o models 10 R a t i o n i n g 46,136,138,144 R e a l e s t a t e 147,165 R e c o m p o s i t i o n 198 R e f i n a n c e m e n t 138 R e g i s t e r e d mortgage 152 R e g r e s s i o n 104,111,112,114,116,170,174,175,184 Re v e r s e c o n v e r t e r 85 R i g h t s o f f e r i n g 97 R i s k 191

- a d j u s t e d 30,98,100 a v e r s i o n 7,17,19,21,25,27,36,47,55,95

, d i f f u s i o n 93 - f a c t o r 166

, jump measure 10,11 n e u t r a l i t y 14,94,95,140 premium 166,169

, s y s t e m a t i c 117 - t a k i n g 35

R i s k l e s s i n t e r e s t r a t e 82,94,123 bond 89 h e d g i n g 95

R i s k n e u t r a l v a l u a t i o n r e l a t i o n s h i p 34 Ro b u s t n e s s 107,109,111

Sample s i z e 102,103,107 S c h o l e s - W i l l i a m s ( p r o c e d u r e ) 175,176,177 S e a r c h i n g c o s t 136,137 SEC ( S e c u r i t i e s and Exchange Commission) 95,119 S e c u r e d d e b t 137,139 S e c u r i t y agreement 4,135 S e g m e n t a t i o n 4,163,166,167,171 S e l f - f i n a n c i n g 87,94 S e m i - e x p e c t a t i o n 15 S e m i - i n t e r q u a r t i l e r ange 15 S e m i s t a n d a r d - d e v i a t i o n 11 S e m i v a r i a n c e 11,12,13,14 S e p a r a b l e p r e f e r e n c e f u n c t i o n a l 31,32 S e p a r a t i o n p r o p e r t y 25,32,73

theorem 190,198,200 Share 9,22,87,98,103

p r i c e 27,28 S h a r p e - L i n t n e r model (= CAPM) 163,154,169,170,171,175,177,178,180,

181,184,185 S h o r t hedge p o s i t i o n 106

227

S h o r t s a l e s r e s t r i c t i o n 7,42,43,44 s e l l i n g 3,18,22,26,23,40,41,42,56,71,72,103 - t e r m T r e a s u r y Bond 119

S h r i n k i n g 116,122 S i m u l a t e d d a t a 108 Skew 111 S l a c k n e s s - c o n d i t i o n 42 S l o p e c o e f f i c i e n t 114 S m a l l

economy 4 f i r m a s s u m p t i o n 9,14,45

S p h e r i c a l l y d i s t r i b u t e d 17,18 S p o t p r i c e 199 S p r e a d i n g s t r a t e g y 118 S t a b l e d i s t r i b u t i o n 15,16 S t a n d a r d d e v i a t i o n 108 S t a t e (of n a t u r e s , o f t h e w o r l d ) 154,196 S t a t e - p r e f e r e n c e - a p p r o a c h 59 S t a t i o n a r y 109 S t e i n ( e s t i m a t o r ) 116 S t o c h a s t i c dominance 7,18,20 S t o c k 87,103,108,122

p r i c e 82,85,86,89,90,91,92,94 S t r i k e p r i c e 81,108,114,115,122

Tangency p o r t f o l i o 12,163,169 T a r g e t

r a t e 12,14 v a l u e 11,13,15

T a s t e 9,21,191 Tax 1,3,4,22,34,35,36,37,38,81,98,99,142,156,166

d e d u c t i b l e 34 Tender o f f e r 92 Term d e p o s i t 193,201

s t r u c t u r e 96 T e s t 4,9 8,99,101,104,107,108,109,111,113,116 T h i n n e s s 107 T h i n t r a d i n g 174,175,177,178,186 Time l a g 98,101 Time premium 82 Time v a l u e 83 T o r o n t o S t o c k Exchange 173,174 T r a d i n g f l o o r 99,106

s t r a t e g y 98,102,103,118 T r a n s a c t i o n s c o s t s 1,94,98,101,102,104,106,107,117,119 T r e a s u r y B i l l o p t i o n s 1 21 T w o - l e v e l (approach) 59,60,62,65

U n b i a s e d n e s s 107,108,113 U n c e r t a i n t y 55,59,60,66,77,81,121,136,154,191,192 U n d e r p r i c e d 9 7,108,116,118 Undervalued 89,112,113,114,116 U n i t o f time 123 U n p r o t e c t e d 84 Up jump 123 Up movement 90 U.S. 41,9 3,99,101,104,163,166,171,181,184,185,186 U t i l i t y

, e x p o n e n t i a l 3,21,55,59 f u n c t i o n 10,18,47,55,94

, l i n e a r 10

228

U t i l i t y

, q u a d r a t i c 9,18,19,81

V a l i d i t y 97,99,107 V a r i a n c e 11 ,15,89,90,92,93,122,1 26

r e d u c t i o n 45 V o l a t i l i t y 30,91 ,92, 108, 109,1 1 2, 1 1 3,1 1 4,1 1 6, 1 21 ,1 22,1 26 W a l l S t r e e t J o u r n a l 120 Wa r r a n t 97 Zero b e t a 178 Zero coupon d e b t 1 24