Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Disclosure, risk sharing, and valuation under asymmetric information Hughes, Patricia J. 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A1 H83.pdf [ 7.45MB ]
Metadata
JSON: 831-1.0096410.json
JSON-LD: 831-1.0096410-ld.json
RDF/XML (Pretty): 831-1.0096410-rdf.xml
RDF/JSON: 831-1.0096410-rdf.json
Turtle: 831-1.0096410-turtle.txt
N-Triples: 831-1.0096410-rdf-ntriples.txt
Original Record: 831-1.0096410-source.json
Full Text
831-1.0096410-fulltext.txt
Citation
831-1.0096410.ris

Full Text

DISCLOSURE, RISK SHARING, AND VALUATION UNDER ASYMMETRIC INFORMATION by PATRICIA JANE HUGHES B.A., Duke Un ivers i ty , 1965 M.B.A., The Un ivers i t y of P i t t sburgh , 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF GRADUATE STUDIES (Faculty of Commerce and Business Administrat ion) We accept t h i s thes is as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JUNE, 1984 Q P a t r i c i a Jane Hughes, 1984 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Q T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e i i ABSTRACT This d i s se r t a t i on analyzes r i sk sharing between an entrepreneur of a f i rm and i t s i nves to rs , and valuat ion of the f i rm when there is an informational asymmetry between the entrepreneur and i n ves to r s . Two types of informational asymmetries are examined: the adverse se l e c t i on problem and the moral hazard problem. In the adverse se l ec t ion problem, the entrepreneur knows an exog-enous parameter of value which is unobservable by i nves to r s . While maximizing his own wel fare , he se lec ts a level of d i r ec t d i sc losure in order to communicate his information to i nves to rs . A v e r i f i c a t i o n ro le for a t h i r d party is developed such that the v e r i f i e d d i sc losure i s c red ib le due to a cos t l y penalty which is imposed i f the d i s c l o -sure is f a l s e . An equ i l ib r ium is derived in which investors co r r e c t l y value the f irm a f te r observing the d i s c l o s u r e . In the moral hazard problem, f irm value is dependent upon the behavior of the entrepreneur where that behavior is unobservable. The entrepreneur se lec ts cos t l y ownership in his own f irm to c red ib l y communicate his behavior to i n ves to r s . An equ i l ib r ium is der ived in which investors co r rec t l y value the f i rm a f te r observing the entrepreneur 's investment p o r t f o l i o . In the conc lus ion , the two informational problems are integrated in order to ind ica te the s im i l a r nature of the problems. i i i TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES v ACKNOWLEDGEMENTS vi CHAPTER ONE. INTRODUCTION 1 CHAPTER TWO. THE ADVERSE SELECTION PROBLEM 5 Introduction 5 1. The Adverse Se lect ion Problem 5 2. The Adverse Se lect ion Problem in the Capita l Market. . 11 3. The Role of Accounting Under Adverse Se l e c t i on . . . . 18 CHAPTER THREE. THE ROLE OF THE INVESTMENT BANKER IN THE NEW ISSUES MARKET 27 Introduct ion 27 1. S igna l ing and the New Issue Market 27 2. D isc losure and Contingent Contracts 29 3. Intermediation and Asymmetric Information 36 4. The Role of the Investment Banker Under Asymmetric information 43 5. The Regulatory Environment 60 i v CHAPTER FOUR. SIGNALING BY DIRECT DISCLOSURE: A BIVARIATE SIGNALING MODEL 67 Introduct ion 67 1. Risk Sharing in a Perfect Market 67 2. Risk Sharing Under Asymmetric Information 77 3. S igna l ing through Direct D isc losure 82 4. Empir ical Implicat ions of the S ignal ing Model . . . . 120 CHAPTER FIVE. RISK SHARING AND VALUATION UNDER MORAL HAZARD. . 126 Introduct ion 126 1. The Pr incipal-Agent Problem 126 2. The Pr incipal-Agent Problem in a Market 130 3. Risk Sharing and Valuat ion With Moral Hazard. . . . 144 4. An Example 163 5. Empir ical Implicat ions 168 CHAPTER SIX. RISK SHARING AND VALUATION UNDER ADVERSE SELECTION AND MORAL HAZARD 171 BIBLIOGRAPHY 181 APPENDIX 186 Appendix 1. The P o r t f o l i o Problem of the Underwriting Syndicate 186 Appendix 2. Second-Order Condit ions to the B ivar ia te S igna l ing Model 189 Appendix 3. Second-Order Condit ions to the Moral Hazard Problem Problem 199 V LIST OF FIGURES Page Figure 3.1 Poster ior D i s t r i bu t i on of p 35 3.2 Of fer ing Pr ice Function 55 4.1 Equi l ibr ium S igna l ing Schedules 81 4.2 Cost of C e r t i f i c a t i o n Function for D i f f e ren t Levels of a 2 87 4.3 x(a,y) Inference Schedule 108 2 4.4 S ignal ing u,o by Jo int Choices of cx,y . . . . 112 5.1 Perqu is i te Transformation Function 148 5.2 Choice of F(a*) 151 5.3 The Entrepreneur 's F(a) Choice 152 vi ACKNOWLEDGEMENTS I want to thank the ind iv idua l members of my d i s se r t a t i on commit-tee who advised me: Jerry Feltham, whose comments, and questions about my work helped me to think more i n t u i t i v e l y about the problems I was addressing and to reach a deeper level of understanding; Rob He inke l , who spend many hours with me l i s t e n i n g to and d iscuss ing my ideas and work in the e a r l i e r stages of my research; and Rex Thompson, who asked me questions which made me think about my work from a d i f f e r en t perspect i ve . I could not have solved the b i va r i a t e s igna l i ng model of Chapter Four without the mathematical help of Eduardo Schwartz. I am very grateful to the accounting f i rm of D e l o i t t e , Haskins, & S e l l s for f i nanc i a l support while I wrote th i s d i s s e r t a t i o n . F i n a l l y and most important ly , I thank my husband and three ch i ld ren who never stopped encouraging me during these past yea r s . 1 CHAPTER ONE INTRODUCTION The s e c u r i t i e s market provides the l i n k between the consumption and investment dec is ions of ind iv idua l consumers and the product ion and investment dec is ions of f i rms. A fundamental separat ion r esu l t [Fama and M i l l e r , Ch. 4] in economics and f inance i s that in a per -f ec t and complete market the object ive of the f i rm should be to maximize the wealth of i t s shareholders. The f i rm ( i . e . , i t s man-agers) should d isregard the ind iv idua l preferences of i t s d iverse shareholders by making product ion , investment, and f inanc ing d e c i -s ions which maximize the market value of the f i rm ' s s e c u r i t i e s . Secur i ty holders then w i l l make t he i r ind iv idua l consumption and investment dec is ions according to t he i r ind iv idua l preferences. Therefore s u f f i c i e n t condi t ions fo r maximal e f f i c i e n c y (or maxi-mum soc ia l welfare) in the economy in terms of a l l o ca t i ons of r e -sources among firms and of wealth among ind i v idua l s are: 1. Perfect and complete markets 2. Firms maximize market value. When these s u f f i c i e n t condi t ions are s a t i s f i e d , there i s no demand or ro le fo r informat ion. In order for there to ex i s t any ' s o c i a l value ' to in format ion, i t i s necessary that there ex i s t a v i o l a t i o n of the per fec t markets or complete markets assumption. If f u l l a l l o ca t i ona l e f f i c i e n c y i s poss ib le in the absence of in format ion, then that information cannot be used to make any ind iv idua l bet ter o f f without impair ing the welfare of another i n d i v i d u a l . I f , however, there does ex i s t a market imperfect ion or incompleteness, i t i s poss ib le that 2 the add i t ion of information to the economy w i l l lead to a Pareto-improvement in a l l o ca t i ons of wealth and resources. In a per fec t cap i t a l market, information i s c o s t l e s s l y and simultaneously ava i l ab le to a l l market pa r t i c i pan t s . One poss ib le market imperfect ion i s that information i s an economic good which i s not c o s t l e s s l y ava i l ab le to a l l market pa r t i c ipan t s because i t s a c q u i s i t i o n or reve la t ion i s cos t l y . Such an imperfect ion can r e su l t in an asymmetry of information between i n d i v i d u a l s ; where information d i f fe rences can be about an exogenous c h a r a c t e r i s t i c of product qua l i t y (the adverse se l e c t i on problem), or about an unobservable ac t i on on the part of one ind iv idua l which a f f ec t s product qua l i t y (the moral hazard problem). Both the adverse se l e c t i on and the moral hazard problems can ex i s t between the manager of a f i rm and i t s shareholders, and e i the r information problem may generate a demand from shareholders fo r informat ion. S t i g l i t z (1982) has summarized the r e l a t i onsh ip between i n f o r -mation and p r i c e s : " It i s c l ea r that centra l to an understanding of the cap i t a l market i s an ana lys is of 1. the incen t i ves , wi th in a market economy, fo r an ind i v idua l to acquire in format ion; 2. the extent to which market pr i ces r e f l e c t the information of informed i n d i v i d u a l s ; and 3. the ro le that market p r i ces play in determining the behavior of managers of f i r m s . " (p.120) 3 The t yp i ca l l y-de f i ned ro le of accounting as the measurement and communication of economic information re levant to dec is ion making impl ies that there i s a market imperfect ion which generates a demand fo r informat ion. In order to determine whether f i nanc i a l repor t ing w i l l serve as a v iab le supply of information demanded by inves to rs , the nature of accounting report ing can be re la ted to the issues def ined by S t i g l i t z . An ex ante informational asymmetry can be assumed to ex i s t which obviates the f i r s t i ssue. Such informational d i f fe rences a r i s e due to the manager being an i ns ide r and the share-holders outs iders to the f i r m ' s operat ions. The second and t h i r d can be addressed by analyz ing whether market p r i ces w i l l motivate the manager to communicate ins ide information through f i n anc i a l repor t ing and i f such communication i s perceived by investors as c red ib le so that market p r i ces adjust to r e f l e c t the informat ion. The environment in which f i nanc i a l repor t ing occurs i s descr ibed by Beaver (1981) as cons i s t i ng of f i v e cons t i tuenc ies : i nves to rs , management, information in te rmediar ies , r egu la to rs , and aud i tors . Due to the existence of r egu l a t i on , f i nanc i a l report ing i s manada-tory . However, i t i s poss ib le that incent ives ex i s t in the market for a manager to communicate vo l un t a r i l y through f i nanc i a l reports while at the same time act ing in his own s e l f i n t e res t . The purpose of th i s d i s s e r t a t i on i s to analyze such incent ives fo r d i sc losure and the r e su l t i ng impact on secur i t y p r i ces when the manager has informa-t ion about the value of the f i rm which investors do not have. The manager's informational advantage a r i ses because he can observe a c h a r a c t e r i s t i c of the f i rm which i s unobservable by investors due to his pos i t i on in the f i rm , or because he can a f f e c t the value of the 4 f i rm through his act ions which are unobservable by inves tors . The f i r s t three pa r t i e s descr ibed by Beaver have major ro les in the ana lys is in the fo l lowing chapters. Auditors are assumed to be an information intermediary and regulators are t angen t i a l l y inc luded in that t he i r economic ro le i s that of enforc ing contracts . Chapter Two descr ibes the formulat ion of and so lu t ion of the adverse se l e c t i on problem in the economics l i t e r a t u r e ; and a survey of f inance and accounting l i t e r a t u r e addressing the problem is p re -sented. In Chapter Three, the ro le of an information intermediary under asymmetric information i s developed. The resu l t s of Chapter Three are used to formulate and solve a b i va r i a t e s i gna l i ng problem in Chapter Four. Chapter Five analyzes the problem of an informa-t iona l asymmetry about unobservable managerial behavior in the cap-i t a l market. A synthesis of the adverse se l ec t i on problem of Chapter Four and the moral hazard problem of Chapter Five i s presented in Chapter S ix. •5 CHAPTER TWO THE ADVERSE SELECTION PROBLEM: A LITERATURE REVIEW INTRODUCTION This chapter reviews the formulat ion of the adverse se l e c t i on problem and so lut ions to the problem in the economics, f inance , and accounting l i t e r a t u r e . In Sect ion 1, the problem and several s o l u -t ions to resolve the problem are d iscussed. L i te ra ture on the ad-verse se l e c t i on problem in cap i t a l markets i s reviewed in Sect ion 2. Sect ion 3 discusses a ro le fo r accounting under asymmetric informa-t i o n . 1. THE ADVERSE SELECTION PROBLEM The adverse se l ec t i on problem was formulated by Aker lo f (1970) as an informational asymmetry between buyers and s e l l e r s in a product market. The s e l l e r knows the exogenously determined qua l i t y of the product he brings to the market, while buyers are unable to observe the qua l i t y . Aker lo f presents the example of the used car market to i l l u s t r a t e th i s information problem. If buyers know only the d i s t r i -bution of used car q u a l i t y , they w i l l not be w i l l i n g to pay more than the p r i ce of an average-qual i ty car fo r any p a r t i c u l a r car . S e l l e r s of cars of above-average qua l i t y w i l l therefore withdraw t h e i r cars from the market due to t he i r i n a b i l i t y to reveal qua l i t y and receive an above-average p r i c e . As a consequence, the average qua l i t y of the cars remaining in the market w i l l dec l i ne , which leads to the w i th -drawal of cars with qua l i t y above the new average. This process continues un t i l the only cars remaining in the market are those of 6 the lowest qua l i t y . The product market f a i l s . Aker lo f suggests that i n s t i t u t i o n s such as guarantees, l i c e n s i n g , and reputat ion ex i s t so as to e l iminate the market f a i l u r e which can r e su l t from uncerta inty as to product qua l i t y . As Aker lof suggests, s e l l e r s of products of above-average qua l -i t y have incent ives to develop i n s t i t u t i o n s which w i l l enable them to s e l l t h e i r products at above-average p r i c e s . Reputation i s a charac-t e r i s t i c which a s e l l e r can earn over time a f t e r repeated market t ransac t ions . I f a s e l l e r enters the market fo r the f i r s t t ime, or does not intend to enter the product market aga in , then reputat ion cannot ex i s t . In the used car example, reputat ion cannot reduce the adverse se l ec t i on problem for an ind iv idua l s e l l i n g his personal used ca r , or a newly-formed used car dea lersh ip o f f e r i ng i t s f i r s t used car fo r sa le . For such an i n i t i a l or one-time entry into the market, mechanisms such as guarantees and l i c ens i ng may appear as v iab le means of e l im ina t ing the adverse se l e c t i on problem. There are two general types of mechanisms which may prevent A k e r l o f s extreme market f a i l u r e . The f i r s t general so lu t ion i s to increase average product qua l i t y so that the lemons are not the sole surv i vors . A second mechanism is one which resu l t s in d i s c losure of product qua l i t y to buyers. Examples discussed below of the f i r s t type are Lei and (1979) and Heinkel (1981), and of the second are Grossman (1981) and Spence (1974) Leland (1979) examines l i c ens i ng and the imposi t ion of minimum qua l i t y standards in markets charac ter ized by adverse s e l e c t i on . He looks at the e f f e c t s of the information asymmetry on soc ia l we l fa re , where soc i a l welfare i s def ined r e l a t i v e to a s ing le product and i s 7 maximized when there i s no consumer or producer surp lus . He shows that uncerta inty about product qua l i t y serves as a hinderance to trade with the r e su l t that product qua l i t y suppl ied to the market i s less than that which is s o c i a l l y opt imal . He then shows that soc ia l welfare can be improved i f minimum qua l i t y standards are imposed such that the supply of poor qua l i t y products i s e l iminated , thereby r a i s i n g average qua l i t y . The unravel ing seen in A k e r l o f ' s used car market w i l l a lso occur in Lei and's market such that a l l products w i l l have the same qua l i t y which i s that prescr ibed as the minimum by the regulatory group. It i s necessary to Leland's model tha t the regu la -tory agent be able to observe qua l i t y ex ante in order to enforce the regu la t ion . Consequently the set of markets fo r which l i c e n s i n g w i l l mit igate the adverse se l ec t i on problem is r e s t r i c t e d . In He inke l ' s (1981) model, product qua l i t y i s exogenous, but can be increased by the s e l l e r through cos t l y maintenance. Buyers are unable to observe qua l i t y or maintenance. Se l l e r s of poor qua l i t y products are induced to invest in cos t l y maintenance, thereby i n -creas ing average qua l i t y in the market, due to the imposi t ion of an imperfect ex post t es t of qua l i t y and a penalty i f the t es t reveals that qua l i t y i s below an acceptable l e v e l . Like Lei and, Heinkel f inds that soc ia l welfare i s increased through the t e s t i ng and pena l -ty mechanism because of the increase in average qua l i t y of the pro -duct suppl ied to the market. Although Heinkel does not state i t as an assumption, i t i s essent ia l to his model that buyers know to ta l maintenance expenditures in order to know average post-maintenance qua l i t y . I f they do not know such expenditures, the market w i l l f a i l so that even the lowest qua l i t y product is removed from the market. 8 In He inke l ' s d i scuss ion of his numerical so lu t i ons , he does not re fe r to two unusual and i n t e r es t i ng r e su l t s : with the imperfect t e s t i ng technology, d i f f e r e n t product q u a l i t i e s ex i s t in the market and consumers are bet ter o f f than they would be under per fec t informa-t i o n . Presumably the f i r s t r e su l t holds because of the noise in the t e s t i ng technology, and the second because consumer welfare i s i n -creas ing in qua l i t y and poor qua l i t y has been e l iminated. The set of markets fo r which the ex post t e s t i ng w i l l mit igate the adverse se l ec t i on problem a lso i s r e s t r i c t e d because the s e l l e r must be able to improve the qua l i t y of his product and ex post t e s t i ng must be f e a s i b l e . The e l im ina t ion of low qua l i t y products may reduce the adverse s e l e c t i on problem in p a r t i c u l a r markets. A second type of so lu t ion involves communication of product qua l i t y . Grossman (1981) analyzes the information provided by d i r e c t d i s c losure and product warrant ies. He f i r s t looks at the market fo r products fo r which qua l i t y i s cos t -l e s s l y v e r i f i a b l e ex post and f inds that a s e l l e r w i l l d i s c l ose the exact qua l i t y of his product and o f f e r a f u l l guarantee. Overstate -ment of product qua l i t y i s e l iminated because a s e l l e r w i l l not guarantee such a d i s c l o su r e , and such lack of guarantee w i l l be in terpre ted by buyers as misrepresentat ion. Understatement of p ro -duct qua l i t y a lso w i l l not occur because a s e l l e r i s always bet ter o f f by a t ru th fu l d i sc losure ( e . g . , a statement such as " t h i s box contains at l eas t s ix oranges" w i l l be in terpreted by buyers as there being s ix oranges in the box). For such products , buyers w i l l know product q u a l i t y , and there i s no ro le fo r d i sc losure laws. However, ex post v e r i f i c a t i o n of qua l i t y may be p r o h i b i t i v e l y cos t l y fo r some 9 products. For these products , there may occur a future observable event with a p r o b a b i l i t y of occurrence dependent only on product q u a l i t y , such as automobile breakdown. The s e l l e r then can o f f e r a warranty under which a payment i s made to the buyer i f the event occurs , where the s e l l e r knows the p r o b a b i l t i y of breakdowns fo r his product. When buyers are r i s k averse, the r e su l t i ng equ i l ib r ium pr i ce and warranty o f fe red provide f u l l insurance to consumers. While consumers cannot i n f e r qua l i t y or p r o b a b i l i t y of breakdown from the o f fe red con t rac t s , they know that they are f u l l y insured as to product qua l i t y and therefore market f a i l u r e is avoided. In Spence's (1973, 1974) job-s igna l ing model, the adverse s e l e c -t i on problem i s e l iminated through the s e l l e r ' s investment in a cos t l y observable s ignal which i s used by the buyer in va luat ion of the product such that the buyer 's inference i s s e l f conf i rming. The se t t i ng i s a job market in which workers ( s e l l e r s ) have d i f f e r e n t endowments of an unobservable a t t r i bu te such as a b i l i t y (qua l i t y ) which determines t he i r p roduc t i v i t y . In the absence of asymmetric in format ion, prof i t-maximiz ing employers (buyers) pay each worker a wage equal to the worker 's p roduc t i v i t y . Market f a i l u r e i s avoided because workers can invest in a cos t l y s ignal co r re l a ted with a b i l -i t y , such as educat ion, when the leve l of education se lected i s observable and thus can serve as a subs t i tu te fo r unobservable qua l -i t y in the wage schedule o f fe red by employers. A more prec ise des-c r i p t i o n of Spence's model fo l lows. Let n = underly ing a b i l i t y s(n) •= p roduc t i v i t y 10 y = education w(y) = wage schedule c (y ,n) = cost of education Spence proves that education w i l l serve in the market as a s ignal fo r p roduc t i v i t y such that : i ) Workers se l ec t education to maximize net income, w1 = Cyj and i i ) employers co r r e c t l y i n f e r p roduc t i v i t y from the leve l of education and o f f e r a wage schedule dependent on y a lone, w(y) = s(y(n)) = s(n) when ce r t a in cost condi t ions are s a t i s f i e d . The necessary cost condi t ions are 1) c y > u > t n 6 c o s t ° f education i s increas ing in the leve l s e l e c t ed , and 2) ^ n ^ ' m a r 9 i n a ^ c o s t ° f education i s decreasing in a b i l i t y . The second cond i t ion i s the c r i t i c a l cond i t ion which prevents mis-representat ion. The existence of the s i gna l i ng mechanism permits buyers to pe r f e c t l y i n f e r qua l i t y . A l l s e l l e r s except that with the lowest qua l i t y product invest in the cos t l y s ignal because there are benef i ts to s i gna l i ng . For the lowest qua l i t y s e l l e r there are no benef i ts to be gained from cos t l y s i gna l i ng . The adverse se l ec t i on problem i s f u l l y reso lved. However, Spence shows that the r e su l t i ng a l l o c a t i o n of resources may be suboptimal compared to the a l l o c a t i o n under per fec t information due to an overinvestment in the s i g n a l . 11 2. THE ADVERSE SELECTION PROBLEM IN THE CAPITAL MARKET The economic r e su l t of the mechanism discussed in Sect ion 1 is a r e d i s t r i b u t i o n of wealth among buyers and s e l l e r s of a p a r t i c u l a r product. While the welfare of buyers and s e l l e r s has been improved, nothing can be sa id about the e f f e c t on a l l o ca t i ons of wealth in the economy. As an example, consider the f a i l u r e of A k e r l o f s used car market. While a l l o ca t i ons of wealth among buyers and s e l l e r s of used cars may be improved i f used car dealers o f f e r Grossman's warranties against future breakdown, i t cannot be sa id that the r e su l t i ng re -a l l o c a t i o n is Pareto-optimal in the economy where many ind i v idua l s and firms are making investment and product ion dec i s ions . It could be poss ib le that i t i s Pareto-optimal fo r the used car market to f a i l so that used cars are scrapped. In order to move from questions about micro e f f i c i e n c y in a product market to those about macro e f f i c i e n c y in the economy, the impact of the adverse se l ec t i on prob-lem and i t s r eso lu t ion on product ion and investment dec is ions of a l l economic agents must be considered. The ro le of secur i t y pr i ces in the a l l o c a t i o n of resources in an economy was descr ibed in Chapter One. The a l l o ca t i ona l ro le of secur i t y p r i ces w i l l be impaired in the presence of a market imper-f e c t i on such as asymmetric information between issuers of s e cu r i t i e s and inves tors . Therefore the existence of an adverse s e l e c t i on problem in the cap i t a l market and the means of reso lv ing the problem w i l l have an impact on the e f f i c i e n c y of a l l o ca t i ons wi th in the economy. An adverse se l ec t i on problem ar i ses in the cap i t a l market when the entrepreneur/manager of a f i rm i s endowed with ins ide information 12 about the value of his f i rm. Investors in the market know the d i s -t r i b u t i o n of f i rm va lues , but cannot observe the value of a p a r t i -cu lar f i rm. There are two types of models of mechanisms which may resolve the adverse se l e c t i on problem in the s e cu r i t i e s market. In both models, investors i n f e r value from an observable managerial ac t ion . The f i r s t type of mechanism i s a contingent contract s im i l a r to Grossman's guaranty and warranty cont rac ts . The manager se lec ts an act ion which investors observe and use to i n f e r value. A penalty fo r misrepresentat ion w i l l be imposed on the manager i f ex post observat ion of value or some event determined by value reveals that the manager was s igna l i ng f a l s e l y by his ac t ion . S igna l ing with a contingent contract i s genera l ly considered to be cos t l ess because appropriate pena l t i es induce t ru th fu l act ions and the s igna le r in such models i s r i s k neut ra l . The second type of model i s an exten-s ion of Spence's model where education was a s ignal of qua l i t y . The manager se lec ts an act ion which investors observe and use to i n f e r value. However th i s type of s ignal d i f f e r s from the contingent contract because the manager bears the cost of the ac t ion ex ante. The cost of the s ignal must be appropriate to induce t ru th fu l s i g n a l -ing in order to be used by investors in va lu ing the f i rm. As a consequence i t i s not necessary that value or some event determined by value i s observable ex post. Examples of f i nanc i a l s i gna l i ng models to be discussed are Ross (1977), which i s a model of con t i n -gent con t r ac t i ng , and Lei and and Pyle (1977) and Bhattacharya (1979), which have both a contingent contract and a cos t l y s i g n a l . Ross (1977) addresses the question of whether the Modig l ian i-M i l l e r p ropos i t ion that the value of the f i rm is independent of i t s 13 cap i t a l s t ruc ture would hold in an imperfect market where manager-ins ide rs possess ins ide information about f i rm value. In Ross 1 model, where f irms d i f f e r in va lue, the s e cu r i t i e s market w i l l f a i l as A k e r l o f s used car market f a i l e d because each manager knows the value of h is f i rm and investors know only the d i s t r i b u t i o n of values. The r i sk-neutra l manager's only act i s to se l ec t the amount of debt issued by his f i rm and he se lec ts a debt issue in order to maximize his compensation. A l i nea r managerial compensation scheme i s assumed in which the manager's end-of-period compensation i s an increas ing funct ion of the market p r i ce of the f i rm at the beginning of the pe r i od , and includes a penalty i f the f i rm is bankrupt at the end of the per iod . The manager s igna ls his f i r m ' s value through his debt choice in that a high value f i rm w i l l issue more debt than a low value f i rm. Investors i n f e r f i rm value from the amount of debt issued and the manager's compensation therefore i s increas ing in the amount of debt. Debt serves as a c red ib le s ignal because a low value f i rm which s igna ls high value through a large debt issue w i l l be unable to repay the debt at the end of the per iod and w i l l go bank-rupt , r e su l t i ng in a penalty imposi t ion on the manager. Since the compensation contract i s determined by an unspec i f ied t h i r d party which presumably a lso imposes the pena l ty , i t i s essent ia l that the t h i r d party i s able to observe the event of bankruptcy and that the occurrence of bankruptcy i s dependent only on f i rm value a f t e r debt has been issued. However the penalty w i l l never be imposed s ince the threat of imposi t ion i s assumed to be s u f f i c i e n t to deter f a l s e s i gna l i ng . The contingent contract of Ross' model i s s im i l a r to Grossman's warranty contract in that the warranty i s not contingent 14 on ex post v e r i f i c a t i o n of va lue, but on the observable event of bankruptcy which depends only on value. The motivat ions fo r the warranties d i f f e r . Grossman's warranty i s o f fe red to buyers of a product in order to increase the market p r i ce of the product which d i r e c t l y increases the s e l l e r ' s wealth. Ross's warranty i s o f fe red to e x i s t i n g owners of the product in order to increase the market p r i ce of the product which i n d i r e c t l y increases the manager's wealth and d i r e c t l y increases the product owner's wealth. Ross's cost of mispresentat ion i s d i s s i p a t i v e where Grossman's i s nond iss ipa t i ve . S igna l ing through such contingent contracts i s cos t l ess because the event 's p r o b a b i l i t y of occurrence depends only on value which i s t r u t h f u l l y communicated. The Mod ig l i an i-M i l l e r theorem that the value of a f i rm is dependent only on the d i s t r i b u t i o n of cash flows generated by i t s investments therefore i s i n v a l i d when investors cannot observe that d i s t r i b u t i o n . Firm value w i l l be dependent upon whatever c red ib le s ignal can be suppl ied to investors by managers. In Leland and Py le ' s (1977) s igna l i ng model an entrepreneur i s endowed with information about the value of a product ive technology and can acquire the cap i ta l necessary fo r investment in the techno l -ogy through i ssu ing r i s k l e s s debt or s e l l i n g equity in the future cash flows to be generated by the investment. In the absence of any market imper fec t ion , the r isk-averse entrepreneur would choose to s e l l a l l of the equity in the r i sky cash flows and invest in a wel l-d i v e r s i f i e d market p o r t f o l i o . However, investors do not know the value of the investment pro jec t and w i l l pay some average p r i ce fo r ownership in the p ro jec t / f i rm. The s ignal used by the entrepreneur to communicate his information i s ownership in his own f i rm which i s 15 perceived by the market as c red ib le because of the ex ante cost of the s ignal to the entrepreneur and an ex post penalty for f a l se s i gna l i ng . While Lei and and Pyle focus on the ex ante cost to the entrepreneur of bearing d i v e r s i f i a b l e f i rm-spec i f i c r i s k , i t i s the ex post penalty which makes the s ignal c r ed ib l e . The benef i ts of the s ignal are increases in wealth and the cost i s an increase in r i s k . The leve l of the s ignal se lected i s the level at which the marginal benef i t equals the marginal cost . To consider a simple example, consider two f irms with d i f f e r e n t underly ing ' t r ue ' values and V^. Let V. = true value of f i rm i R.j = f i rm s p e c i f i c r i s k of f i rm i a.j = percentage ownership of entrepreneur in his f i rm V - ) = market's inference of value based upon the s i gna l . Assume that ( i ) the r i s k f r ee rate of i n t e res t is zero ( i i ) > because of d i f fe rences in the expected value of future cash f lows, ( i i i ) V- i s independent of R. ( i v ) RH = R L = R If ot|_| = = a which s igna ls V^, then the increase in wealth at the time of s igna l i ng and the amount of f i rm-spec i f i c r i s k borne are the same for each entrepreneur. The entrepreneur who s igna ls f a l s e l y w i l l be pena l ized at the end of the per iod when aV^ > aV^. The s ignal w i l l be c red ib le i f the cost of f a l se s igna l i ng exceeds the bene f i t , or ( l-a)V(a) + aV H > Cost of R and ( l-a)V(a) + crV, < Cost of R 16 Investors i n f e r f i rm value through observat ion of the entrepreneur 's p o r t f o l i o dec i s ion and understanding of the cost to him of holding an und i ve r s i f i ed p o r t f o l i o . It i s hot necessary that the event upon which the penalty contract i s contingent i s observable because the penalty fo r f a l s e s igna l i ng i s imposed endogenously. The market's inference i s s e l f conf irming in that the react ion of the market to the s ignal i s an t i c ipa ted by the entrepreneur in his se l ec t i on of the s ignal and the inferences are cor rec t in the r e su l t i ng equ i l ib r ium. The ro le of dividends as a s ignal of expected cash flows has been analyzed by Bhattacharya (1979) who assumes that the manager of a f i rm is maximizing af ter-tax shareholders ' wel fare. The motivat ion fo r s igna l i ng i s s im i l a r to that of Ross: the manager of a product i s t r y i ng to maximize the welfare of owners of the product. The cost s t ructure i s s im i l a r to that of Lei and and Pyle: there i s an ex ante cost o f s i gna l i ng and an ex post penalty fo r f a l se s i gna l i ng . The d i s s i p a t i v e cost of dividends i s borne by shareholders in the per -sonal tax on div idend income which exceeds the tax on cap i t a l gains. The penalty fo r f a l s e s igna l i ng i s the cost to the f i rm of ' b a i l out' f inanc ing or forced l i q u i d a t i o n of assets i f the r ea l i z ed cash flow i s less than the promised div idend payment. At the time dividends are dec la red , the end-of-period cash flow i s a random var i ab le and therefore there i s some r i s k of a cash d e f i c i t under t ru th fu l s i g n a l -ing. The cost of such r i s k i s not re levant to the model because r i s k neu t r a l i t y i s assumed. As in the Ross model, i t i s not necessary that the r e a l i z ed cash flow i s observable. The ac t ion which the manager undertakes given a cash flow d e f i c i t must be observable to the market. As with the Ross and Lei and and Pyle models, the threat 17 of a penalty fo r f a l se s igna l ing induces t ru th fu l s igna l i ng and the market's inferences are s e l f conf i rming. The s igna l i ng models descr ibed in th i s sect ion s a t i s f y the two c r i t e r i a essent ia l fo r s igna l i ng to be a v iab le means of reso lv ing asymmetric informat ion: the s igna le r must be motivated to undertake the a c t i v i t y and the s ignal must have a cost s t ructure which makes i t c r ed ib l e . Each of the papers had a d i f f e r e n t mot ivat ion: Ross's manager maximized the expected value of his compensation, Lei and and Py le ' s entrepreneur maximized his expected u t i l i t y , and Bhatta-charya 's manager maximized shareholders ' wealth. The Leland and Pyle model addressed the adverse se l ec t i on problem about va luat ion of a product o f fe red fo r sa le . Ross and Bhattacharya address the problem of va luat ion of a product owned. The Leland and Pyle s igna le r is s e l l i n g the product where the Ross and Bhattacharya s igna le rs manage the product. Potent ia l shareholders and e x i s t i n g shareholders have d i f f e r e n t object ive funct ions . Current shareholders are bet ter o f f i f share p r i ce i s maximized so that they can make optimal consumption and investment dec i s ions . Potent ia l shareholders c l e a r l y would l i k e shares to be undervalued, but they cannot d i s t i ngu i sh undervalued shares from overvalued shares. Therefore , the adverse se l e c t i on problem in the cap i t a l market i s of a d i f f e r e n t nature than that in a product market because the shares are not consumed as other products are. The three papers discussed in th i s sect ion are the seminal f i nanc i a l s igna l i ng models and have spawned much in te res t in s i g n a l -ing in the cap i t a l market. They ignore or dismiss any ro le fo r communication of ins ide information through accounting reports . 18 Bhattacharya s t a tes , "We ignore the incorporat ion of other sources of information ( e . g . , accountant 's reports ) on the ground tha t , taken by themselves, they are fundamentally unre l i ab le ' s c reen ing ' mechanism because of the moral hazard involved in communicating p r o f i t a b i l i t y . " Such a statement i s inherent ly f a l s e s ince the f i nanc i a l s igna l i ng models use contingent contracts to induce t ru th fu l s i gna l s . Truthfu l communication through accounting reports presumably could be induced through appropriate contingent contracts . 3. THE ROLE OF ACCOUNTING UNDER ADVERSE SELECTION Bhattacharya (1979) dismissed any ro le fo r accounting reports under asymmetric information because they are ' v i t i a t e d by moral hazard ' . However, Bhattacharya (1980) states that accounting reports may be c red ib le ind i ca to rs of ex post p r o f i t a b i l i t y f ree of moral hazard. He develops a nondiss ipat ive s igna l i ng model in which d i v i -dends (or earnings forecas ts ) are cos t l ess s igna ls of f i rm value at the beginning of a per iod when end-of-period cash flows can be cos t -l e s s l y communicated due to the absence of moral hazard in accounting reports . The manager's ob ject ive funct ion i s to se l ec t a div idend to maximize the value of the f i rm at time zero and at time one. The market i n fe r s time zero value as a funct ion of the leve l of promised d i v idend , and penal izes time one value i f the ex post cash flow ind ica tes f a l se s i gna l i ng . I f a low value f i rm declares a large div idend payment, i t w i l l be valued by the market as a high value f i rm at time zero. However, the penalty imposed by the market at time one when cash flow i s observed w i l l be of s u f f i c i e n t s i ze to deter f a l s e s i gna l i ng . A comparison of Bhattacharya (1979) and 19 Bhattacharya (1980) w i l l ind ica te that i t i s not true that the f i r s t model i s d i s s i p a t i v e and the second nondiss ipat i ve . I f taxes are e l iminated in the f i r s t model as they are in the second, the ro le df accounting reports i s i den t i ca l to that of cos t l y ba i l-out f inanc ing : both are observable events which provide a basis for contingent cont rac t ing . In Bhattacharya (1979), i t i s not necessary that ex post cash flows are observable, but that the event of a cqu i s i t i on of ba i l-out f inanc ing i s observable. In Bhattacharya (1980) i t i s assumed that ex post cash flows are observable, or c o s t l e s s l y are t r u t h f u l l y communicated through accounting reports . The f i rm o f f e r s a warranty contract in Bhattacharya (1979) and a guaranty contract in Bhattacharya (1980). In Grossman's warranty model, buyers use the warranty o f fe red as a basis fo r product va luat ion because the event upon which the warranty payment i s contingent ( i . e . , product break-down) i s independent of any act ions of e i the r the s e l l e r or buyer ( i . e . , no moral hazard). Such an assumption is non t r i v i a l when accounting reports provide the basis fo r cont rac t ing . There c l e a r l y i s a moral hazard problem assoc iated with accounting repor t s , which l i m i t s t h e i r usefulness in cont rac t ing in the absence of v e r i f i c a t i o n or monitor ing. The add i t ion of v e r i f i c a t i o n or monitoring to Bhatta-charya' s model would make i t more pa l a t ab l e , but a lso would add costs which would change the model and i t s r e su l t s . Feltham and Hughes (1983) recognize two potent ia l v e r i f i c a t i o n ro les fo r accounting reports in a scenario s im i l a r to that of Leland and Py le ; but they assume the ro les rather than der ive or analyze them. The i r ana lys is of a s igna l i ng mechanism is more general than that of Leland and Pyle in that Feltham and Hughes do not assume 20 l i n ea r contracts and do hot assume that a f u l l y revea l ing separat ing equ i l ib r ium w i l l be the optimal so lu t ion to the adverse se l ec t i on problem. The r isk-averse agent/manager of a f i rm issues s e cu r i t i e s in order to acquire cap i t a l fo r investment and product ion and to share r i sks with investors . The f i r m ' s cash flows are determined by both general economic events and f i rm-spec i f i c events. In the ab-sence of asymmetric in format ion, optimal r i s k sharing i s a t ta inab le where investors bear a l l f i rm-spec i f i c r i sks and systematic r i sks are shared. Both investors and the manager have homogenous b e l i e f s about general economic events ( i . e . , nond i ve r s i f i ab l e market r i s k ) . Inves-tors have homogenous b e l i e f s about f i rm-spec i f i c events ( i .e . . , diver-s i f i a b l e r i s k ) and know that the manager has ins ide information about the f i rm-spec i f i c events which a f f e c t cash f lows. At the beginning of the per iod when the manager issues s e c u r i t i e s , he a lso issues a prospectus. The prospectus d i sc loses the product ion p l an , div idend p o l i c y , the manager's investment p o r t f o l i o , and a message about his ins ide informat ion. Two potent ia l ro les fo r accounting reports are ex ante v e r i f i c a t i o n and ex post v e r i f i c a t i o n : the i nc lus ion of an accounting report in the prospectus which v e r i f i e s d i s c losure in the prospectus, or the se l e c t i on of an accounting system which w i l l produce end-of-period accounting reports v e r i f y i ng d i sc losures made in the prospectus. In the Feltham and Hughes model, the second ro le of ex post v e r i f i c a t i o n i s assumed, and the manager d i sc loses the repor t ing system in the prospectus. D isc losures in the prospectus, other than the message, are assumed to be t ru th fu l due to the e x i s -tence of pena l t i es which w i l l be imposed on the manager i f the ex post v e r i f i c a t i o n process ind icates that he was l y i n g . The message 21 about his ins ide information i s not v e r i f i e d and investors know that he se lec ts d i sc losure in order to maximize his s e l f i n t e res t . In add i t i on , pos i t i v e d i sc losure i s assumed under which the manager does not l i e , but does not necessar i l y reveal the en t i re t ru th . If the manager's ins ide information i s good news, the expected value of cash flows exceeds that be l ieved by the market, and investors would pay more f o r the f i rm ' s s e cu r i t i e s i f they knew the ins ide informat ion. The manager se lec ts a prospectus in order to maximize his expected u t i l i t y of end-of-period consumption, where his consumption i s equal to the r ea l i z ed cash flow plus the return on his investment p o r t f o l i o less dividends paid to investors . Feltham and Hughes' r e su l t i s that whether a manager reveals his information in his message depends upon the p r i o r b e l i e f of inves tors : ( i ) I f investors be l ieve that there i s a high p r o b a b i l i t y that the manager has good news, a pool ing equ i l ib r ium resu l t s in which no message i s reported by the manager with good news. The f i rm i s undervalued by investors by a small amount. Due to the undervaluat ion, the manager does not t r ans fe r a l l f i rm-spec i f i c r i s k , but bears some in order to side bet with investors . In other words, the manager agrees to s e l l some of his f i rm at an undervalued p r i c e , but w i l l not s e l l a l l at that p r i c e . The manager with bad news a lso bears f i rm-spec i f i c r i s k , not to side bet , but to d isgu ise his bad news and be overvalued by investors , ( i i ) I f investors be l ieve that there i s a high p r o b a b i l i t y that the manager has bad news, a separat ing equ i l ib r ium resu l t s in which the manager sends a message and bears f i rm-22 s p e c i f i c r i s k to 'guaranty' the message. There i s no s ide be t t ing since investors co r r e c t l y value the f i rm. The manager with bad news does not bear f i rm-spec i f i c r i s k s ince i t i s too cos t l y for him to t r y to d isgu ise his bad news. While Feltham and Hughes re fe r to accounting repor t s , i t seems that the cont r ibu t ion of the paper i s in showing that a separat ing s igna l i ng equ i l ib r ium cannot be assumed to be optimal fo r the manager and the choice between separat ing and pool ing depends upon inves tors ' p r i o r b e l i e f s . There have been a number of empir ica l studies which have a l luded to the a b i l i t y of the manager of a f i rm to communicate his ins ide information through accounting numbers. Gonedes (1976) tes ts the r e l a t i v e a b i l i t i e s of d iv idends, income, and extraordinary items to ' s i g n a l ' information about the unobservable d i s t r i b u t i o n of cash f lows. Gonedes states that he i s not d i r e c t l y t e s t i ng the managerial motivat ion to s ignal or the c r e d i b i l i t y of the s i gna l s , and states in a footnote: "Note that a s igna l ing management need not th ink of i t s e l f as a c tua l l y engaging in s igna l i ng . The c r i t i c a l issue i s whether i t ends up prov id ing observables that are p o t e n t i a l l y useful in making inferences about unobservable cha r a c t e r i s t i c s of i t s product ion- invest -ment and f inanc ing d e c i s i o n s . " (p.29) In a s igna l i ng scenar io , as has been discussed in th i s chapter , the manager does indeed th ink of himself as engaging in s igna l i ng in his a n t i c i p a t i o n of the react ions of investors in his se l ec t i on of the s i gna l . It appears tha t , although Gonedes re fers to Spence 1s work on s i g n a l i n g , he i s not t e s t i ng a s i gna l i ng hypothesis , but rather i s t e s t i ng fo r co r r e l a t i on among va r i ab les . The quest ion he appears to 23 be asking i s : given that income numbers are cor re la ted with the pr i ce of a f i r m ' s secur i t y and can be used to expla in cash f lows, does the add i t ion of div idend changes and/or extraordinary items add more explanatory power? In order to t es t a s igna l i ng hypothesis , i t would be necessary to der ive such an hypothesis from a model in which there was motivat ion fo r and c r e d i b i l i t y of communication of ins ide information through such act ions as d i sc losure of extraordinary i terns. Many empir ica l papers suggest that a managerial act or choice may be cor re la ted with f i rm value without reference to a s igna l ing model. These papers provide empir ica l evidence without attempting to expla in managerial motivat ion for such ac t ions . Pa te l l (1976) exam-ines the e f f e c t of voluntary corporate forecasts of earnings per share on secur i t y p r i c e s , and f inds that the market reacted to the voluntary forecasts such that forecasts of earnings greater than the market's naive expectat ion were preceded by pos i t i v e p r i ce ad jus t -ments and those less than the expectat ion were preceded by negative p r i ce adjustments. For both groups, there was a pos i t i v e p r i ce react ion in the week of the forecast . Pate l l does state that one cannot d i s t i ngu i sh between the inference that the forecasted numbers convey information or that the act of fo recas t ing i s informat ive. Harr ison (1977) examines market react ions to d i s c re t i ona ry and nondiscret ionary changes in accounting methods. He states that poss ib le motivat ions fo r a d i s c re t i ona ry change ( e . g . , a switch from acce lerated deprec ia t ion to s t r a igh t l i ne ) may be to avoid v i o l a t i o n of bond covenants, to smooth income, or to communicate ins ide i n f o r -mation about future cash flows. Nondiscret ionary changes ( e . g . , a 24 switch from the equity method to the cost method of va luat ion of equity investments) are mandated by a regulatory agent. The s t a t i s -t i c a l l y s i g n i f i c a n t empir ica l r esu l t s are that f irms which made d i s c re t i ona ry changes which increased income earned a lower return than f irms making no changes, and firms which made nondiscret ionary changes which increased income earned a higher return than no-change f i rms. He suggests that the d i s c re t i ona ry act provides information to investors about changes in e i the r systematic or res idual returns. While no c l ea r motivat ion fo r such voluntary act ions i s presented, and no explanat ion of why investors would react to such ac t i ons , Har r i son ' s study does present evidence that managerial d i s c r e t i on i s an intervening var iab le in the market react ion to accounting changes. The object ive of Penman's (1980) empir ica l study of f irms making voluntary earnings forecasts i s to provide evidence useful in eva lu -a t ing the benef i t of a mandatory fo recas t ing regu la t ion . He there -fore addresses two quest ions: do such voluntary forecasts provide information to investors and do a l l f irms vo l un t a r i l y provide f o r e -casts? His empir ica l r esu l t s are : ( i ) Earnings of f irms making forecasts are , on average, higher than the market's expectat ion (def ined in terms of a mar-t inga le with d r i f t ) , ( i i ) Forecast ing f irms have higher unexpected earnings than the average f i rm in the economy, ( i i i ) Excess returns are earned by the forecast f i rms , on aver-age, on the day p r i o r to the forecast date. 25 ( i v ) The sample of f irms making forecasts earned, on average, greater returns than the market p o r t f o l i o during the per iod s tud ied. Penman concludes that voluntary forecasts do provide information to investors and that the f irms which s e l f - se l e c t into the group of f irms making forecasts are not representat ive of a l l f i rms. However, he a lso concludes that his empir ica l f ind ings cannot be in terpre ted as evidence that forecasts should be mandatory, because f irms that do not forecast may communicate information through some other a c t i on , such as d iv idends. In add i t i on , the act of not fo recas t ing may be in fe r red as communication of poor earnings. Ricks (1982) analyzes earnings performance and market perform-ance fo r f i rms switching from the FIFO method of inventory va luat ion to LIFO in 1973. His empir ica l r esu l t s are: ( i ) Firms that switched were more p r o f i t a b l e in the year of switch than a control group of non-switching f i rms , and would have been even more p r o f i t a b l e had they not switched, ( i i ) Firms that switched showed lower secur i t y returns than the non-switching f i rm. Ricks admits that there are several potent ia l explanations fo r the poor market performance. A change in LIFO during i n f l a t i o n has one real economic impact: a reduct ion in taxes, which presumably i n -creases f i rm value through the increase in af ter-tax cash f lows. Therefore the act of switching to LIFO must convey negative informa-t i on to investors such that they reduce t he i r i n fe r red value of the f i rm. 26 The empir ica l studies summarized above reveal that f irms which issue voluntary forecasts of earnings and firms which vo l un t a r i l y change accounting methods are not representat ive of a l l f irms in the economy. A frequent c r i t i c sm of these types of studies i s tha t the resu l t s are biased because f irms which undertake such voluntary act ions are s e l f - s e l e c t i n g into a p a r t i c u l a r group of f irms and that any market react ion may not be a response to the changed accounting number or to the forecast earnings, but to the act of changing or fo recas t ing . However, i t i s exact ly th i s react ion to s e l f - s e l e c t i o n which i s i n t e r es t i ng empir ica l evidence. While the motivat ion fo r such voluntary act ions are not understood, the empir ica l studies do provide evidence that a manager of a f i rm may convey information to the market by a choice of an accounting report ing system. 27 CHAPTER THREE THE ROLE OF THE INVESTMENT BANKER IN THE NEW ISSUES MARKET INTRODUCTION This chapter develops the v e r i f i c a t i o n role of the investment banker. Section 1 describes how the informational asymmetry ex i s t i ng in the new issues market may motivate s igna l ing a c t i v i t i e s . Sect ion 2 shows how a contingent contract between the i ssuer of a new secur i t y and investors may be used to resolve such an informational asymmetry. A review of the l i t e r a t u r e on intermediat ion and asymmetric information appears in Section 3. The ro le of the investment banker as an intermediary which provides c red ib le v e r i f i c a t i o n of d i sc losure is developed in Section 4. It is shown in Sect ion 5 that the ro le of the investment banker developed in Sect ion 4 is consistent with the role as defined by ex i s t i ng regulat ion of the secu r i t i e s market. 1. SIGNALING AND THE NEW ISSUES MARKET New issues of equity s e cu r i t i e s can be c l a s s i f i e d as seasoned or unseasoned. Seasoned issues are new issues of s e cu r i t i e s which are pub l i c l y held and for which a market e x i s t s . There is no ex i s t i ng 28 publ i c market for unseasoned new issues which are s e cu r i t i e s of firms which have been p r i va te l y held and now are 'going p u b l i c ' . A pub l i c o f f e r i n g of unseasoned common stock can be viewed as a s i t ua t i on in which a s e l l e r (the entrepreneur of the firm) o f fe rs for sa le to buyers (the investors in the secu r i t i e s market) a product (shares of common stock) which has a qua l i t y or value which is unobservable. Investors can be assumed to know the average q u a l i t y , or the d i s t r i b u t i o n of q u a l i t y , based upon t he i r p r io r in format ion, such as information about other pub l i c firms in the same indust ry ; however, they cannot observe the qua l i t y or value of the s e cu r i t i e s of each ind iv idua l new i s sue . When a f irm is p r i va te l y he ld , investors can-not trade in i t s s e cu r i t i e s and there consequently is no demand for or production of information about the f i r m . The entrepreneur/owner of the p r i va te l y held f i rm however can be assumed to know the value of the f irm due to his information about future cash flows which he acquires during his managerial a c t i v i t i e s within the f i r m . The informational asymmetry ex i s t i ng in th i s scenario is the same as that descr ibed by Aker lof (1970) and Spence (1973), and consequently is a s i t ua t i on in which there ex is ts a demand for a s igna l ing mechanism such as those described in Chapter Two. The previous chapter ind icated the two essent ia l elements in a s i gna l i ng model: the s e l l e r is motivated to undertake s igna l i ng a c t i v i t i e s and the s ignal is c red ib le to the market of buyers. The s ing l e entrepreneur/owner of a f i rm or technology who is attempting to s e l l equity shares in his f i rm/technology, where the value of that 29 f i rm exceeds the market's average va lua t i on , c l e a r l y is motivated to communicate his ins ide information because he w i l l gain personal ly i f the market increases i t s va luat ion of his f i rm 's s e c u r i t y . The motivat ion to s ignal in such a scenario is more apparent than those in other scenarios discussed in the previous chapter where the manager of a f i rm is assumed to be motivated to maximize the value of the f i r m . The communication w i l l be c red ib le to the market only i f i t is cos t l y in the sense described by Spence, or i f a contingent contract can be wri t ten on some ex post r e a l i z a t i on of value and s ignaled va lue. If the motivation and cost condit ions are met, then the i ssuer of s e cu r i t i e s w i l l be motivated to s ignal and w i l l invest in a cos t l y s ignal i f the benef i ts of such c red ib le communcation exceed i t s cos t s . 2. DISCLOSURE AND CONTINGENT CONTRACTS Spence (1976) descr ibes two types of s igna l ing dev ices : exogeneously cos t l y s i g n a l s , and contingent con t rac t s . As was descr ibed in Chapter Two, the f i nanc i a l s igna l ing models of Bhattacharya (1979) and Leland and Pyle (1977) are combinations of exogeneously cos t l y s igna ls and contingent con t rac t s . In such models the informational asymmetry is reso lved; but the s igna l ing equ i l ib r ium is i n e f f i c i e n t due to the d i s s i p a t i v e costs i n cu r r ed . Ross 's (1977) study is an example of a model of contingent contract ing in which there is a penalty imposed on the r isk-neutra l manager of the f i rm i f he s igna ls f a l s e l y . Ross's model a lso is d i s s i p a t i v e because any penalty imposed on the manager is not d i s t r i bu t ed to the shareholders who have overvalued the f i r m . 30 However, i f the potent ia l penalty is appropr ia te , the manager w i l l be induced to make t ru th fu l d i s c l o s u r e s . Ross does not consider any costs of i n e f f i c i e n t r i sk sharing because the manager is r isk n e u t r a l . As Spence i n d i c a t e s , i f the s igna le r is r isk averse and there is res idual uncerta inty about product q u a l i t y , then the contingent contract ing s igna l ing equ i l ib r ium may resu l t in non-optimal r i sk shar ing . The entrepreneur of a f i rm which is going publ ic can resolve the informational asymmetry through the fo l lowing contingent contract ing process: ( i ) The entrepreneur states the ex ante expected value of his f i r m . ( i i ) Investors in the market p r i ce the f i rm as a funct ion of the entrepreneur 's statement, ( i i i ) If actual ex post value is found to be less than that s t a t ed , a monetary penalty is imposed upon the entrepreneur and the penalty is r ed i s t r ibu ted to shareholders . The above contract is nondiss ipat ive and w i l l resu l t in e f f i c i e n t r i sk sharing i f the entrepreneur is r i sk neutral or there is no r e s i -dual uncerta inty about actual va lue . However, actual end-of-period value is a r e a l i z a t i on of a random var iab le and may be low due to i t s being an outcome in the lower t a i l of the d i s t r i b u t i o n . If a penalty were to be imposed upon the entrepreneur when the rea l i zed value was less than the stated expected va lue, there is a high p robab i l i t y ( i . e . , 50% when the random var iab le has a symmetric d i s t r i bu t i on ) of a penalty imposit ion even when the entrepreneur d isc loses the true expected va lue . Such a penalty would induce the entrepreneur to d i s c l o se an expected value less than the true expected va lue, while 31 never reducing the p robab i l i t y of a penalty imposit ion to zero under t r u t h - t e l l i n g . While t r u t h - t e l l i n g , or not overstat ing value has been induced, a penalty w i l l be incurred for low r ea l i za t i ons in order to induce that t r u t h - t e l l i n g , and such a penalty w i l l be due only to the randomness of ex post f i rm va lue . The legal and regulatory system does indeed impose such a penalty scheme upon issuers of new s e c u r i t i e s . The Secur i t i es Act of 1933 gives purchasers of an issue the r ight to recover any damages they may su f fe r as a resu l t of a p r i ce dec l ine i f the r eg i s t r a t i on s t a t e -ment or prospectus contained an untrue statement of a material fact or mater ia l l y misleading statement or omiss ion.* Due to the SEC Act , a l l i nves to r s , inc lud ing those who never read the prospectus, may t ry to recover damages. C lea r l y a l l investors would l i k e to recover damages i f the pr i ce dec l i nes ; however the courts must be provided with proof that there was a material omission or misleading statement in the prospectus in order to award damages. I f t n e swards damages to i nves to rs , the i ssuer of the secur i t y must buy back the shares from the investors at the o f f e r ing p r i c e . The penalty imposed by the SEC therefore is the d i f f e rence between the pr i ce paid by investors when the s e cu r i t i e s were issued and the current market p r i ce of the s e c u r i t i e s . The contingent contract descr ibed above is cos t l y to the entrepreneur in terms of i n e f f i c i e n t r i sk sharing i f the entrepreneur i s r i sk averse and the penalty is contingent upon the r e a l i z a t i o n of a random v a r i a b l e . 32 The process by which the market in fers value and penal izes the entrepreneur is descr ibed below. A more prec ise formulat ion of the process is developed in sect ion 4. The value of the f i rm is assumed to be a funct ion of the expected value of future cash f lows. For a s p e c i f i c f i r m , there is an underly ing d i s t r i b u t i o n of future cash flows which is assumed to be a normal d i s t r i b u t i o n in th i s d i s cus s i on . x ~ N ( p , a 2 ) end-of-period cash flow expected value of x variance of x 2 The entrepreneur knows the value of u and a for his f i r m . The market has a p r io r normal d i s t r i b u t i o n on u: u ~ N ( x 0 , a 2 ) In the absence of addi t iona l c red ib le in format ion, the market w i l l value a l l firms as a funct ion of x the average value of u, which w i l l lead to A k e r l o f s market f a i l u r e . The object ive of the entrepreneur is to maximize his expected u t i l i t y of end-of-period wealth. The d i sc losure w i l l be of the form "The expected value of future cash flows is y . " The market w i l l value the f irm based only upon the entrepreneur 's d i s c l o s u r e : where x = y = 2 _ a -33 market value = V(y) and w i l l not use i t s p r i o r information in va lua t ion . The market and entrepreneurs have i m p l i c i t agreement about a penalty funct ion under which the entrepreneur must buy back the shares i f the rea l i zed value of x is s u f f i c i e n t l y low r e l a t i v e to y . The threatened penalty w i l l induce t ru th fu l d i sc losure from the entrepreneur i f i t is of s u f f i c i e n t s i ze and is perceived by the entrepreneur as c r e d i b l e . To be c r e d i b l e , the penalty must be imposed for low r ea l i za t i ons of x, even though investors know that the entrepreneur was induced to t e l l the t r u t h . If i t were not imposed for low r e a l i z a t i o n s , i t would not provide an incent ive for t r u t h - t e l l i n g . The investors and entrepre-neur precommit to the penalty scheme. The entrepreneur 's end-of-per iod wealth is reduced by any penalty imposed upon him. Both f i rm va luat ion and the amount of the threatened penalty depend upon y: the higher is y , the greater is V(y) and the proceeds of the stock i s sue ; and the higher is y , the greater is the p robab i l i t y that a penalty w i l l be imposed at the end of the pe r iod , and the higher w i l l be the penalty which is equal to V (y ) . Therefore y w i l l be perceived by the market as a c red ib le s ignal of va lue. At the end of the pe r iod , investors observe a s ing le r e a l i z a t i o n x which is the end-of-period cash f low. Investors know that x is a random var iab le and that to impose a penalty when x < y w i l l induce the entrepreneur to d i s c lose y < < u rather than y = u in order to avoid a pena l ty . In order to induce the entrepreneur to reveal p, a penalty is imposed i f x < L < y . In the determination of L, investors form a pos ter io r estimate of y from the i r p r i o r estimate 34 and the r e a l i z a t i o n x, form a pos te r io r confidence in terva l around the pos te r io r est imate, and penal ize the entrepreneur i f y f a l l s above the confidence i n t e r v a l . The pos te r io r d i s t r i b u t i o n of y is der ived fo l lowing deGroot (1970, p. 166-68). u ~ N(x 1 ,o^) - 2 2 x o ° + X a o where x^  = ?; jf" (3.2.1) a + a 0 is a weighted sum of x Q , the p r i o r estimate of y, and the r e a l i z a t i o n x. The larger is the variance of x, the greater is the weight placed upon the p r io r est imate. Investors form confidence in te rva l s around x x s u c n that L = x^ + an increas ing funct ion of a, such as x^  + 2o which is a commonly used confidence in terva l in s t a t i s t i c a l hypothesis t e s t i n g . If y > x 1 + 2o, the entrepreneur is pena l i zed . Then n = P robab i l i t y {y > x^^ + 2a} . represents the p robab i l i t y that the entrepreneur w i l l be pena l i zed . Figure (3.1) i l l u s t r a t e s the pos ter io r d i s t r i b u t i o n of y and the penalty p r o b a b i l i t y . 35 The stages in the process therefore are: 1) At the beginning of the pe r iod , i ) the entrepreneur knows u. i i ) Investors bel ieve that the expected value of cash flows i s x o . i i i ) The entrepreneur reveals y , investors i n fe r V (y ) , and the s e cu r i t i e s are sold for V(y ) . 2) At the end of the pe r i od , i ) investors and the entrepreneur observe x. i i ) Investors form a pos ter io r estimate of the expected value of cash f lows, x^  from x Q and x. i i i ) Investors form a confidence in terva l such that L > x^ and penalyze the entrepreneur i f y > L. 36 iv) If y > L, the entrepreneur buys back the secu r i t i e s for V(y) which have a current market value < V(y) and bears a loss V(y) - V^. Since the entrepreneur knows the expected value and variance of cash f lows, he knows the value of n at the beginning of the pe r iod . The p robab i l i t y that y > x^  + 2 a is expressed as n (y ;u ,a 2 ) = n(y > ^ + 2a) and the expected value of the penalty condi t ional on y > x^  + 2a, is n-[V(y) - E (V X ) ] The end of period loss depends upon the r ea l i z a t i on of x and therefore is a random va r i ab l e . The random var i a t ion in ex post observed value imposes r i sk upon the r isk-averse entrepreneur. Therefore , even i f t r u t h - t e l l i n g is induced by the contingent cont rac t , the s igna l ing mechanism is cos t l y to the entrepreneur in terms of addi t iona l r i sk which he must bear. In Section 4 i t w i l l be shown that the cost of th i s contingent contract can be reduced through the use of an intermediary . 3. INTERMEDIATION AND ASYMMETRIC INFORMATION A potent ia l role for an intermediary may be the reso lu t ion of an informational asymmetry. Leland and Pyle (1977) suggest at the end of the i r paper that f i nanc i a l intermediar ies may be the most e f f i c i e n t producers of information i f there are economies of sca le to information product ion . Information may be produced at a cos t , but cannot be sold d i r e c t l y to the market at a pr ice r e f l e c t i n g i t s true 37 value due to i t s pub l i c good nature. Therefore the return to cos t l y information production can be rea l ized through returns on a p o r t f o l i o of assets which are purchased on the basis of ins ide in fo rmat ion . To overcome the moral hazard problem involved in communicating the value of i t s in format ion, the organizers of the intermediary can s ignal the value of t he i r information and resu l t ing p o r t f o l i o through t h e i r investment in the equity of the intermediary. Leland and Pyle only suggest that there may be economies of scale in information production in order to j u s t i f y the existence of an intermediary . However, s ince the ind iv idua l entrepreneur can c red ib l y communicate his ins ide information to the market through his equity pos i t i on in his own project or f i r m , a demand for the intermediary w i l l not a r i se unless the intermediary can resolve the informational asymmetry at a smal ler cost to the entrepreneur than his cost in terms of lack of d i ve r s i f i c a t i o n . Campbell and Kracaw (1980) develop a model of f i nanc i a l intermediat ion fo l lowing the suggestion of Leland and Pyle that intermediat ion resolves the problems of moral hazard and app rop r i ab i l i t y associated with information production and communication. They assume that firms cannot s ignal to resolve the asymmetry themselves. Such an assumption is used to j u s t i f y the existence of the intermediary and demand for i t s informat ional production s e r v i c e s . However, i t may be the case that an intermediary can produce and c red ib ly communicate the entrepreneur 's ins ide information at less cost than the entrepreneur 's cost of c red ib le communication; and therefore that such an assumption may not 38 be necessary. In t he i r model, undervalued firms pay information producers to undertake cos t l y production of information which w i l l reveal the true value of the f i rms . Such information is c red ib le to the market because the information producer invests in the intermediary . The informational asymmetry is reso lved , but the need fo r the producer to invest in the intermediary provides a wealth const ra in t on information production which may preclude e f f i c i e n t information producers from enter ing the information production market. Therefore , the cost to the undervalued firms of c red ib l y communicating the i r value may be great due to the potent ia l exc lus ion of e f f i c i e n t information producers. The Campbell/Kracaw analys is ind icates that d i r ec t communication of information creates a moral hazard problem which can be reso lved, but at a cos t . Since a l l investors are assumed to be r i sk neu t ra l , the cost is not r i sk-bear ing , but a less e f f i c i e n t production of information due to the exclus ion of potent ia l producers with i n s u f f i c i e n t wealth to s a t i s f y the wealth cons t r a in t . Such a so lu t ion appears to be somewhat a r t i f i c i a l s ince there ar i ses the motivat ion for the poor, e f f i c i e n t producers to s ignal t he i r e f f i c i e n c y in order to borrow to s a t i s f y the wealth cons t r a i n t . There also is no a p r i o r i demand for the information producer i f a l t e rna t i ve ways of s igna l ing were permit ted. The authors do suggest at the end of t he i r paper that a more promising explanation for the existence of intermediar ies might be that they produce information and provide other s e r v i c e s . It does appear that they have not adequately j u s t i f i e d the demand for an intermediary to undertake cos t l y production and cos t l y communication of ins ide in format ion . 39 Thakor (1982) models debt insurers as t h i r d party information producers when borrowers know the i r defaul t p r o b a b i l i t i e s and potent ia l lenders do not . The insurers invest in cos t l y information product ion and o f f e r insurance to borrowers at premia which are a funct ion of insurance coverage and defaul t p r o b a b i l i t y . A borrower purchases insurance coverage which s igna ls i t s true defau l t p robab i l i t y and compensates insurers for the defau l t r i sk borne and the cost of information product ion . If a l l market pa r t i c ipan ts are r i sk neu t r a l , the demand for insurance w i l l ex i s t because of i t s s igna l i ng bene f i t s . Under r i sk avers ion , the intermediary provides an insurance serv ice in addi t ion to information product ion . Therefore , with r isk avers ion , there is a demand which j u s t i f i e s the existence of the intermediary aside from the demand for a s igna l ing mechanism. Thakor does assume that borrowers cannot s ignal d i r e c t l y and that no other intermediar ies or c red i t rat ing agencies e x i s t . Therefore there is no analys is of the e f f i c i e n c y of s igna l ing through debt insurance. The intermediar ies described by Lei and and Py le , Campbell and Kracaw, and Thakor are information producers who invest in cos t l y production of information which is already known by one market pa r t i c i pan t : the entrepreneur or borrower. There is a potent ia l ro le for an intermediary as a v e r i f i e r of information already known by the f i r m . The cost of v e r i f i c a t i o n of information may be less than the production cost of dupl i ca te in format ion. Indeed, i t may be impossible to produce information without examination and v e r i f i c a t i o n of the information provided by the entrepreneur/f i rm. The actual ro le of f i nanc i a l intermediar ies and debt insurers may be 40 that of v e r i f i c a t i o n and supplementation of information provided by f irms about past and projected cash f lows. Diamond (1984) analyzes the ro le of intermediat ion as delegated monitoring rather than information production and develops condi t ions under which th i rd-par ty monitoring of an entrepreneur w i l l be less cos t l y than d i r e c t monitoring by investors when there is asymmetric information between investors and the entrepreneur. In Diamond's model, the entrepreneur and investors have homogeneous be l i e f s about the d i s t r i b u t i o n of x, the cash flows generated by the f i r m . The end-of-period r e a l i z a t i o n x is observable only by the entrepreneur, and monitoring costs are s u f f i c i e n t l y high so that the free r ider problem w i l l p roh ib i t expenditures on monitoring a c t i v i t i e s by any i nves to r . As a consequence, investors w i l l only agree to purchase a debt secur i t y promising a f ixed end-of-period re turn , and w i l l provide the debt cap i ta l only i f they bel ieve that the expected return exceeds the expected return on an a l t e rna t i ve investment. Since x cannot be observed by lenders , the entrepreneur can claim that x<z when x>z, make a payment less than z to lenders , and pocket the d i f f e r e n c e . The optimal debt contact between the entrepreneur and lenders involves a non-pecuniary penalty ( e . g . , bankruptcy) to be imposed i f lenders do not receive a minimum expected re tu rn . Since x i s a random var iab le bounded below by zero , there is some pos i t i v e p robab i l i t y that x w i l l be less than the minimum return and that the penalty w i l l be imposed (assuming that the entrepreneur has no other weal th) . The deadweight penalty is due to the unobservabi1ity of x. The entrepreneur would be better o f f i f x were observable and he could share the r isk of x with equity secu r i t yho lde r s . 41 Diamond introduces an intermediary delegated to monitor the entrepreneur 's in format ion. The intermediary borrows from lenders at a promised ra te , loans to the entrepreneur, spends K to monitor the r e a l i z a t i o n x, and receives a payment from the entrepreneur which is unobservable by i t s depos i to r s . The intermediary is v iab le i f ( i ) i t s depositors receive an agreed upon minimum expected re tu rn , ( i i ) the intermediary receives a return of at least zero a f te r incur r ing monitoring costs and deadweights pena l t i e s , and ( i i i ) the entrepreneur is no worse o f f than i f he contracted d i r e c t l y with the depos i to rs/ lenders . The unobservabi l i ty of the payment received by the intermediary from the entrepreneur gives r i se to the same moral hazard problem which ex is ted between the entrepreneur and lenders . As a consequence, pena l t ies w i l l be imposed i f the actual payment made to depositors is less than the promised re tu rn , and iden t i ca l deadweight losses are i n cu r r ed . Therefore a s ing le intermediary monitoring a s ing le entrepreneur is not v iab le because the deadweight loss has not been reduced and an addi t iona l cost of monitoring has been incu r red . Diamond proves condit ions under which delegat ion is v iab le under both universal r i sk neu t ra l i t y and r isk avers ion . Under r isk n e u t r a l i t y , delegat ion is v iab le i f the intermediary monitors more than one entrepreneur and projects have less than perfect c o r r e l a t i o n , and delegat ion costs reach a minimum when projects are i d e n t i c a l l y and independently d i s t r i b u t e d . Deadweight losses are reduced because penal t ies are imposed when the r e a l i z a t i on x is in 42 the extreme lower t a i l , and the p robab i l i t y of the average return across projects being in that t a i l is decreasing as the number of entrepreneurs monitored inc reases . If the number is large and returns are independent, the cost per entrepreneur of monitoring approaches K. In order to focus on the d i v e r s i f i c a t i o n of r i sk under r i sk ave rs ion , Diamond el iminates the deadweight penalty cost by assuming that the entrepreneur has no wealth cons t r a i n t . The entrepreneur cannot share r i sks with i t s lenders due to the unobservab i l i t y of x. He can, however, share r i sks with the intermediary and w i l l do so i f the r isk premium charged by the intermediary is less than the entrepreneur 's r i sk premium. One type of d i v e r s i f i c a t i o n is when one ind iv idua l in the intermediary monitors many entrepreneurs. If a l l agents in the market have a negative exponential u t i l i t y f unc t i on , and project returns (condi t ional on the market) are independent, then the r i sk aversion toward the Nth independent gamble is a constant , not decreas ing, funct ion of N and therefore the intermediary 's r i sk premium is the same as the ent repreneur ' s , regardless of the s i ze of N. A second type of d i v e r s i f i c a t i o n which does resu l t in a reduced r i sk premium is when there are many bankers in the intermediary who share information as well as r i s k s . As the number of agents in the intermediary grows l a rge , the average r i sk premium grows small and the cost of delegat ion approaches K. There fore , Diamond has i d e n t i f i e d a set of condit ions which lead to d i v e r s i f i c a t i o n within f i nanc ia l intermediar ies so that delegated monitoring is preferred by entrepreneurs. They are: ( i ) Risk neu t ra l i t y and the intermediary monitors N entrepreneurs with project returns less than per fec t l y c o r r e l a t e d . 43 ( i i ) Risk aversion and N agents within the intermediary share r i s k s . Under each of these cond i t i ons , as N grows very l a rge , the costs of delegated monitoring approach K. The intermediary of Diamond provides v iable monitoring of the unobservable ex post r e a l i z a t i o n of x. In the fo l lowing ana l y s i s , where there is asymmetric information about the ex ante expected value of x, an investment banker is viewed as an intermediary who v e r i f i e s (or monitors) the statements made by the entrepreneur about the value of the ex ante mean u. It w i l l be shown that the investment banker is able to provide such v e r i f i c a t i o n at less cost than the entrepreneur due to sub-div is ion of r i sk within the intermediary . 4. THE ROLE OF THE INVESTMENT BANKER UNDER ASYMMETRIC INFORMATION It was seen in the preceding sect ion that an e f f i c i e n t reso lu t ion Of an informational asymmetry may be f eas ib l e through the use of an intermediary . The investment banker's role w i l l be shown to be that of such an intermediary . It w i l l be shown that (a) such a ro le emerges from the prov is ion of other serv ices for which there is a demand (as in Thakor) and, (b) the intermediary is v iab le (as in Di amond). In the absence of asymmetric information between an entrepreneur and the market, the investment banker can provide three types of serv ices to the i ssuer of a new secu r i t y : ( i ) insurance, ( i i ) d i s t r i b u t i o n of s e c u r i t y , and ( i i i ) advice about market condit ions and p r i c i ng of the s e c u r i t y . 44 The f i r s t serv ice is provided when the banker underwrites the issue under a f i rm commitment or a stand-by agreement. In the former, the i ssuer s e l l s the ent i re issue to the underwriter at an agreed upon p r i ce and the underwriter bears the en t i re r isk of meeting adverse market cond i t i ons . In the l a t t e r , the underwriter agrees to buy whatever amount of the secur i t y the i ssuer has been unable to s e l l d i r e c t l y at a spec i f i ed p r i c e . There is no underwrit ing or insurance provided in a best-ef for ts agreement where the banker only agrees to use his best e f fo r t s to s e l l the issue and does not buy any of i t from the i s sue r . The d i s t r i b u t i o n serv ice is purchased when the banker s e l l s the issue because he may be better able to generate demand due to his contacts and experience in the market, because he has a c l i e n t e l e , or because he has a " reputa t ion" which the i ssuer l a c k s . Baron (1982) a l ludes to the potent ia l a b i l i t y of the banker to c e r t i f y the issue in his d iscuss ion of how the banker may generate demand due to his reputat ion behind i t . T h e o r e t i c a l l y , the banker could provide the underwrit ing serv ice without ac tua l l y s e l l i n g the i s sue , but such contracts are not observed in North America (they are observed in England). The t h i r d serv ice is provided when the banker has better information about market condit ions than the i s s u e r . Therefore , there is a demand for the serv ices of an investment banker in the absence of an informational asymmetry between the entrepreneur and inves to rs . When an asymmetry does e x i s t , the underwriter provides a fourth se r v i ce : v e r i f i c a t i o n of information contained in the s e l l i n g document. As w i l l be discussed in Sect ion 5, due to the regulatory environment within which new s e c u r i -t i e s are i s sued , the underwriter is l i a b l e for damages i f a future 45 pr ice dec l ine can be proven to be a t t r ibu tab le to misrepresentat ion or fraud in the s e l l i n g document. The s e l l i n g document, or prospec-t u s , contains information about the f i rm or planned investment pro -j ec t which is provided to the market by the entrepreneur. It is a d i r e c t d i sc losure about f i rm va lue . The s e l l i n g document therefore is also a d i sc losure document and as such is subject to d i s c losure r egu la t i on . It is from these two natures of the prospectus that the benef i ts and costs of such d i r ec t d i sc losure emerge. As a s e l l i n g document, i t s contents are re lated to s e l l i n g pr ice in that the higher the value indicated in the prospectus, the higher w i l l be market va lua t i on . As a d i sc losure document, i t s contents are re la ted to legal l i a b i l i t y in that the higher the value i nd i c a t ed , the greater the p robab i l i t y of misrepresentat ion and consequent legal l i a b i l i t y for pr i ce d e c l i n e . It is th i s cost of such d i r e c t d i s c l o -sure which makes the d i sc losure c r e d i b l e . It is not c lear that such regulat ion by a governmental agency is necessary. As long as the government enforces cont rac ts , the entrepreneur or underwriter and investors could negotiate contingent contracts based upon d i r ec t d i sc losure and ex post r ea l i za t i ons for each secur i t y i s sue . However, i t is not the purpose of th i s paper to evaluate the e f f i c i e n c y of governmental s p e c i f i c a t i o n of contingent con t r ac t s , but to take i t s regulatory existence as g iven, while recogniz ing that there may be v iab le market so lut ions to the problem of prov id ing c r e d i b i l i t y to d i r ec t d i s c l o s u r e . The model in the sub-sequent sect ion requires only that contingent contracts are enforced. It was shown e a r l i e r in th i s chapter that the i ssuer could assume l i a b i l i t y for f raud , which could e l iminate the demand for v e r i f i c a -t i on of d i sc losure by the investment banker. In a competit ive 46 market, the i s s u e r w i l l compensate the banker f o r i t s assuming the l i a b i l i t y . In the absence of r e g u l a t i o n , the investment banker w i l l be a v i a b l e provider of v e r i f i c a t i o n i f i t i s l e s s c o s t l y to the i s s u e r to use the banker rather than to provide c r e d i b l e v e r i f i c a t i o n h i m s e l f . I t w i l l be shown that s i n c e the banker reduces r i s k through r i s k d i v i d i n g , i t can provide v e r i f i c a t i o n at l e s s cost than the r i s k - a v e r s e entrepreneur. Therefore, i t i s not necessary to the a n a l y s i s that the government regulate that the underwriter i s l i a b l e s i n c e i t i s l i k e l y that he would emerge as an e f f i c i e n t p r ovider of v e r i f i c a t i o n i n the market. In r e a l i t y , due to r e g u l a t i o n , i f an i s s u e r purchases the underwriting or d i s t r i b u t i o n s e r v i c e s of an investment banker, i t must al s o purchase c e r t i f i c a t i o n s e r v i c e s . Optimal contracts between the i s s u e r and investment banker f o r the insurance, d i s t r i b u t i o n , and p r i c i n g s e r v i c e s have been derived i n several published papers. Mandelker and Raviv (1977) look at the insurance f u n c t i o n under d i f f e r e n t assumptions about r i s k a t t i t u d e s . Issuers are i n f e r r e d to be r i s k averse i f they seek insurance against the r i s k of adverse market c o n d i t i o n s . I f the i s s u e r i s r i s k n e u t r a l , he w i l l bear a l l r i s k and w i l l c ontract with an investment banker only i f s e r v i c e s other than insurance are provided, i n which case a best e f f o r t s agreement where the banker bears no r i s k i s o p t i m a l . I f both i s s u e r and underwriter are r i s k averse, r i s k s are shared through a stand-by agreement. I f the i s s u e r i s r i s k averse and the underwriter r i s k n e u t r a l , a f i r m commitment contract where the underwriter bears a l l r i s k i s o p t i m a l . The Mandelker/Raviv r e s u l t s 47 are standard Pareto-optimal r i sk-shar ing resu l ts when there are no problems of moral hazard and/or asymmetric informat ion. . Baron (1979) analyzes the moral hazard problem ex i s t i ng when the investment banker recommends an o f f e r i ng pr i ce and the s e l l i n g e f f o r t s of the banker are unobservable. A low pr i ce promotes good re l a t ionsh ips between the banker and his customers and permits a reduction in the amount of e f f o r t required to s e l l the i s sue . If the i ssuer is r isk averse and the banker r isk neu t r a l , the optimal contract is f i rm commitment in which the issuer determines the o f f e r i ng p r i c e . In such a cont rac t , the banker bears a l l of the cost of his s h i r k i n g . An incent ive problem ex is ts only when the banker is r i sk averse and in such a case the optimal contract is a stand-by agreement with a bonus paid to the banker when the issue is so ld out . Therefore , Pareto-optimal r i sk sharing between issuer and banker is a t ta inab le when the banker is r i sk neu t r a l . An issuer of a new secur i t y w i l l seek advice about p r i c i ng when an informational asymmetry ex is ts between issuer and banker about market cond i t i ons . Baron and Holmstrom (1980) inves t igate contract ing under asymmetric information when the banker obtains his super ior information a f te r the time of con t rac t i ng . It may be in the best in teres ts of the banker to suggest a low s e l l i n g pr i ce in order to benef i t favored customers and achieve a quick s a l e . If the banker i s r isk neu t r a l , a f i rm commitment contract is opt imal , even when the i ssuer is r i sk neutral and no insurance is demanded, because the banker then bears the consequences of mispr ic ing the i s sue . When the banker is r i sk averse, his compensation is based upon o f f e r i ng pr i ce 48 in order to induce him to set a higher p r i c e . Again, Pareto-optimal r i sk sharing is a t ta inab le i f the banker is r isk neu t r a l . Baron (1982) analyzes the contract ing problem under both asymmetric information and moral hazard when the i ssuer demands both advisory and d i s t r i b u t i o n s e r v i c e s . Both issuer and banker are assumed to be r isk neutral in order to e l iminate the demand for underwr i t ing. From the e a r l i e r r e s u l t s , i t is c lear that a f i rm commitment contract w i l l be optimal i f the banker obtains his super ior information a f te r con t r ac t i ng . However, i f the banker has super ior information about market condit ions p r io r to con t r ac t i ng , the f i r s t -bes t f i rm commitment contract is not a t t a i nab l e . Whether the i ssuer w i l l ac tua l l y issue the secur i t y depends upon cap i ta l market condit ions and therefore upon the banker's in format ion . The banker must be provided an incent ive to t r u t h f u l l y communicate his information to the i s s u e r . Due to the addi t ion of a t r u t h - t e l l i n g cons t r a i n t , optimal r isk sharing is not a t ta inab le and a f irm commitment contract w i l l not be opt imal , even when the investment banker is r isk neu t r a l . The resu l ts of the above papers can be summarized as fo l lows : a f i rm commitment contract is optimal and resu l ts in Pareto-optimal r i sk sharing between issuer and investment banker when the banker is r i sk neu t r a l , unless the banker has an informational advantage about cap i t a l market condit ions p r io r to con t rac t i ng . The moral hazard problem due to the banker supplying unobservable d i s t r i b u t i o n e f f o r t and the information problem due to the banker's gaining an informational advantage a f te r contact ing can be e l iminated by imposing a l l r i sk on the banker. If the investment banker is r i sk 49 averse, optimal contracts involve r isk sharing and prov is ion of i n cen t i v e s . Due to these contract ing r e s u l t s , modeling the investment banker as a v e r i f i e r of information w i l l be s i m p l i f i e d considerably i f : ( i ) the investment banker is r i sk neu t r a l , and ( i i ) there is no informational asymmetry between issuer and banker at the time of con t r ac t i ng . If ( i ) and ( i i ) ho ld , any moral hazard and/or asymmetric information problems between banker and issuer can be ignored and a f i rm commitment contract w i l l be opt ima l . In any underwrit ing agreement, the underwriter bears some of the r i sk of adverse market cond i t i ons . If the banker is r i sk averse, i t i s cos t l y to him i f the ent i re issue is not s o l d . The r i sk to the banker can be reduced by d i v id ing the r isk with another banker. In the model to be analyzed in Chapter Four, i t w i l l be shown tha t , in the absence of asymmetric in format ion, i t is optimal for the r isk-averse entrepreneur to s e l l 100% of the r isky equity in his f i r m . If the investment banker has the same preferences and a t t i tude toward r i sk as the entrepreneur, i t w i l l be as cos t l y to the banker i f he does not s e l l 100% of the issue as i t would be for entrepreneur. Since the entrepreneur must compensate the investment banker for a l l co s t s , the entrepreneur is no better o f f than s e l l i n g the issue d i r e c t l y to the market. However the banker can reduce r i sk by d i v id ing the r i sk with another banker so that each owns 1/2 of the equity in the f i r m . As the number of r isk-averse bankers grows to n, 50 each buys — of the shares sold by the entrepreneur. The risk added to 1 2 the portfolio of each banker is —^a . Therefore as n grows large, n the risk borne by each member of the underwriting group becomes very small, so that a large underwriting group behaves as if it were risk neutral. Since the notation necessary for a formal proof of this reasoning is not developed until Chapter Four, the proof appears in Appendix 1. It will be assumed that n is sufficiently large that the underwriter is risk neutral. It also will be assumed that there is no informational asymmetry between issuer and banker at the time of contracting. Therefore a firm commitment contract is optimal. In addition to risk sharing, the underwriter provides advisory, distribution, and verification services. Since the underwriter is risk neutral, its objective function is to maximize net income, where the issuer compensates the underwriter for all costs which it incurs in supplying the services. The contract between entrepreneur and underwriter will be analyzed because the cost to the entrepreneur of purchasing the services of the underwriter will enter the signaling problem in the next chapter. The information sets and actions of the entrepreneur, underwriter, and market at various points of time will be described, (i) Prior to contracting: (a) The entrepreneur knows y, a . (b) The market has prior information about the distribution of y and knows <£. (c) The underwriter knows about the selling conditions in the capital market. (d) During the period of time prior to contracting, the underwriter investigates and verifies the information provided by the entre-preneur about firm value. 51 ( i i ) Time of c o n t r a c t i n g between entrepreneur and underwriter: (a) The entrepreneur and the underwriter have i d e n t i c a l information sets about y, a^, and market c o n d i t i o n s . (b) The market has received no a d d i t i o n a l information with which to r e v i s e p r i o r d i s t r i b u t i o n of u. (c) At the time of c o n t r a c t i n g , the entrepreneur and underwriter agree as to the share to be received by the entrepreneur. Since the underwriter i s r i s k neutral and the entrepreneur i s r i s k averse, a f i x e d payment to the entrepreneur i s the Pareto-optimal r i s k sharing arrangement. The entrepreneur s e l e c t s y, where y i s his d i r e c t d i s c l o s u r e about y. (d) During the period of time p r i o r to the i s s u e , the underwriter exerts e f f o r t i n p r e - s e l l i n g a c t i v i t i e s which may provide him with b e t t e r information about market c o n d i t i o n s . (e) The market observes y and values the f i r m based upon the s i g n a l . ( i i i ) Time of i s s u e : (a) The entrepreneur s e l l s the equity i n the p r o j e c t to the underwriter f o r the agreed upon p r i c e . (b) The underwriter s e l e c t s the o f f e r i n g p r i c e and s e l l s the e n t i r e i s s u e . (c) I t w i l l be assumed that the underwriter does not ov e r p r i c e the i s s u e . The e n t i r e issue i s s o l d . The cost of d i r e c t d i s c l o s u r e was described e a r l i e r i n t h i s chapter as an end-of-period penalty i f a s u f f i c i e n t l y low outcome occurs. The expected penalty, or l o s s , was shown to be L(y) = n{y>v,°2)[V{y) ~ E (V . ) ] , c o n d i t i o n a l on y > x, + 2a where n = Prob{y > x. + 2a} Let P Q = V ( y ) , the i s s u e , or o f f e r i n g p r i c e . I t w i l l be assumed f o r ease of a n a l y s i s that i s s u f f i c i e n t l y small i f a penalty i s inc u r r e d that the expected l o s s w i l l be: 52 L(y) = P 0 n (y ; y , a 2 ) In order to obtain an expression for n, subst i tu te for x^  using (3 .2 .1 ) : - 2 2 x o + xo\ Prob {y > -2-^ + 2<J} a + a o (y-2a) (a 2 + a 2 ) - W Prob {x < 9_ } a o which is the correct way to express n, given y , because x is the r e a l i z a t i o n of the random va r i ab l e . II can also be expressed as: *(y; v a2) = J T f (x)dx (y-20)(a 2+o- 2) - X Q a 2 where T = ^ °o f(x) is the normal density funct ion of x. Consider some cha ra c t e r i s t i c s of the loss f unc t i on . ( i ) 8^ *3y^ > 0 because the loss occurs when y > x^  + 2a, Therefore n increases with y . ( i i ) 3 L ( y ) < 0 because p is the mean of the underly ing dp d i s t r i b u t i o n . As p inc reases , x^  w i l l increase because the d i s t r i b u t i o n of 53 x sh i f t s to the r ight and higher r e a l i -zat ions x are more l i k e l y . because the confidence in terva l is _ 2 2 x a + xa"" o o 2 + 2 a + a o + 2a ? ? - - ? 7 (a^+a )x -x a - xa^ O 0 0 0 ( 2. 2 X2 (o Q+a ) + 2 a^(x -x) 0 0 (a Q+a ) + 2 0 i f x < x + 2a 2 + 4 a 2 + — o o „ a o 2 which w i l l be assumed to be so . 2 If a increases while u is constant , there is greater weight in both t a i l s of the d i s t r i b u t i o n and therefore a greater p robab i l i t y of a higher or lower x. With the symmetric d i s t r i b u t i o n , these two p r o b a b i l i t i e s w i l l o f f se t each other in 54 determining whether a higher or lower x is more l i k e l y . L(y) changes in response to a due to the e f f e c t on the confidence i n t e r v a l . As <j2 inc reases , the confidence in terva l increases as long as x < >L + 2a 2 + 4a 2 + — . o o 0 a o 2 The resu l t of an increased confidence in terva l is ^Lll < o . 3 a In summary, the loss funct ion is increas ing in y and decreasing in u 2 and a . The underwr i ter 's se l ec t i on of P q a f te r y has been opt imal ly chosen by the entrepreneur is analyzed below. The entrepreneur 's choice of y is the subject of Chapter Four. Let PQ = Proceeds of issue received by the underwri ter . = Of fer ing pr i ce x Number of shares sold = P 0 (e ,e) Where e is the underwri ter 's unobservable d i s t r i b u t i o n e f f o r t such that 3PQ/3e > 0 G represents the state of the cap i ta l market about which the underwriter may have super ior i n f o r -mation . T n e P 0 funct ion is a demand pr i ce funct ion and represents the maximum pr i ce that can be obta ined, given a se lected level of e f f o r t . In Figure 3.2, i f is the rea l i zed state of nature and e* is 55 the leve l of s e l l i n g e f f o r t chosen by the underwriter , the P* is the maximum o f f e r i ng pr ice obta inab le . e* Figure 3.2 Of fe r ing Pr ice Function Let P^  = i^et proceeds to entrepreneur Pp: = Equi l ibr ium pr ice based upon u. The underwriter and entrepreneur negotiate P^ and the underwriter se lec t s P . If PQ = Pr;, the issue is so ld at equ i l ib r ium p r i c e . If PQ < P^, the issue is underpriced by the underwri ter . Then P £ - P^ = Cost of i ssu ing shares through the underwri ter . It is compensation for r i sk-sha r ing , adv ice , s e l l i n g e f f o r t s , and v e r i f i c a t i o n . 56 The value of the f irm is P ,^ but the entrepreneur receives only P N for the equity s o l d . The problem of the r isk-neutra l underwriter is to se lec t optimal e f f o r t in order to maximize p r o f i t , or : Max P ro f i t = P (e,e) - PN - K(y) - L(y,P ) - g(e) (3.4.1) e where K(y) = d i r ec t out-of-pocket costs of v e r i f i c a t i o n L(y ,P Q ) = present expected value of end-of-period l o s s . P n (y ;y ,a 2 ) = - ^ - ^ (3.4.2) g(e) = d i s u t i l i t y of e f f o r t where g'(e)>0 The f i r s t -o rde r condi t ion to the maximization i s : 8 P ro f i t _ ^ o _ J L _ . j ^ o _ , ( e ) = 0 3e 3e 3P_ 3e or i r - » ' < e > + # : - i r ( 3 - 4 - 3 ) It is seen in (3.4.3) that the level of e f f o r t is se lected so that the marginal benef i t of that e f f o r t is equal to the marginal co s t . 3P The marginal benf i t o i s the increase in income a r i s i ng from the 3e underwr i ter 's share in the o f f e r i ng p r i c e . Marginal costs are the marginal d i s u t i l i t y of e f f o r t g'(e) and the marginal increase in future loss a r i s i ng from the increased o f f e r ing p r i c e . 57 There i s a large amount of e m p i r i c a l evidence that unseasoned new 4 issues are, on average, underpriced. Equation (3.4.3) suggests that such underpricing would r e s u l t due to the underwriter's d i s u t i l i t y of e f f o r t and the dependency of future l o s s on o f f e r i n g p r i c e . Baron (1979) a l s o noted that the d i s u t i l i t y of d i s t r i b u t i o n e f f o r t would provide i n c e n t i v e s to the underwriter to underprice. The underwriter s e l e c t s e f f o r t a f t e r y has been d i s c l o s e d , and the underwriter assumes l e g a l l i a b i l i t y f o r the t r u t h f u l n e s s of the entrepreneur's d i s c l o s u r e . The s i g n a l y i s c r e d i b l e because the contingent contract between the underwriter and the market pr e s c r i b e s t h a t a penalty w i l l be imposed on the underwriter i f the r e a l i z a t i o n of x i s s u f f i c i e n t l y low r e l a t i v e to y that the courts w i l l b e l i e v e t h a t y was a misrepresentation of y. The d i s c l o s u r e i s made by the entrepreneur, but the contingent contract i s between the underwriter and the market. The entrepreneur w i l l compensate the underwriter f o r i t s expected l o s s . However, the loss to the r i s k - n e u t r a l underwriter i s smaller than the e f f e c t i v e l o s s would be to the r i s k - a v e r s e entrepreneur i n a contingent contract between the entrepreneur and the market because of the randomness of the outcome reduced by the regulatory system. Therefore the r o l e of the underwriter to v e r i f y y and assume l i a b i l i t y f o r y i s v i a b l e . In a competitive market f o r the s e r v i c e s of investment bankers, the banker w i l l be compensated so that i t earns zero net p r o f i t i n e q u i l i b r i u m . From (3.4.1), zero p r o f i t s are earned when P 0-P N = K(y) + L(y) + g ( e ) . (3.4.6) 58 The underwr i ter 's share of the proceeds of sa le i s compensation for d i r e c t cos t s , the expected future l o s s , and the d i s u t i l i t y of e f f o r t . In summary, the f i na l optimal contract between the entrepreneur and the underwriter is a f i rm commitment contract in which: ( i ) The entrepreneur and the underwriter agree as to the entrepreneur 's share P^. Such a r i sk-shar ing arrangement i s optimal because the entrepreneur is r isk averse, the underwriter is r i sk neu t r a l , and underwriter e f f o r t is unobservable. ( i i ) The entrepreneur se lec ts y . The se lec t ion of y w i l l be analyzed in Chapter Four. ( i i i ) The underwriter v e r i f i e s y at a d i r ec t cost K(y) and has a contingent contract with the market about the t ru th fu lness ( iv ) The entrepreneur exact ly compensates the underwriter for a l l costs and the present value of expected future l i a b i l i t y losses so that the underwriter earns zero net p r o f i t s . (v) The underwriter se lec ts the o f f e r i ng pr i ce and bears the en t i r e r isk of i t s sh i rk ing in d i s t r i b u t i o n e f f o r t . The cost to the entrepreneur of i ssu ing secu r i t i e s through the intermediary is It was shown above (in 3.4.4) that the payment to the underwriter is of y . C(y) = P e - P. N (3.4.5) where P „ is the true value of the f i r m . PN = K(y) + L(y) + g(e) I f P o then C(y) = K(y) + L(y) + g (e ) , 59 o r t h e c o s t t o t h e e n t r e p r e n e u r i s equa l t o t h e payment t o t h e u n d e r w r i t e r . The c o m b i n a t i o n o f (3.4.4) and (3.4.5) r e s u l t s i n C(y) = P e - P 0 + K (y ) + L ( y ) + g(e) . (3.4.6) T h e r e f o r e t h e c o s t t o t h e e n t r e p r e n e u r exceeds t h e payment t o t h e u n d e r w r i t e r i f P Q < P . The d i f f e r e n c e i s a g a i n t o t h e s h a r e h o l d e r s who p u r c h a s e t h e s e c u r i t i e s a t an o f f e r i n g p r i c e wh i ch i s l e s s t h a n e q u i l i b r i u m v a l u e . T h i s s h a r e h o l d e r g a i n i s a n e c e s s a r y c o s t t o t h e e n t r e p r e n e u r due t o t h e agency p r o b l e m a r i s i n g f rom t h e unobse r-v a b i l i t y o f t h e u n d e r w r i t e r ' s e f f o r t . The use o f t h e u n d e r w r i t e r by t h e e n t r e p r e n e u r i s a v i a b l e means o f c r e d i b l e c o m m u n i c a t i o n o f i n s i d e i n f o r m a t i o n t o t h e marke t i f t h e t h r e e c o n d i t i o n s i d e n t i f i e d by Diamond a r e s a t i s f i e d : 1. The e n t r e p r e n e u r r e c e i v e s a r e t u r n a t l e a s t as h i g h as he wou ld by c o n t r a c t i n g d i r e c t l y w i t h t h e m a r k e t . 2. The u n d e r w r i t e r / i n t e r m e d i a r y e a rns a z e r o e x p e c t e d r e t u r n . 3. I n v e s t o r s r e c e i v e t h e same r e t u r n s t h a t t h e y wou ld i f t h e y c o n t r a c t e d d i r e c t l y w i t h t h e e n t r e p r e n e u r . C o n d i t i o n one has been shown t o be s a t i s f i e d because t h e c o s t t o t h e r i s k - n e u t r a l i n t e r m e d i a r y o f t h e p o s i t i v e p r o b a b i l i t y o f a f u t u r e p e n a l t y i s l e s s t h a n t h e c o s t t o t h e r i s k - a v e r s e e n t r e p r e n e u r , and t h e e n t r e p r e n e u r compensates t h e i n t e r m e d i a r y f o r t h e e x p e c t e d p e n a l t y . I f t h e r e i s an agency p r o b l e m such t h a t t h e i n t e r m e d i a r y ' s d i s t r i b u t i o n e f f o r t i s u n o b s e r v a b l e , t h e r e i s an a d d i t i o n a l c o s t t o 60 the entrepreneur. However, as with any p r i n c i p a l - a g e n t problem, the p r i n c i p a l contracts with an agent only i f there i s b e n e f i t i n doing so (e.g., i t would cost more f o r the entrepreneur to d i r e c t l y d i s t r i b u t e the s e c u r i t i e s ) . Condition two was shown to be s a t i s f i e d . C ondition three i s s a t i s f i e d because the penalty t h r e a t induces t r u t h t e l l i n g such that i n v e s t o r s w i l l never pay more than P g f o r the shares. Investors w i l l be be t t e r o f f under the agency problem when P < P . o e 5. THE REGULATORY ENVIRONMENT The issuance of new s e c u r i t i e s i s regulated by the S e c u r i t i e s and Exchange Commission according to the S e c u r i t i e s Act of 1933. The sta t e d purpose of the Act i s to protect i n v e s t o r s against f r a u d . The i s s u i n g f i r m i s required to provide a minimum amount of information about the f i r m , i t s business environment, and i t s f i n a n c i a l c o n d i t i o n so that i n v e s t o r s can value the f i r m . The Act s p e c i f i e s c o n d i t i o n s under which i n v e s t o r s can claim damages i f the d i s c l o s u r e s made by the i s s u i n g f i r m can be l a t e r proven to be misleading or fraudulent or i f material information i s omitted. There are three p r i n c i p a l p a r t i e s to a t y p i c a l stock i s s u e : the 5 i s s u i n g f i r m , i n v e s t o r s , and the investment banker. The investment banker provides various s e r v i c e s to the i s s u e r which were discussed i n Section f o u r . However, i n the eyes of the SEC, the c h i e f r o l e of the investment banker/underwriter i s to provide a d d i t i o n a l p r o t e c t i o n to the i n v e s t o r s . 61 "The underwri ters 's ob l iga t ions and his central ro le as the intermediary between the i ssuer and the invest ing publ i c r i g h t f u l l y cause the publ i c to look to the underwriter for protec t ion against defects in the prospectus and to expect him to ve r i f y the accuracy of statements in the r eg i s t r a t i on statement. By assoc ia t ing himself with a proposed o f f e r i n g , an underwriter impl ied ly represents that he has made an inves t iga t ion in accordance with profess ional standards. Investors properly re ly on th i s added protect ion which has a d i r e c t bearing on t he i r appraisal of the r e l i a b i l i t y of the representat ions in the prospectus" [SEC 1933 Act Release, No. 5274, July 26, 1972.] There fore , the SEC c l e a r l y views the investment banker as a th i rd-par ty intermediary whose role is to ve r i f y d i sc losures made by the entrepreneur. The investment banker is l ega l l y l i a b l e (along with d i rec to rs of the company and i t s auditors) for damages i f p r i ce dec l ines within three years and material omissions or misstatements are in the prospectus. A f i rm can s e l l unseasoned shares d i r e c t l y to the pub l i c market. Since v i r t u a l l y a l l new issues are so ld through underwr i ters , i t is c l ea r that there is a demand for the adv isory , insurance, d i s t r i b u -t i o n , and v e r i f i c a t i o n roles provided by the investment banker. The i ssu ing f i rm and the investment banker enter into an i n f o r -mal agreement up to s ix months p r io r to the issue date . During the months before i s sue , the investment banker is required by the SEC to conduct an intens ive inves t iga t ion along with lawyers, aud i to r s , and engineers into the contents of the S-l r eg i s t r a t i on statement. When the r eg i s t r a t i on statement is f i l e d , a pre l iminary prospectus ( i . e . , the red herr ing) is published which contains most of the information which w i l l appear in the f i na l prospectus i f i t is approved by the SEC . 6 The o f f e r i ng pr i ce and de t a i l s about the underwrit ing agree-ment and the syndicate membership do not appear in the pre l iminary prospectus . If the SEC does not f ind the r eg i s t r a t i on d e f i c i e n t , i t 62 becomes e f f e c t i v e w i t h i n a few weeks. At that time, the underwriting agreement i s signed, an o f f e r i n g p r i c e i s chosen, the f i n a l prospec-tus i s p u blished, and the issue goes to market. The i s s u i n g f i r m receives the net proceeds of s a l e from the investment banker about a week a f t e r i s s u e . No p r e s e l l i n g or market c o n d i t i o n i n g a c t i v i t i e s are permitted p r i o r to the r e g i s t r a t i o n f i l i n g . A f t e r f i l i n g , u n r e s t r i c t e d o r a l and p r e s c r i b e d w r i t t e n communications are permitted. The p r e s e l l i n g a c t i v i t i e s of the underwriter include a m u l t i - c i t y road show which i s an important part of the marketing f u n c t i o n . ^ There are three types of underwriting agreements between the i s s u e r and investment banker. In a f i r m commitment agreement, the banker agrees to purchase the e n t i r e issue from the f i r m at an agreed upon p r i c e and then bears the e n t i r e r i s k of s e l l i n g the issue to the market at the s t a t e d o f f e r i n g p r i c e . In a best e f f o r t s agreement, the banker merely agrees to use his best e f f o r t s to s e l l the shares at the o f f e r i n g p r i c e . The t h i r d and l e s s common type i s an a l l - o r -nothing agreement where the banker agrees to s e l l the e n t i r e issue at the o f f e r i n g p r i c e w i t h i n a p r e s p e c i f i e d period of time, or the agreement i s c a n c e l l e d . In a f i r m commitment agreement, the p r i n -c i p a l underwriter forms a l a r g e syndicate of investment bankers to s e l l the issue i n order to reduce r i s k . The o f f e r i n g p r i c e i s determined by the banker and i s s u e r and appears on the cover of the f i n a l prospectus. The p r i c e cannot be increased by the banker. The banker however can prevent p r i c e d e c l i n e before a l l shares are s o l d by s t a b i l i z i n g the issue through pegging the market at the o f f e r i n g p r i c e and buying back shares at the o f f e r i n g p r i c e . Therefore the banker i n a f i r m commitment issue 63 bears the risk of price decline, but does not benefit directly in a price increase. A partner of the investment banker, Alex Brown and Sons, stated that this after-market support was an important factor g in gaining credibility of disclosure. From this brief description of the regulatory environment for new issues, it is clear that the assumptions of the theoretical role of the investment banker in the preceding section are consistent with the real world. It was assumed that the investment banker and issuer had identical information about the firm at the time the security is sold to the public. Such an assumption is realistic because of the long investigation period prior to issue. A syndicate is formed for firm commitment agreements and therefore the assumption of risk neutrality is appropriate. The preselling activities do require that the underwriter expend effort and may provide the underwriter with information about market conditions which is useful in setting the offering price. 64 Footnotes to Chapter Three "Sec . 11. (a ) . In case any part of the r eg i s t r a t i on statement, when such part became e f f e c t i v e , contained an untrue statement of a material fact or omitted to state a material fac t required to be stated there in or necessary to make the statements there in not mis lead ing , any person acqui r ing such secur i t y (unless i t is proved that at the time of such acqu i s i t i on he knew of such untruth or omission) may, e i ther at law or in equ i t y , in any court of competent j u r i s d i c t i o n , sue — (1) every person who signed the r eg i s t r a t i on statement; (2) every person who was a d i r e c to r of (or person performing s im i l a r funct ions) or partner i n , the issuer at the time of the f i l i n g of the part of the r eg i s t r a t i on statement with respect to which his l i a b i l i t y is asser ted ; (3) every person who, with his consent, is named in the r eg i s t r a t i on statement as being or about to become a d i r e c t o r , person performing s im i l a r func t ions , or partner ; (4) every accountant, engineer, or appra iser , or any person whose profess ion gives author i ty to a statement made by him, who has with his consent been named as having prepared or c e r t i f i e d any part of the r eg i s t r a t i on statement, or as having prepared or c e r t i f i e d any report or va luat ion which is used in connection with the r eg i s t r a t i on statement, with respect to the statement in such r eg i s t r a t i on statement, r epor t , or va lua t i on , which purports to have been prepared or c e r t i f i e d by him; (5) every underwriter with respect to such s e c u r i t y . (g) In no case sha l l the amount rece ivable under th i s sect ion exceed the pr i ce at which the secur i t y was of fered to the p u b l i c . " [U.S. Government P r in t ing O f f i c e (1976)] A recent example of such a lawsuit was reported in the September 7, 1983 Mall Street Journal• A shareholder of Computer Dev ices , Inc. sued the company, i t s d i r e c t o r s , i t s underwr i ters , and i t s accountants for f a i l u r e to d i sc lose post-palance sheet losses in the Ju ly 8, 1983 issue of one m i l l i o n shares at $11.25 per share. The pr i ce on the date of the lawsuit was $6.25. John Shad of the S .E .C . implied that the motivation for legal ac t ion i s pr i ce de l ine rather than new information about fraud when he sa id that once the market breaks and pr ices d e c l i n e , lawsuits re lated to new issue d i sc losure w i l l s ta r t f l y i n g (Venture, September, 1983). 65 Such precommitment can be compared to cost variance inves t iga t ion in a pr inc ipa l/agent se t t ing where the p r inc ipa l knows that the threat of variance inves t iga t ion induces the des i red act ion from the agent. If i nves t iga t ion is c o s t l y , why would i t be undertaken when i t is known that the agent acted opt imal ly? Unless the p r inc ipa l precommits to cos t l y i nves t iga t ion for ce r ta in outcomes, the rat ional agent w i l l not be induced to take the des i red a c t i o n . Studies by R e i l l y and Ha t f i e ld (1969), McDonald and F isher (1972), and Logue (1973) found that unseasoned new issues were underpr iced. Ibbotson (1975) studied aftermarket performance of unseasoned new issues in the 1960's and concluded that the average return in the f i r s t month was 11.4% and was not due to market i n e f f i c i e n c y . None of these authors could s a t i s f a c t o r i l y expla in the underpr i c ing . R i t t e r (1983) examined the "hot i ssues " market of 1980 and found that the average i n i t i a l return of 48.4% was a t t r i bu tab l e to natural resource issues which earned a 110.9% re tu rn . An explanation of the pe r s i s t i ng underpr ic ing phenomenon was of fered by Rock (1982) in a model in which some investors have ins ide information about values of new s e c u r i t i e s . As a resu l t of t h i s informational asymmetry, the informed oversubscribe to undervalued issues and the uninformed subscr ibe equal ly to over-and undervalued i s sues . Therefore , in order for there to ex is t uninformed demand, the issuer must o f f e r the new shares at a d i scount . Rock's resu l t appears to depend upon the two quest ionable assumptions that the i ssuer is uninformed and informed demand is less than the s i ze of the i s sue . The audi tor of the f i nanc i a l statements contained in the prospectus is a fourth party who shares in the legal l i a b i l i t y for d i sc losures made in the prospectus. The aud i to r ' s ro le is not considered in th is d i s s e r t a t i o n . The intermediary could be viewed as a combined investment banker and aud i to r . The information contained in the prospectus inc ludes : a) Audited f inanc ia l statements b) Proposed use of proceeds c) Out l ine of underwrit ing agreement d) L i s t of underwriters in syndicate and the commitment of each e) Five-year summary of income f) Deta i led desc r ip t ion of business g . Deta i led information about d i rec to rs and executive o f f i c e r s , inc lud ing age, remuneration, and shareholdings before and a f te r i s sue . "Wi l l iam F.X. Grubb, president of Imagic, one of the hottest new-issue prospects , is now spending more time peddling his company's soon-to-be-issued shares than i t s 'Demon Attack' home video games. Grubb and two of his top executives ~ prompted by a cadre of underwriters and armed with impassioned speeches, a s l i d e 66 show, and game samples — have swept through seven U.S. and f i ve fore ign c i t i e s in the past few weeks, p i t ch ing t he i r company to potent ia l i n ves to r s . " [Business Week. December 6, 1982,p. 100] 8. Venture. March, 1983. p. 92. 67 CHAPTER FOUR SIGNALING BY DIRECT DISCLOSURE: A BIVARIATE SIGNALING MODEL INTRODUCTION This chapter develops a s i g n a l i n g model i n which there i s asym-metric information about two parameters of the d i s t r i b u t i o n of future cash flows. An entrepreneur has i n s i d e information about the two paramaters and s i g n a l s his information with two c o s t l y s i g n a l s . Section 1 derives optimal r i s k sharing i n a pe r f e c t market. Section 2 shows how optimal r i s k sharing i s unattainable when there i s a market imperfection such as asymmetric i n f o r m a t i o n . The b i v a r i a t e s i g n a l i n g model i s formulated and analyzed i s s e c t i o n 3. Empirical i m p l i c a t i o n s of the a n a l y s i s are discussed i n Section 4. 1. RISK SHARING IN A PERFECT MARKET Pareto-optimal r i s k sharing i s a t t a i n a b l e i n a c a p i t a l market when market p a r t i c i p a n t s have i d e n t i c a l b e l i e f s about the d i s t r i b u -t i o n of the future cash flows to be generated by the firm's i n v e s t -ments. The c a p i t a l asset p r i c i n g model describes v a l u a t i o n of a f i r m or an investment p r o j e c t i n a per f e c t market when i n v e s t o r s ' preferences are defined over two parameters of the d i s t r i b u t i o n of cash fl o w s . Under the c a p i t a l asset p r i c i n g model, the expected r e t u r n / r i s k r e l a t i o n s h i p of a c a p i t a l asset i s : p _ r ,(Fm - r ) ' C ° V ( r j , rM> (4.1.1) j 2 68 random return on secur i ty of f i rm j random return on market p o r t f o l i o r i sk f r ee rate of in te res t covariance between random returns on f i rm j and the market p o r t f o l i o variance of returns of the market p o r t f o l i o Expected return is increas ing in only the systematic r i sk of the asset because investors are able to e l iminate f i rm-spec i f i c non-sytematic r i sk through investment in a we l l -d i v e r s i f i ed p o r t f o l i o of s e c u r i t i e s . Market value in terms of the r isk-adjusted present value of future cash flows is derived from the cap i ta l asset p r i c i ng model by convert ing expression (4.1.1) from returns to va lues . where C o v ( r j 'rM> Let V = current value of the f i rm V m = current market value of the market p o r t f o l i o x = random end-of-period value of the f i rm M = random end-of-period value of the market p o r t f o l i o r = r i sk f r ee rate of in te res t T h Q n : _ [x - v] _ x , Then r. = 1 j, = V " 1 69 [M - V m] m m V m M T m m m where o m i s the variance of values of the market p o r t f o l i o CovCr^, r M ) = Cov Vm 'V VV . Cov(x, M) The above four expressions are s u b s t i t u t e d i n t o (4.1.1) which then becomes: (u/V) - 1 = r + _M - 1 - r 'm L J "1 . r o : m . Cov (x, M) '-m —1 (4.1.2) where u = expected value of X M = expected value of M A f t e r a l g e b r a i c manipulations, expression (4.1.2) s i m p l i f i e s t o : p - X° Cov(x, M) r — (4.1.3) M - (l+r)V , ,o m where X = « 0™ m 70 or V = j* ~ p , l e t t i n g X=X° Cov (x, M) (4.1.4) In expression (4 .1 .3 ) , f i rm value is expressed as the r isk-adjusted present value of future cash flows where: X° Cov(x, M) is the r i sk adjustment in which the covariance term represents r isk and A 0 is the market pr i ce of r isk (1 + r) is the present value operator . Again, the r i sk adjustment is for systematic covariance r i sk on ly , y is the end-of-period expected value of the future stream of cash f1ows. Risk sharing in a per fect market with symmetric information w i l l be analyzed by der iv ing the r isk-shar ing contract between a r isk-averse entrepreneur seeking to ra ise funds to f inance a c a p i -t a l investment and r isk-averse investors who invest in a wel l-d i v e r s i f i e d p o r t f o l i o of s ecu r i t i e s in other firms or p ro j e c t s . The entrepreneur 's object ive is to maximize expected u t i l i t y of his end-of-period wealth, which is composed of returns from his own investment in his project or f i r m , the market p o r t f o l i o , and the r i sk l e s s asset . His problem can be expressed as: Max E { U ( W , ) } a,e subject t o : W Q + (1 - a ) V - I - B V m - Y = 0 (4.1.5) where W-, = a x + 3 M + (1 + r)Y (4.1.6) 71 Equation (4.1.5) i s the budget c o n s t r a i n t of the entrepreneur, i n which he has an i n i t i a l endowment of wealth, WQ, and w i l l make a c a p i t a l investment of I d o l l a r s , which i s valued by the market according to expression (4.1.3). He s e l l s to the market a propor-t i o n 1-a, where 0 < a < 1, of ownership i n the future cash flows to be generated by the p r o j e c t ; the s e l l i n g p r i c e i s 1-a times the present r i s k - a d j u s t e d value of the future cash flows, V. Any wealth remaining a f t e r the c a p i t a l expenditure i s invested i n the market p o r t f o l i o and the r i s k l e s s a s s e t . Market value of the market p o r t f o l i o i s V m and 3 i s the proportion of the market port-f o l i o owned by the entrepreneur. Y represents the amount of his investment i n the r i s k l e s s a s s e t . In order to s i m p l i f y the a n a l y s i s of the problem, two assump-t i o n s wi11 be made: 1. The entrepreneur has a negative exponential u t i l i t y func-t i o n : U(W) = -e -bW (4.1.7) 2. Returns on a l l s e c u r i t i e s are normally d i s t r i b u t e d : -bW ~ N(bW, b2o., ) In order to determine the d i s t r i b u t i o n of U(W), take logarithms of equation (4.1.7): log {-U(W)} = -bW Using the d i s t r i b u t i o n of bW, log {-U(W)} ~ N(-bW, b 2 0 2 ) 72 T h e r e f o r e -U(W) has a l o g n o r m a l d i s t r i b u t i o n such t h a t -bw + V2b2o. E{-U(W)} = e and Max E(U) = Max G{W (4.1.8) b L e t H ( a , 3 ) = w - - a. 2 1 2 ( 4 . 1 . 9 ) Then G(H) = e i s a m o n o t o n i c a l l y i n c r e a s i n g f u n c t i o n o f H such t h a t : To s o l v e t h e e n t r e p r e n e u r ' s p r o b l e m , s u b s t i t u t e f o r Y i n ( 4 . 1 . 6 ) , u s i n g ( 4 . 1 . 5 ) . A f t e r s u b s t i t u t i o n f o r V u s i n g ( 4 . 1 . 4 ) and s i m p l i c a t i o n , ( 4 . 1 . 1 1 ) becomes W1 = o (x - p + X) + 3(M - 0+ r ) V m ) + p - X + ( l + r ) ( W 0 - I) ( 4 . 1 . 1 2 ) The e x p e c t e d v a l u e and v a r i a n c e o f ( 4 . 1 . 1 2 ) a r e E(WT) = W ] = aX + 3(M - 0 + r ) V m ) + p - X + (1+r) (WQ - I) ( 4 . 1 . 1 3 ) 2 2 o u = a2 a2 + 3 2 a m + 2a3 Cov (x ,M ) ( 4 . 1 . 1 4 ) a r g Max E{U(W,)} = a rg Max H a , 3 a ,3 (4.1 .10 ) W1 = ax + 3M + (1 + r ) [WQ + (1-a) V - I - 3 V J ( 4 . 1 . 1 1 ) 73 F i r s t order condi t ions are der i ved , using (4 .1 .9 ) , (4 .1 .10 ) , (4.1.13) and (4 .1 .14 ) . They are: = X - ab a2 - 3 b Cov(x,M) = 0 (4.1.15) -21 = M - ( l+r)V m -3b a m - ab Cov(x,M) = 0 (4.1.16) To so l ve , subst i tue for 3b in (4.1.15) using (4 .1 .16) : M - (l+r)V - ab Cov(x,M) from (4.1.16) 3b = ^5 ^o ab Cov(x,M) a m (4.1.15) becomes: X - ab o 2 - [ X ° - ^ C o v ( x » M ) 1 Cov(x,M) = 0 o 2 m ? ? - ~ 2 r ° CTm - C0V(X ,M ) _ or ab [ DJ 2 — ] = 0 (4.1.18) a m There are three poss ib le condit ions under which the necessary equl ibr ium condi t ion (4.1.18) w i l l be s a t i s f i e d : (a) b = 0. This so lu t ion requires a r isk-neutra l entrepreneur who is d i f f e r en t to the level of a because he is d i f f e r en t to the amount of r i sk imposed on him. The entrepreneur has been descr ibed as r i sk averse and therefore b > 0. 74 o - ~ p (b) a am - Cov(x,M) = 0. This expression can be derived from the valuat ion expression (4.1.13) M - (l + r )V„ y = (l+r)V + Cov(x,M) m Then: x = (1+r) V + (M - (l+r)V ) Cov(x,M) + m Condit ional the Market (4.1.19) 2 2fTov(x,Mr| and a = cr 2 m 2 + a or a 2 2 \ 2  a a m - Cov(x.M) Therefore th i s so lu t ion requires that the project has zero non-sysematic r isk and that x and M are pe r fec t l y cor re la ted s ince C o v ( x > M ) = p(x,M~) a °m Cov(x,M) 2 = p(x,M) 2 2 2 0 Cf m 75 Then 2 > . 2 2 2 a = 0 -»• Cov(x.M) = a a + p = + 1 e ' m — An investment in the new project is a perfect subs i tute for an investment in the market p o r t f o l i o so that the r isk-averse entrepreneur is i nd i f f e r en t to the amount of his investment in his own p ro j ec t . While such a so lu t ion is poss ib l e , i t is not i n t e res t i ng for the purpose at hand. (c) a = 0 means that the entrepreneur w i l l s e l l 100% of the equity in his p ro j e c t . The r isk-averse entrepreneur wants to bear no unsystematic r i s k , while the we l l -d i v e r s i f i ed market can e l iminate f i rm-spec i f i c r i s k . The optimal so lu t ion is a* = 0 x° 3*= — from (4.1.17) when a = 0 The r isk-averse entrepreneur w i l l s e l l the f irm and invest in only the market p o r t f o l i o and r i sk l e s s asse t . The amount he invests in the market depends upon his degree of r isk aversion b and the market pr i ce of r isk X ° . This so lu t ion is consistent with r i sk-shar ing resu l ts in agency theory and p o r t f o l i o separat ion resu l ts in p o r t f o l i o theory . A standard r isk-shar ing resu l t f i r s t derived by Borch (1962) is that Pareto-optimal r i sk sharing between a p r inc ipa l and agent requires tha t : 76 [ji |yt j = k in every s t a t e . This expression states that the ra t io of marginal u t i l i t i e s of payoffs to the p r inc ipa l and agent must be equal to a constant in every s t a t e . Investors in the market are r isk neutral as to f irm-s p e c i f i c r i sk because i t can be e l iminated through p o r t f o l i o d i ve r -s i f i c a t i o n . The market can be viewed as a r isk-neutra l p r inc ipa l whose marginal u t i l i t y is a constant . In order to maintain the constant ra t io in every s t a t e , i t is necessary that the r isk-averse agent 's marginal u t i l i t y is a constant , which necess i tates that he receive a constant payof f . Therefore , i t is Pareto-optimal for the market to bear a l l f i rm-spec i f i c r i s k . P o r t f o l i o separat ion looks at the optimal sharing of r i sks of s e cu r i t i e s among many inves to rs . The basic two-fund separat ion resu l t is that a l l investors w i l l d iv ide t he i r wealth between one r i sky asset and a r i s k l e s s asset and that the equ i l ib r ium pr ice of the r isky asset w i l l be independent of ind iv idua l preferences or weal th. P o r t f o l i o separat ion obtains under the cap i ta l asset p r i c i ng model, and more general ly when u t i l i t y functions exh ib i t l i n ea r r i sk to lerance [Cass and S t i g l i t z (1970)] (such as with the negative exponential ) and when returns are normally d i s t r i bu ted [Ross (1976)]. A l l of the assumptions were used in the present model. The optimal d i v i s i o n of wealth between the r isky and r i s k l e s s assets for an ind iv idua l w i l l depend upon his degree of r i sk aversion [Mossin (1973)]. The entrepreneur therefore w i l l bear no nonsystematic r i sk and w i l l bear some proport ion of the systematic r i sk of a l l r i sky 77 assets through his optimal holding of the market p o r t f o l i o . It should be noted that i t has been assumed that the entrepreneur 's f i rm is s u f f i c i e n t l y small in r e l a t ion to the market p o r t f o l i o so that the parameters: 2 °m Cov(x.j, M) i = l , . . . , N firms in the market are unchanged a f te r the entrepreneur s e l l s his f i rm to the market. The formulat ion of the problem in th i s sect ion has followed that of Leland and Pyle with the exception that a perfect market is assumed. The equ i l ib r ium optimal so lu t ion to the problem of th i s sect ion is a " f i r s t - b e s t " so lu t ion when no constra ints are added due to a market imper fec t ion . The so lu t ion represents an ideal so lu t ion against which to compare resu l ts when there ex is ts an informational asymmetry. 2. RISK SHARING UNDER ASYMMETRIC INFORMATION The model of the preceding sect ion w i l l be modif ied by assuming that the market knows the d i s t r i b u t i o n of y such tha t : M ~ N(x 0 . o 0 2 ) The entreprenur has perfect information about y, and both the market and entrepreneur have perfect information about Cov(x,M), a , and o m . Market va luat ion then i s : x - X > y - X V = _ ° o 1+r < 1+r This scenario is analogous to that of Ake r l o f ' s in that the market knows the average value of y, the entrepreneur knows his y. In 78 Ake r l o f ' s model, the market unravels un t i l only the lemons are t r aded . The formulat ion of the problem is as in the preceding s e c t i on , with the exception that market va luat ion of the present r isk-adjusted value of future cash flows is V Q . F i r s t order condit ions analogous to those of sect ion 1 are: an 7 ~ ~ - 2 i l = u - x + A - a b a - B b Cov(x,M) = 0 (4.2.1) H = M - 0 + r )V m - 3b a m - ab Cov(x.M) = 0 (4.2.2) (4.2.1) and (4.2.2) are combined to solve for a*: a2 am2 - C o v U , M ) 2 m (4.2.3.) According to (4.2.3): a = 0 i f x Q = y when market co r rec t l y values f i rm a > 0 i f x Q < y when market undervalues f i r m , a < 0 i f x Q > y when market overvalues f i r m . C l e a r l y , such a story could ex is t only when the market is i r r a -t i o n a l . Assuming for the moment that such i r r a t i o n a l i t y does e x i s t , the informational asymmetry does not resu l t in Ake r l o f ' s market f a i l u r e because the product is r isky and the r isk-averse s e l l e r w i l l s e l l some of his product at an undervalued pr i ce because he can d i v e r s i f y r i sk with the proceeds. Since a* is 79 decreasing in b in (4 .2 .3 ) , a more r isk-averse entrepreneur w i l l s e l l a greater proport ion of the f i rm at an undervalued p r i c e . However, the above resu l t is not a rat ional equ i l ib r ium because investors w i l l know that the f irm is undervalued i f a > 0. Investors seeking more of the undervalued secur i t y w i l l bid up the p r i ce un t i l a = 0 and the equ i l ib r ium pr ice is reached. The entrepreneur 's act ion of invest ing in his own secur i t y conveys information to the market. The above scenario also allows for some deception because the entrepreneur might be able to hold a small equity pos i t i on in order to bid the pr i ce above true va lue . The above problem must be formulated r a t i ona l l y where the market in fe rs value as a funct ion of a . Leland and Py le ' s model analyzes the above problem with a as a cos t l y s ignal of u. The formulation of the problem is the same as above except: where x(a) is the market's inference about u. An addi t iona l constra int to the problem is tha t , in equ i l i b ru im: x(a*(u)) - u This const ra int is the market r a t i o n a l i t y cons t r a i n t . The necessary equ i l ib r ium condi t ion to t he i r problem i s : 80 (4.2.4) This expression equates the marginal benef i t and marginal cost of s igna l i ng with a: ( l - a ) x a = marginal increase in proceeds <xb[«] = marginal cost in terms of r i sk If ct* > 0, Pareto-optimal r i sk sharing is not achieved because of the informational asymmetry. The asymmetry is completely reso lved , but at the cost to the entrepreneur of his bearing p ro j e c t - spec i f i c r i sk which can be cos t l e s s l y t rans fer red to the market in a perfect market. Leland and Pyle solved the d i f f e r e n -t i a l equation in (4.2.4): a 2 a 2 - Cov(x,M) 2 x(a) = -b 2 [log(l-a) + a] + K (4.2.5) a m This expression defines a family of inference schedules. The Pareto-optimal schedule is one in which the f i rm with the minimum value does not s i g n a l . The equ i l ib r ium schedule i s : ; ( o ) = _ b gV - COV(X-,H)2 [ L O G ( 1 . O ) + O ] + ( 1 + R ) I + A ( 4 . 2 > am (l-a)x = ab 2 2 m - Cov(x.M)' 8 1 a 2 o m 2 - Cov(x*,M)2 and V(o) = -b ? [log(l-o) + a] + I (4.2.7) a m 1+r It is essential to Lei and and Pyle's model that the market knows a , o m , and Cov(x,M) (as well as b) in order to interpret the signal a because the cost of a depends upon the magnitude of firm specific risk. I ; a —Figure 4.1. Equilibrium Signaling Schedules a 2 a m 2 - Cov(x,M)2 If the value of o £ = ^ 1 S n o t known by the °m market, a will not be a fully-revealing signal i f there is more 2 than one possible value of o £ , as is shown in Figure 4.1. For a 2 given a, the marginal cost is increasing in a £ . If the market 82 observes a* and knows the d i s t r i b u t i o n of a , i t would have to £' 2 i n f e r o £ . Otherwise there would be an opportunity for f a l se s i g n a l i n g . Then the entrepreneur whose project has high f irm-2 s p e c i f i c r i sk a w i l l be motivated to communicate his i n fo r 3 2 mation so that the market can co r rec t l y value the f i rm at V(a*, a ) 2 Firm value appears to be independent of a when expressed as V=(p - X) / (1+r). However, when f i rm value under asymmetric information is expressed as a funct ion of a as in (4 .2 .7 ) , i t is a 2 funct ion of a a l s o . Therefore, i f an informational asymmetry 2 ex i s t s about a as well as y, the entrepreneur cannot s ignal f i rm value with a s ing le s ignal when the cost of that s ignal depends 2 upon a . Market uncertainty about the value of the second para-meter w i l l provide a se t t ing where two cos t l y s igna ls w i l l be used 2 to communicate ins ide information about u and a . The s igna l ing model w i l l be analyzed in the next s e c t i on . 3. SIGNALING THROUGH DIRECT DISCLOSURE The motivation ex i s t i ng for an entrepreneur to invest in a cos t l y s ignal is the same as in Section 2. The entrepreneur is endowed with i n i t i a l wealth and a technology. In order to r ea l i ze returns on the technology, a cap i ta l investment in the amount of I must be made. The entrepreneur knows a l l the parameters of the d i s t r i b u t i o n of future cash flows to be generated by the inves t -ment. Investors in the market know only the d i s t r i b u t i o n of u, and 2 do not know a . In the Leland and Pyle model, investors presumably 2 know a s ince they are assumed to know the value of f i rm s p e c i f i c r i sk as well as parameters of the d i s t r i b u t i o n of returns on the 83 market p o r t f o l i o . In a perfect market, f i rm value is independent 2 of a s ince only systematic r i sk is p r i c e d . However, as was discussed in sect ion 2, i f value is in fe r red from a s ignal which 2 2 has a cost funct ion dependent upon a , the market must know a in order to in te rpre t the s i g n a l . Therefore a second s ignal may be necessary so that investors can in te rpre t the f i r s t s ignal c o r r e c t l y . The entrepreneur chooses to communicate his ins ide information about M by a d i r ec t d i sc losure about the value of his project to the market. The d isc losure takes the form of a piece of i n f o r -mation which is the entrepreneur 's estimate of y. In other words, he makes a statement such as "the expected end-of-period value of the project in terms of future cash flows is y . " The entrepreneur seeks the serv ices of a r isk-netura l intermediary/investment banker to share r i s k s , help in s e l l i n g the s e c u r i t y , and provide t h i rd-party v e r i f i c a t i o n of the d i s c l o s u r e . The proof that a large underwrit ing group behaves as i f i t were r isk neutral was not pre -sented in Chapter Three because the notat ion is developed in th i s chapter . The proof appears in Appendix 1, The cost of the i n t e r -mediary 's serv ices was derived in Chapter Three. Investors then i n f e r the value of the project from y . In order to be able to solve the s igna l ing problem, i t is necessary to spec i fy a funct ional form for the cost funct ion of y . In sect ion four of Chapter Three the cost funct ion was shown in expression (3 .4.6. ) to be C(y)= K(y) + L(y) where K(y) = d i rec t costs of v e r i f i c a t i o n 84 Po n ( y ;u , a ) L(y) = T+F f r o m (3-4-2) Present value of expected future l o s s . The p robab i l i t y of loss was shown in sect ion two of Chapter Three as: T n ( y ; y ,o 2 ) = / f(x) dx — oo 2 2 2 (y-2o) ( a + a ) - x Q a where T = ^ °o f(x) = normal density funct ion of x. There does not ex is t a closed form so lu t ion to the n expression and i t therefore w i l l be approximated by a funct ion which possesses ce r ta in necessary c h a r a c t e r i s t i c s . Cha rac te r i s t i c s of L(y) were shown in sect ion two of Chapter Three to be: 1) L y > 0 2) L < 0 y 3) L 2 < 0 The d i r ec t costs of d i sc losure w i l l be assumed to be such that : K 2 = 0 85 which means that out-of-pocket inves t iga t ion costs are increas ing 2 in the level of stated q u a l i t y , but are unrelated to u and a . Addi t iona l necessary cha r a c t e r i s t i c s are: 4) Cy y < 0 from Spence's cost condi t ion to exclude imi ta t ion of the s i g n a l e r ' s behavior by an entrepreneur with a project with a lower va lue . 5) C * 0 is frequently necessary to s a t i s f y second-order cond i t i ons . The cost of y w i l l be approximated by: C(y; P,O2) = (4.3.1) 1 ( l+r)uo which s a t i s f i e s : 3 p0 • y 2 > 0 ( l+r)uo 2) C = u - p o • y 3 ( l + r ) u 2 o 2 < 0 for y > 0 < 0 ( l+r )pa 4 4) C -3P 0 * y 2 < 0 ( l + r ) y 2 a 2 6 P cb y 5 C = D - l l ( l+r )ya 86 In (4 .3 .1 ) , the components of the cost of y are combined so that p • y 3 C(y) - K(y) + L(y) =-2 ? (1 + r) ya An i n t u i t i v e explanation of th i s cost funct ion fo l l ows . ( i ) C(y) > for y > 0 because there are d i rec t costs of ce r -t i f i c a t i o n of y from the K(y) term even when L(y) is very sma l l . ( i i ) As y becomes greater , the p robab i l i t y of a penalty becomes a more s i g n i f i c a n t port ion of the cost of c e r t i f i c a t i o n . ( i i i ) 4 is a s ca l i ng constant to ensure that 0 < n < 1 and to prevent the penalty from being so high that y is uneconomic. 2 It is c l ea r that a must be known in order to in te rpre t the s ignal 2 y because the cost and marginal cost of y are decreasing in a . 2 Figure 4.2 i l l u s t r a t e s C(y) and how C(y) var ies with a . Investors w i l l be unable to i n fe r f i rm value from y when they do not know y 2 or a and both appear in the cost funct ion of y . A second s ignal w i l l be a, entrepreneuria l ownership in his own project or f i r m . 2 . The cost of a was seen to be increas ing in a in sect ion II. 2 Therefore a and y have d i f f e r en t re la t ionsh ips to a . A high value 2 for a combined with a ce r ta in y w i l l ind ica te a low a , and vice ve rsa , y conveys information about y, and a conveys information about the cost of y . 87 C(y) 2 C(y; o~ ) 2 C(y; a 2 ) C(y; a, ) 2 2 > a 2 2 > a 3 2 Figure 4 .2 . Cost of C e r t i f i c a t i o n Function for D i f f e ren t Levels of Talmor (1981) formulates and attempts to solve a s igna l ing problem in which dividend po l i cy and cap i ta l s t ructure are modeled as simultaneous s igna ls of f i rm value when there i s an i n f o r -mational asymmetry between ins iders in the f irm and the market about the mean and variance of before-tax earnings from opera t ions . The cost of debt is the p robab i l i t y of bankruptcy when earnings are i n s u f f i c i e n t to meet promised payments. Dividends are cos t l y s igna ls because cos t l y sources of funds must be found i f earnings are i n s u f f i c i e n t to meet promised dividend payments. The cost of s igna l i ng with dividends depends upon the debt level because the p robab i l i t y of meeting dividend payments with earnings is nega t i -vely re lated to the level of outstanding debt. Talmor was unable 88 to der ive the market's inference schedule about f i rm value because of the complexity of his model. The problem of the entrepreneur in the b i va r i a te s igna l ing model presented here is to maximize expected u t i l i t y of his end-of-per iod wealth which is the same object ive funct ion as that in sect ion one. In addi t ion to se l ec t ing investments in his own f i rm and the market p o r t f o l i o , a and 3, he chooses a d i sc losure y , where y is a s t a t e -ment about y . To s imp l i f y ana l y s i s , i t is assumed that Cov(x,M) = 0: future cash flows generated by the project are uncorrelated with cash flows on the market p o r t f o l i o . It was shown in sect ion one that systematic market r isk w i l l be shared opt imal ly through a market p o r t f o l i o . The r isk-shar ing resu l t in sect ions one and two which is of in te res t is the sharing of f i rm-spec i f i c r i sk in an imperfect market. Therefore i t is assumed with l i t t l e loss of genera l i t y that the ent i re r isk of the project is p ro j e c t - spec i f i c r i sk so that the value of the f i rm is W, = a x + 3M + (1+r) Y (4.3.2) V = (4.3.3) The s igna ls a and y are cos t l y to the entrepreneur, thus serv ing as c red ib le s igna ls of value to the market. Investors observe the entrepreneur 's choices a* and y* and value the f i rm as 89 ( ' y } ~JTr (4.3.4) where x(a*, y*) is the value of u in fe r red by investors from a* and y* . It is being assumed that a s ing le separat ing equ i l ib r ium ex is ts where entrepreneurs of firms with d i f f e r en t values se lec t d i f f e r en t l eve l s of a and y such that investors co r rec t l y i n f e r value in equ i l i b r i um . The existence of such an equ i l ib r ium has been questioned [ e . g . , R i ley (1979)] because a l t e rna t i ve types of e q u i l i b r i a , such as mul t ip le or poo l ing , may dominate. Feltham and Hughes (1983) state that mul t ip le e q u i l i b r i a occur when the buyers o f f e r sets of zero-prof i t contracts to s e l l e r s who are constrained to se lec t one contract from the s e t . When a s e l l e r o f fe rs the con t rac t s , as in th i s chapter, he w i l l o f f e r only that contract which maximizes his welfare and a s ing le equ i l ib r ium contract w i l l r e s u l t . Feltham and Hughes prove that i t is the p r i o r be l i e f s of investors which determine whether a pool ing or separat ing equ i l ib r ium is opt ima l . Therefore , a basic assumption to the model in th i s chapter is that investors do not have p r i o r be l i e f s which w i l l resu l t in a pool ing equ i l i b r ium: that i s , they do not have a p r i o r b e l i e f that the f irm has a high va lue. When there is a con-tinum of va lues , th i s condi t ion must hold for every sub- in te r va l . The problem of the entrepreneur now i s : Max E{U(WX)} a,3,y s . t . WQ + ( l-a)V(a,y) - C(y) - I - 3Vm - Y = 0 (4.3.5) 90 (4.3.6) C(y*;y,a 2) = where P = P <j> o T from (4.3.1) (4.3.7) (1+r) vo The maximization problem is subject to three const ra ints which are : 1. The budget const ra int (4.3.5) ind icates that the entrepre -neur s e l l s a proport ion 1-a of equity in future cash flows for 1-a times the market's in fe r red valuat ion of the cash flows based upon the two observed s i g n a l s . The proceeds of the sale of equity are reduced by the cost of v e r i f i c a t i o n C(y ) . 2. Equation (4.3.6) is the market r a t i o n a l i t y const ra int which states that the market's inference is correct in equ i l i b r i um. 3. The t h i r d const ra int (4.3.7) is a competivity const ra int which states tha t , in equ i l i b r i um, the underwriter is exact ly com-pensated for i t s costs so that zero p r o f i t s are earned. The budget const ra in t (4.3.5) can be better understood by re-expressing i t in the notat ion used in Chapter Three. The cost of d i r e c t d i sc losure when the underwriter d i s t r i b u t e s , p r i c e s , and c e r t i f i e s the issue was shown in equation (3.4.7) to be Since the entrepreneur is s e l l i n g a port ion of the equity is his f i r m , the cost can be re-expressed as c(y) = P E - P N 91 C(y) = (1-a) (P e-P N) or ( l-a )P N = (l-a)P - C(y ) , where P g and PM re fer to the pr ices of a l l shares, not jus t those sold to i nves to r s . Since P g is the equ i l ib r ium p r i c e , ( l-o)P N = ( l - o ) V - C(y) and a f te r subs t i tu t ing ( 4 . 3 . 6 ) , ( l-o)P N = ( l-a )V(a ,y ) - C(y ) , Therefore the budget constra int ( 4 . 3 . 5 ) can be rewritten as WQ + ( l - a ) P N - I" 3Vm - Y =0 which more c l e a r l y indicates that the entrepreneur s e l l s (1-a) of the equity to the market for ( l -a )V ( a , y ) , receives ( l - a ) ? ^ and then invests in the market p o r t f o l i o and the r i sk l e ss asse t . The assumption of normally d i s t r i bu ted cash flows and constant absolute r i sk aversion s t i l l hold so that the object ive funct ion s i m p l i f i e s t o : h 2 Max H = W1 - -2- a w (4 .3.8) a ,B,y 1 ( 4 . 3 . 5 ) and ( 4 . 3 . 6 ) are used to ca l cu la te Wn. Wn = ax + BM +(l + r)[W 0 + ( 1 - a ) ^ j^X - C(y) - I - 0 V J ( 4 . 3 . 9 ) After s i m p l i f i c a t i o n , ( 4 . 3 . 9 ) becomes: 92 W, = a[x - x(a,y ) ] + 3 [M - ( l + r ) V j + x(ct ,y) + (1+r) [ W n - C(y) - I] 1 m U (4.3.10) The expected value and variance of (4.3.10) are: w, = a[u - x (a ,y ) ] + 3 [M - ( l + r ) V j + x(a,y) + (1+r) [ W n - C(y) - I] 1 m U (4.3.11) 2 2 2 2 2 o w = « o + 3 a m (4.3.12) F i r s t-order Condit ions to (4.3.8) are obta ined, using (4.3.11) and (4 .3 .12) : _3H = u - x(o,y) + (1-a) x - aba 2 = 0 (4.3.13) 9a a _9H = M - ( l+r)V m - 3ba m 2 = 0 (4.3.14) 83 iH = ( l -a )x v - (l+r)C = 0 (4.3.15) 9 y y y Expressions (4.3.13) and (4.3.14) show that a and y w i l l be se lected so that marginal cost equals marginal benef i t for each. Any remaining wealth w i l l be invested in the market p o r t f o l i o and X° and r i sk l e s s asset such that 3 = , where o M " ( 1 + r ) V m X = 2 1 S the market pr i ce of r i s k . a m 93 Equations (4 .3 .13) , (4 .3 .14) , and (4.3.15) are a system of three equations in the three unknowns a, 3, and y . However, a d i r e c t so lu t ion is not poss ib le because i t is not known, a p r i o r i , what the s p e c i f i c form of x(a , y ) i s . It i s necessary in equ i l ib r ium that x(a* , y * ) = p, but pa r t i a l der i va t i ves of the inference schedule appear in (4.3.13) and (4.3.15) and these are not known. In order to der ive the x(a , y ) inference schedule, equations (4.3.13) and (4.3.15) w i l l be combined with the market r a t i o n a l i t y and competivity cons t r a i n t s . These four equations def ine the necessary equ i l ib r ium condit ions and together they per -mit so lu t ion of x(ot ,y ) : p - x(a,y) + (1-a) X a = a b a 2 (4.3.13) ( l-a ) x y = 0 + r ) C y (4.3.15) x(a*,y*) = p (4.3.6) 3 C(y*; p,a 2)= 7 (4.3.7) (1+r) pa Di f f e r en t i a t e (4.3.7) and subst i tu te into (4.3.15) 2 3Py 2 (1+r) pa Then (4.3.15) becomes: pa (4.3.16) 94 Since (4.3.13) and (4.3.16) must hold at the optimal choices of a and y , condi t ion (4.3.6) must hold a l s o . Therefore (4.3.6) can be subst i tu ted into (4.3.13) and (4 .3 .16 ) . (4.3.13) becomes: (l-o)x = aba 2 (4.3.17) a (4.3.16) becomes: 2 (l-a)x = ^ (4.3.18) x a Equations (4.3.17) and (4.3.18) are a system of simultaneous par-t i a l d i f f e r e n t i a l equations to be solved for x(a,y) where the 2 inference schedule cannot depend upon a which is unobservable. Solve (4.3.17) for a 2 : ( l-a)x 2 and subst i tu te for a in (4 .3.18) : (l-a)x y = b . (4.3.20) x (l-a)x a Rearrange (4 .3 .20) : ? 2 ( 1 - a r x x x = 3a b Py (4.3.21) J 95 o Because (4.3.17) and (4.3.18) both contain a which must be e l i m i -nated, i t was poss ib le to convert simultaneous pa r t i a l d i f f e r e n t i a l equations into a s ing le equat ion. The method of so lu t ion of (4.3.21) is the method of separat ion of var iab les [Boyce and Diprima (1969), p. 422-425] whereby a s o l u -t i on w i l l be found of the form x(a,y) = g(a) h (y) (4.3.22) Subst i tu t ion of (4.3.22) into (4.3.21) y i e l ds ( l-a ) 2 (g a h) (h y g) (gh ) = 3a b Py 2 (4.3.23) Equation (4.3.23) is equivalent t o : 2 (1-a) 2 g g 2 = 3 b Py , J- (4.3.24) a h \\ y In (4.3.24) the left-hand s ide depends only on a and the right-hand s ide on y and exogenous parameters. In order for (4.3.24) to hold in equ i l i b r i um, i t is necessary that both sides be equal to the same constant . The constant of separat ion w i l l be ca l l ed 6. Then (4.3.24) becomes: 2 2 2 (1-a) g g 3 b Py a - = (5 (4.3.25) a 2 V and (4.3.25) resu l ts in two ordinary d i f f e r e n t i a l equations for g(o) and h(y) : 96 g a g _ 6 , (4.3.26) 3 b P,y (4.3.27) The method of separat ion of var iab les has permitted replac ing a p a r t i a l d i f f e r e n t i a l equation with two ordinary d i f f e r e n t i a l equations and has s i m p l i f i e d the der iva t ion of x ( a , y ) . In order to solve for g (a ) , integrate (4 .3 .26) : i_ g 3 = <srr + in d - a ) + k f l 3 Ll-o 'J or g(a) = {36 p_ + In (1-a) + kjj} 1/3 (4.3.28) where k-j is the constant of i n t eg r a t i on . S i m i l a r l y , the in tegra t ion of (4.3.27) y i e lds 1 . 3 _ bP r + k5 or h(y) ={^~- Cy3 + k2]} 1/3 (4.3.29) where k2 is the constant of in tegra t ion , Combine (4 .3 .22) , (4 .3 .28) , and (4.3.29) to a r r i ve at x(a,y) = {3 5 - i - + ln ( l-a ) + k, 1-a 1 1/3 } 3 b P 3 A , - f i — y + k 2 .1/3 97 x(a,y) = {9 b P T~— + ln( l -a ) + k, l-a 1 y ° + k. 1/3 } (4.3.30) Expression (4.3.30) defines a family of market inference sche-du l e s . In order to determine the Pareto-optimal schedule which w i l l be the unique equ i l ib r ium schedule, (4.3.30) must be evaluated at the boundaries. There are three boundary condit ions for which (4.3.30) must be evaluated: (a) x(a=0, y=0) (b) x(a = 0, y > 0) (c) x(a > 0, y = 0) The optimal so lu t ion for the entrepreneur with the project with the lowest value is no investment in s igna l ing because the s igna ls are cos t l y and there is no benef i t derived from fa l se s i g n a l i n g . Therefore x(a = 0, y = 0) = the minimum value of y in the market. It was assumed that investors know the d i s t r i b u t i o n of y and the minimum value of y. It w i l l be assumed that the lowest value is y . = 0. If umin = M * ° ' t n e n t n e s ° l L l t i o n ° f t n e inference schedule includes a func-t i on of M which gives r i se to a more complex expression without adding eco-nomic i n t e r e s t . If y^. = 0, V(«=0, y=0) - ^ - 0 (4.3.31) To determine Pareto-optimal values for k-j and kg, combine (4.3.31) and (4.3.30) to obta in : 0 = 9bP [1 + k-,] [ k 2 ] (4.3.32) 98 The values for and k 2 must be consistent with condi t ion (4 .3 .32 ) . C lea r l y (4.3.32) w i l l hold for the values k-| = -1 and/or k 2 = 0 In tu i t ion suggests that x(a,y) = 0 for the three boundaries (a ) , (b) , and (c) s ince one s ignal alone cannot be unambiguously i n t e rp re ted . However, a more rigorous argument w i l l be used. P ropos i t ion 4 . 1 . The boundary condit ions are k-| = -1 and k 2 = 0 which implies that e i ther a*=0, y*=0 or a*>0, y*>0. Proof . The f i r s t -o rde r condit ions (4.3.17) and (4.3.18) must be s a t i s f i e d for a l l a*, y*. Expressions for x (a,y) and x (a,y) w i l l ot y be derived from the x(a ,y) schedule and subst i tu ted into the f i r s t -order cond i t i ons . Inference schedule (4.3.30) is d i f f e r en t i a t ed with respect to a: o 1/3 a [9bP(y i + k ? ) ] x (a,y) = ? - (4.3.33) 2/3 3(1-a) {j-L- + In (1-a) + k ] } Inference schedule (4.3.30) is d i f f e r en t i a t ed with respect to y: 1/3 y 2 {9bP [ ^ + In (1-a) + k^} Cy 3 + k 2] x y(a,y) = ^ 2/3 (4.3.34) Expression (4.3.33) is subst i tuted into f i r s t -o rde r condi t ion (4 .3 .17 ) : 99 o 1/3 a [9bP (y J + k ? ) ] , , = 2/3 = a b / (4.3.35) 3 ( 1 - 0 0 I" + M Expression (4.3.34) is subst i tu ted into f i r s t -o rde r condi t ion (4 .3 .18 ) : ? 1 1/3 9 (1-a) { 9bP [ y i - + ln (1-a) + k,]} 3Py^ ^ L = _ (4.3.36) [ y 3 + k 2 ] 2 / 3 PO Expressions (4.3.35) and (4.3.36) must hold for a l l choices a*, y* . Values for k-| and kg w i l l be determined by evaluat ion of (4.3.35) and (4.3.36) at boundaries (b) and ( c ) . * Case 1. Boundary (b): a = 0, y > 0. When a = 0, (4.3.35) is s a t i s f i e d for a l l values of k-j, kg, and y . When a* = 0, (4.3.36) becomes 1/3 2/3 ua 2 { 9bP [1 + k n]} = 3P [ y 3 + kg] (4.3.37) which must be s a t i s f i e d for a l l y* . (1) Let k-, = -1 Then the left-hand side of (4.3.37) equals zero , and (4.3.37) w i l l hold only i f *3 2 / 3 3P[y + kg] = 0 *3 One f eas ib l e so lu t ion is kg = -y . Such a so lu t ion is not permitted because kg is a constant of in tegra t ion over y and cannot be a funct ion of y . * The only permiss ib le so lu t ion therefore is y =0, kg = 0. ( i i ) Let kg = 0 Then (4.3.37) becomes 100 ua {9bP [1 + k^} = 3Py' One f eas ib l e so lu t ion is 3 2 J 9bP Such a so lu t ion is not permitted because k-| cannot be a funct ion of y s ince (4.3.26) cannot depend upon y . * The only permiss ib le so lu t ion therefore is y =0, k-j = -1. Therefore i t has been proved that when a*=0, i t must be so that k-| = -1 and k 2 = 0 and y* = 0. Case 2. Boundary (c ) : a > 0, y* = 0. •k When y = 0, (4.3.36) is s a t i s f i e d for a l l values of a, k-|, and k 2 . When y* = 0, (4.3.35) becomes. [ 9 b P k 2 ] 1 / 3 = 3(l-a) b a 2 {j^ + In (1-a) + k ] }2/3 (4.3.38) which must be s a t i s f i e d for a l l a* ( i ) Let k 2 = 0 Then the left-hand side of (4.3.38) equals zero and (4.3.38) w i l l hold only i f 2/3 3(l-a*) b a 2 { - \ + In (1-a*) + k, } = 0 1-a 1 Since k-| is a constant of in tegra t ion over a, k-j cannot be a funct ion of * a. The only permiss ib le so lu t ion is a = 0, kn = -1 101 ( i i ) Let k 1 = -1 Then (4.3.38) becomes: [ 9 b P k 2 ] 1 / 3 = 3(l-a) ba 2 + ln (1-a) -1 }2/3 Due to the separable property of the problem, kg cannot be a funct ion of a [from (4 .3 .27 ] . The only permiss ib le so lu t ion then * i s a =0, kg=0 Q.E.D. The value of the constants are k-| = -1 and kg = 0, with the r esu l t i ng Pareto-optimal inference schedule: x (a,y) 9bPy 3 + ln (1-a)} 1/3 (4.3.39) Proposi t ion 4.1 shows that Pareto-optimal s igna l ing is an invest -ment in both s igna ls or in no s i g n a l . Each s ignal is cos t l y and there is no benef i t to be derived from s igna l ing with one s i g n a l . It can be seen in (4.4.39) that x(a=0, y=0) =0 x(a=0, y>0) = 0 x(a>0, y=0) = 0 It remains to be shown that ( i ) the inference schedule used by the market is f u l l y r evea l ing , 102 ( i i ) the market r a t i o n a l i t y condi t ion is s a t i s f i e d , and ( i i i ) the s igna l ing mechansim is incent ive compatible. The f i r s t condi t ion is v e r i f i e d by examining cer ta in propert ies of the inference schedule, the second by ve r i f y ing that x ( a * , y*) = y 2 2 2 and a- ( a * ,y*) = a where is the in fe r red var iance , and the t h i r d by looking at second-order cond i t i ons . P ropos i t ion 4.2 A f u l l y reveal ing equ i l ib r ium ex is ts when the market's inference schedule is 3 1/3 x ( a , y ) = {9bPy + l n ( l - a ) ] } Proof The s igna l i ng equ i l ib r ium is f u l l y reveal ing i f x (a , y ) is s t r i c t l y monotonic in both a and y . To determine monotonicity with respect to a , given y 9x ( a , y ) 3 a b Py 2/3 (4.3.40) 2 8 a (1-a) {9 b P [-2L + l n ( l-a)]} 1-a In order to sign 3x/3a i t is necessary to s ign [y"— + ln (1-a)]: Observe that ^ + ln ( l-a) = 0 when a = 0 and 4^ 3- " a 9 > 0 for 0 < a < 1 3a , Z (1-a) 103 Therefore 9 x j a ' y ) > 0 3a To determine montonicity with respect to y , given a Msrfl = { 9 b P tfL. + l n ( l - a ) ] } 1 / 3 (4.3.41) > 0 because + ln(l-a) > 0 for 0 < a < 1 Q.E.D. Propos i t ion 4.3. The fu l l y- revea l i ng s igna l ing equ i l ib r ium s a t i s -f i e s the market r a t i o n a l i t y cond i t i ons . Proof . The steps in the proof are: ( i ) Use the x(a,y) schedule in f i r s t -o rde r condit ions to der ive a*, y * . ( i i ) Use a*, y* in x(a,y) to determine whether x(a*, y*) = u and of (a* ,y*) = a 2. To der ive a* ,y* , x(a,y) is used in the f i r s t -o rde r con-d i t i o n s . The f i r s t -o rde r condit ions are: ( l-a ) x a = ab a 2 (4.3.17) (l-a)xy = iP^-. (4.3.18) ycr 104 It was seen prev ious ly that: 3 a b P y (1-a) {9 b P [-a- + ln( l-a) ] } l-a 2/3 x y = {9 b P [yS- + ln( l-a) ] } 1/3 Combining (4.3.17) and (4.3.40) y i e lds 7 (1-g) 3a b Py ( l _ a ) {g b P [ _ 2 L + In(l-a)]} = a b a 2/3 or y b a 2(l-a){9 b P C-^ -SL + In(l-a)]} 2/3 3 b P Combining (4.3.18) and (4.3.41) y i e l ds 1/3 0-o) { 9 b P [^L-H ln( l-o)] } = ^ y a 2 _ or y -(1-a) ya {9 b P 3T ° - + ln( l-a) 1-g 1/3 Square (4.3.42) and subst i tu te into (4.3.43) 105 b 2a 4 ( l-a) 2{9 b P T -2 - + ln ( l-a) 1-a 4/3 } (1-a) pa 2 {9 b P 1 - ° - + ln( l-a) 1-a 1/3 2 2 9 b P Expression (4.3.44) can be solved for a: 3P (4.3.44) T ^ r + ln ( l-a*) = 3 b <j (1-a*) (4.3.45) which is an i m p l i c i t funct ion for the choice of a*. To solve for y*, subst i tu te (4.3.45) in to (4.3.42) n *\ 2 2 1/3 which descr ibes the choice of y * . (4.3.46) Subst i tute (4.3.45) and (4.3.46) in to x(a,y) to a r r i ve at: 1/3 2/3 2 1/3 1/3 (9bp) y ( l-a)o y 3P 2 3 b a (1-a) (4.3.47) Thereby proving that x(a*(y ,cr 2 ) ,y*(y,a 2)) = y 2 ... To determine whether market r a t i o n a l i t y for a is s a t i s f i e d : from (4.3.19) 106 .2 _ 0-«)xo o = a b It can be seen that (4.3.19) expresses a as a function of obser-vables. Therefore the market will infer that 2 , (l-g)xg ° i = ^Tb— Combining (4.3.48) with (4.3.40) yields (4.3.48) °1 ( a' y ) = T^b (1-a) . 3 a b Py (l-ar{9 b P — + ln(l-a) -,,2/3 1-a or a i (a*,y*) = 3 Py (l-a){9 b P ° — + In(l-a) 1-a 2/3 (4.3.49) Substitute (4.3.45) and (4.3.46) into (4.3.49) to arrive at: a- (o,y) = 3P 2 1/3 2 2/3 (l-o)o 3 b a (1-a) 3 P • 2/3 (1-a) (9 b P) 2 2/3 (4.3.48) or a. (o*,y*) = a Thereby proving that a 2(a*(p,a 2 ) ,y*(u,o 2 ) ) = a 2 Q .E.D. A proof that the second-order conditions are sat isf ied appears in Appendix 2. 107 The shape of x(a,y) can be determined by examination of several d e r i v a t i v e s . x(a,y) i s increas ing and l i nea r in y s ince x >0 as shown in Proposi t ion 4.2 and x = 0 from (4 .3 .41 ) . %/ yy x(a,y) is increas ing and convex in a s ince x a >0 as shown in Propos i t ion 4.2 and x a a >0 is shown below. An expression for x a a appears in Appendix 2 as equation (A2.13): b(l + a ) y a 2 - 2 ( aba 2 ) 2 X = 5 aa /1 \ 2 (1-a) y which, a f te r s i m p l i f c a t i o n , becomes (l + a)y -2a 2 ba 2 In order to sign the second de r i v a t i v e , consider the values as a approaches zero and one. ba c aa (1-a) y _ p l im x = ba > 0 naa a ->• 0 l im x = co > o . aa a •*• 1 The x(a,y) inference schedule is i l l u s t r a t e d in Figure 4.3 In un ivar ia te s igna l ing models, there is a d i r ec t r e l a t ionsh ip between the observed s ignal and the inference of the unknown para -meter. In the b i va r i a te model, there does not ex is t a d i r e c t r e l a -t ionsh ip between a s ing le s ignal and a s ing le parameter. Rather, the market observes both s igna ls and simultaneously in fe rs the two 108 Figure 4.3 x(a,y) Inference Schedule. 109 parameters of future cash f lows. In a un ivar ia te model, the entrepreneur se lec ts the level of the s ignal so as to equate margi -nal costs and marginal bene f i t s . In the b i va r i a te model, there is an added dimension which is the t rade-of f between the two s igna ls which depends upon r e l a t i ve s igna l ing benef i ts and c o s t s . The s igna ls are se lected simultaneously and the marginal benef i t of each depends upon the leve l of the second s ignal as well as margi -nal cos t . The fo l lowing analys is i d e n t i f i e s some of the re la t ionsh ips among the two s igna ls and various parameters. The entrepreneur 's choice of s igna ls was shown to be: In (4 .3 .45 ) , a appears to be independent of y . This seeming independence is a resu l t of the sequence of subs t i tu t ions used in the a lgebra ic de r i v a t i on . If y had been derived f i r s t , then the 2 2 optimal choices would appear as y=y(u,a ,P) and a = a(y,u,a ,P ) . The choices of a* and y* are functions of : ( i ) Exogenous unobservable parameters of the d i s t r i b u t i o n of 2 cash f lows: u, a . ( i i ) Exogenous observable parameters of the cost func t ions : b, P. + In (1-a*) = (4.3.45) 3 b a (1-a*) (4.3.46) 110 It w i l l be seen that changes in ( i ) or ( i i ) have a cost e f f e c t and a subs t i tu t ion e f f e c t . The f i r s t e f f ec t is a change in the level of a s ignal due to a change in i t s cost func t ion ; and the second is a change in the level of the second s ignal in response to the f i r s t change. P ropos i t ion 4.4. An increase in a* resu l ts in a decrease in y * . P roof . D i f f e r en t i a t e (4.3.46) with respect to a: 2 2 1/3 i -2/3 Q.E.D. The d i r e c t r e l a t ionsh ip between a and y is evident in the f i r s t - o r d e r condit ions (1-ocl x = a b CT J a (1-a) x y = (l + r ) C y . Since a and y enter the inference schedule m u l t i p l i c a t i v e l y , x is a funct ion of y and x w is funct ion of a. A change in one a y s ignal w i l l be accompanied by a change in the second s ignal even i f the p a r t i c u l a r parameter which has changed has no a f fec t on the cost funct ion of the second s i g n a l . The e f f ec t of P ropos i t ion 4.4 w i l l be ca l l ed the Subst i tu t ion E f f e c t . If one s ignal becomes more cos t l y and is therefore reduced, i t w i l l be subst i tu ted for by the second s i g n a l . 2 Propos i t ion 4.5. If o inc reases , for a given u, the e f f ec t on choices of s igna ls w i l l be an increase in y and a decrease in a. I l l Proof. To see that a decreases, rewrite (4.3.45) as a + (1-a) ln (1-a) 3bo and t o t a l l y d i f f e r e n t i a t e with respect to a and a . 1- -jfS - ln ( l - a ) da = v ^ da 2 3 b o or da 2 da _(-y/3)b a "- ln (1-a) < 0 since ln ( l - a ) < 0 for 0 < a < 1 To see that y increases , rewrite (4.3.46) as 1/3 1/3 1/3 3P (1-a) (ac) and d i f f e r e n t i a t e with respect to a : 8a 2 3P 1/3 1 1 / 3 2 j (1-a) (a 2) -2/3 , „ 1/3 (1-> 0 s ince -^y < 0 3a 112 Figure 4.4 i l l u s t r a t e s the t r a d e - o f f between a and y with respect 2 . 2 to a i n i i , a space. Figure 4.4. S i g n a l i n g y, a by J o i n t Choices of a, y. In order to derive the r e l a t i o n s h i p s i l l u s t r a t e d i n Figure 4.4, equations (4.3.45) and (4.3.46) are r e w r i t t e n to express u as a 2 f u n c t i o n of a f o r a given a,y. From (4.3.45): (a) w =  3b(1-a) > 0 a 1-a + In (1-a) Then (b) = 3b(l-a) a 1-a + In (1-a) 113 (d) 3 2 U 2 8 a 8 a 3b 2~ ' TTTaJ- l n ( 1 ' a ) J l l - a ) > 0 From (4.3.46) (a) II = 3Py 1-a 1/2 -1/2 ( a 2 ) Then (b) Xr = 8 a 3 1/2 " 2 -3/2" 3Py ( a ) 1-a 2 < 0 (c) 32U r ( 3 a 2 ) ' 3Py" 1-a 1/2 3(a 2) 5/21 > 0 (d) 3 U r 3P 1-1/2 3/2" 2 (a ) 3 a 3y L - 1 L -l/2~ 3y < 0 (e) 3 2 . 2 3 a 3 a 3Py : (1-a) 1/2 • ( a 2 ) " 3/21 < 0 The convex curve is the plot of (4.3.46a) and the upward-sloping l i n e is (4 .3 .45a) . Each l i n e shows how y or a alone cannot s ignal 2 y because there maybe an i n f i n i t e number of poss ib le y,a combinations cons is tent with a s p e c i f i c choice of y or a. When both s igna ls are observed s imultaneously , a s p e c i f i c p,o pa i r is s i gna l ed . If 114 2 a increases while y i s unchanged, f i rm value has not changed, but the r e l a t i ve costs of the s igna ls have changed. The proba-b i l i t y of a penalty imposit ion decreases and a higher y w i l l be s e l e c t ed , as proved in Propos i t ion 4 .5 . From (4 .3 .46d) , the curve s h i f t s outward to \i(a ' , y ' ) . The market cannot unam-biguously in te rpre t the increase in y i f a is unchanged: e i the r 2 2 v has increased to p' or a increased to a ' . The increase in 2 a has made a more c o s t l y , and therefore a w i l l be reduced as proved in Propos i t ion 4 . 5 . From (4 .3 .45d) , the slope of the l i n e inc reases . Since a decreases, the curve s h i f t s out more according to (4 .3 .46e) . The new a * ' , y * ' ind icate that p is un-2 2 2 changed and o has increased to a ' . A change in g has a cost e f f ec t and a subs t i tu t ion e f f e c t : both s igna ls change in response to the e f f ec t on cost func t ions , and there is an add i -t iona l change due to the s i gna l s ' i n t e r a c t i o n . The t rade-of f 2 between a and y as a var ies i l l u s t r a t e s how the two s igna ls are re la ted through t he i r cost s t ruc tu res , how they are chosen s imultaneously , and how they are used together to s ignal p e f f i -c i e n t l y . P ropos i t ion 4 .6 . The e f f ec t of an increase in the s i ze of the penalty for f a l se d i sc losure is a decrease in y . Proof . D i f f e r en t i a t e (4.3.46) with respect to the penalty P: 1/3 2 ; p (1 - g) g 2 4/3 3 P < 0 Q.E.D 115 If i t becomes more cos t l y to s ignal with y , y* w i l l decrease. The market can observe P and therefore can co r rec t l y in te rpre t the change in y a lone. However the subs t i tu t ion e f f ec t w i l l r esu l t in an increase in a * . Propos i t ion 4 . 7 . The e f f ec t of an increase in the r i sk aversion of the entrepreneur, b, is a decrease in a * . Proof . To ta l l y d i f f e r e n t i a t e ( 4 . 3 . 4 5 ) with respect to a and b: - ln( l-a) d a = " — d b 3 b a o r 0 s ince i n ( l - a ) < 0 Q.E.D. If b inc reases , the cost of s igna l ing with a inc reases , and a * i s reduced. The market knows b can therefore in te rpre t unam-biguously the reduction in a . There w i l l be an increase in y* due to the subs t i tu t ion e f f e c t . P ropos i t ion 4 . 8 . The e f f ec t on a * and y* of an increase in y 2 depends upon the s ize of a . Proof . The cost e f f ec t on y of an increase in y is determined by d i f f e r e n t i a t i n g ( 4 . 3 . 4 6 ) with respect to y , holding a constant : 1/3 - 1 / 3 2 / 3 y > 0 ( ignor ing 8 a / 8 y ) 21 = 3p ( 1 - a ) 3P 116 The cost e f f e c t on a of an increase i n y i s found by t o t a l l y d i f f e r e n t i a t i n g (4.3.45) with respect to a and y. - l n ( l - a ) da = dy 3 b a or da = 1 d p 3ba 2 l n (1-a) > 0 Therefore the d i r e c t cost e f f e c t s of an increase i n y i s an increase i n both s i g n a l s . However, the sign of the s u b s t i t u t i o n e f f e c t depends upon the s i z e of a and t h e r e f o r e on the r e l a t i v e costs of the two s i g n a l s . D i f f e r e n t i a t i n g the above two d e r i v a t i v e s with respect to 2 a y i e l d s : 2 UL 3y 3a > 0 and d a 2 < 0 dy 3a These second-order d e r i v a t i v e s i n d i c a t e that the increase i n y 2 2 i s l a r g e r f o r a high a than a low a , and the increase i n a i s 2 2 s m a l l e r f o r a high a than a low a . Since 3y/3a < 0, a suf-2 f i c i e n t l y large or small a may lead to a s u f f i c i e n t l y large negative s u b s t i t u t i o n e f f e c t to counteract the p o s i t i v e cost e f f e c t on y or a. To prove the above, d i f f e r e n t i a t e (4.3.46) t o t a l l y with respect to y. 1/3 1/3 2/3 ay _ 1-a 1 dai 117 2 1/3 i 9Pp ' l 2 - l^a d p - ' Therefore sign = sign {2 — Subst i tute d a - 1 dp 2 3 b a In (1-a) Then {•} = 2 + *-3 b a (1-a) In(l-a) from (4.3.45) (1-a) In (1-a) = H-g- - a 3 b a 2 p - 3 a b a 2 3 b a Subst i tute th i s expression into {•}: 2 r l _ o j . p 3 b a  {•} - 2+ 2 2~ 3 b a ( p - 3 a b a ) = 2 + 2 p - 3a b a 118 Then > 0 dp < i f 2 + r\ 0 p - 3 a b cr or 2 < 2 p - 3 a b a 2 J_ < _ p - 3 a b a 2 > p < 2 p > - 2 p + 6 a b a < 2 p > 2 a b a From (4.3.45) p = 3 b a 2 [ a + (1-a) In (1-a)] Since [ a + (1-a) In (1-a)] = 0 for a = 0 and •*• 1 for a -»• 1, i t fol lows that p < 3aba2 for 0 < a < 1. 2 2 Therefore p < 2 aba i f a is s u f f i c i e n t l y large (or equ i va l en t l y , a s u f f i c i e n t l y sma l l ) . Then ap > 0 i f < 2 119 = 0 p = 2 a b / <0 2a b a 2 < u < 3 a b a 2 Q.E.D. The cost effect on y of an increase in y is clearly positive. The substitution effect is negative and may exceed the cost effect i f a is very large. A similar argument should hold for a. The cost effect on a of an increase in u is positive. The substitution 2 . effect is negative and may exceed the cost effect i f a is very low. The total change in a* and y* will result in the combined a, y which will efficiently signal that u has increased. A summary of the results of comparative statics is Parameter Direction of Effect on Effect on Changed Changed y* a* b + + (S) (C) - (S) + (C) P + - (C) + (S) + (c) - (S) 2 + + ( c , s ) - (C,S) - (C,S) + (C,S) + high o2 ? + (C,S) low a 2 + (C,S) ? - high a 2 ? - (C,S) low a 2 - (C,S) ? where C is Cost effect S is Substitution effect 120 The f i na l sect ion w i l l d iscuss empir ical impl i ca t ions of the ana lys is in th i s s e c t i o n . 4. EMPIRICAL IMPLICATIONS OF THE SIGNALING MODEL The b ivan 'a te s igna l ing model formulated in th i s chapter was proved to have an equ i l ib r ium so lu t ion which is f u l l y r evea l ing , r a t i o n a l , and incent ive compatible. There are empir ica l imp l i c a -t ions emerging from the analys is which w i l l be d i scussed . The information set ava i l ab le to investors for va luing a new secur i t y includes the contents of the prospectus. The value of a i s c l e a r l y d isplayed in the prospectus, while the value of y is not so obvious. An examination of prospectuses for new issues in 1981 revealed that the prospectuses contain h i s t o r i c a l - cos t f i nanc i a l statements, a summary of h i s t o r i c a l earnings for a maximum of f i ve yea r s , and a cautious d iscuss ion by management of such matters as a desc r ip t ion of the company's bus iness , i t s competit ive environment, and i t s investment p lans . The d isc losures made do not inc lude forward-looking information such as management forecasts of future cash f lows, but appear to be r e s t r i c t ed to h i s t o r i c a l in format ion . It does appear that the potent ia l imposit ion of penal t ies has l im i t ed d i sc losure to "hard" information which can be documented and v e r i f i e d more e a s i l y . The s igna l i ng model of Leland and Pyle has been emp i r i ca l l y tested by Downes and Heinkel (1982) and R i t t e r (1982). Both tes ts used data in prospectuses for a large sample of firms making i n i -t i a l pub l i c o f fe r ings of common s tock , or which were 'going 121 p u b l i c ' . The data used in both tes t included h i s t o r i c a l accounting numbers. Downes and Heinkel performed a nonl inear est imat ion of the form: Where V- = market value of equity of f i rm j measured as o f f e r i ng pr i ce J E • = normalized earnings from an exponential smoothing J model appl ied to a l l ava i l ab le h i s t o r i c a l earnings per share for a maximum of ten years x i = explanatory var iab le a.j = regression c o e f f i c i e n t on i independent var iab le U.- = er ror term J The est imat ion i s , in e f f e c t , of the form E j 1=0 E where the dependent var iab le is the pr ice/earnings r a t i o . The explanatory var iab les used were: 0) Constant * (+) 1) a * (+) 2) Dividend po l i c y dummy * (-) 3) Debt/assets r a t io a f te r issue 4) Industry dummy * (+) 5) Age 6) Sales of most recent f u l l year * (-) 7) Three-year growth rate in sales * (+) 8) Underwriter prest ige * (+) 9) Hot issue market dummy * (+) 122 Those var iab les which had s t a t i s t i c a l l y s i g n i f i c a n t regression c o e f f i c i e n t s ( i . e . , t > 1.96) are noted with as te r i sks and the sign of s i g n i f i c a n t c o e f f i c i e n t s is noted pa r en the t i c a l l y . The div idend po l i c y dummy var iab le is included because of Bhattacharya's (1979) and He inke l ' s (1978) resu l ts on div idend s i g n a l i n g , however the negative c o e f f i c i e n t i s not exp la ined . The reason presented for i n c l us i on of the remaining var iab les is to proxy for r i sk s ince f i rm-spec i f i c r i sk appears in the Leland/Pyle va luat ion equation and is assumed by Lei and and Pyle to be known by i n ves to r s . These surrogate var iab les are assumed by Downes and Heinkel to be ind ices which are exogenous and beyond the control of the entrepreneur. R i t t e r ' s tes t on 559 firms going publ i c in the per iod 1965-73 a lso used h i s t o r i c a l accounting numbers as explanatory var iab les and e x p l i c i t l y used earnings as an independent v a r i a b l e . His e s t i -mation was of the form v 8 - i = I a i x i + U i B. 1=0 J where V. = market value of equity of f i rm j measured as J o f f e r i ng p r i c e . B- = pre-of fe r ing book va lue , used to control for J s i ze . The explanatory var iab les used were: 0) Constant * (+) 1) a " * (+) 2) Age * (+) 3) Sales * (-) 4) Median P/E on ASE * (+) 5) Book Value * (+) 123 6) Earnings in most recent f i s c a l year * (+) 7) Sales growth 8) Investment (I) * (+) Reasons presented for i n c lus ion of some of the explanatory var iab les are to control for heterogeneity of firms and heteroske-d a s t i c y . There was no j u s t i f i c a t i o n presented for i n c lus ion of earn ings , and no d iscuss ion of the highly s i g n i f i c a n t resu l t that the c o e f f i c i e n t on earnings/book value was 13.75, with a standard e r ro r of 0 .98, r esu l t i ng in a t - s t a t i s t i c of 14. R i t t e r did not d iscuss i nc lus ion of a proxy for f i rm-spec i f i c r i s k . The resu l ts of both empir ical tests ind ica te that h i s t o r i c a l accounting numbers are cor re la ted with market value of new s e c u r i -t i e s . Both tes ts inc lude the accounting numbers as exogenous para -meters. However, these numbers c l e a r l y are chosen, c o n t r o l l e d , or at least inf luenced by the entrepreneur of a pr iva te f i rm going p u b l i c . If the entrepreneur can increase market value of the secu r i t y being sold by d i s c l o s i n g high accounting earn ings , there i s a motivat ion for him to do so . However, the market is ra t iona l and must r ea l i z e that accounting earnings can be manipulated. There fore , the i nc lus ion of such numbers in a tes t of r a t i o n a l , incent ive compatible va luat ion derived from a s igna l i ng model without incorporat ing an incent ive for t ru th fu l report ing of accounting numbers seems to lack e i the r r a t i o n a l i t y or incent ive c o m p a t i b i l i t y . The model developed in th i s chapter has a mechanism through which d i s c losu re of h i s t o r i c a l accounting earnings is made c r e -d i b l e . An observable var iab le which could be used as a proxy for y 124 i s the past yea r ' s accounting earnings or normalized earn ings . If the inference schedule i s x (o,y) = {9 b p Q 4, -fSL + ln( l-o) 1-a 1/3 } and Cov(x,M) is s t i l l assumed to be zero , {9 04. P 0 y 3 [ T r ^ + In(l-a)]} then V(a,y) 1/3 where b and <j> are not measurable, but are assumed to be known by i n ves to r s . No r i sk term appears in the va lua t i on , and therefore no proxy is required for the market's estimate of f i rm-spec i f i c r i s k . There fore , the in fe r red valuat ion schedule does have empir ica l con-t e n t . Downes and Heinkel and R i t t e r used o f f e r p r i ce PQ as V . . They both reported obta in ing s im i l a r resu l ts using pr i ce in the a f t e r market. The model developed in th i s chapter s p e c i f i c a l l y uses P^  as V j , a l lowing for an underpriced i s s u e . In order to measure P^, i t would be necessary to estimate when equ i l ib r ium pr i ce is reached. As discussed in Chapter Three, the adjustment process appears to take less than one week on average and f r e -quently is immediate. The resu l ts of comparative s t a t i c s appear to be emp i r i c a l l y t e s t a b l e . 1) The resu l t of Propos i t ion 4.4 that the level of a i s decreasing in y is tes tab le once a proxy for y has been s p e c i f i e d . 125 2 2) Propos i t ion 4.5 showed that y is increas ing in a and a is 2 2 decreas ing . If s t a t i o n a r i t y of a is assumed, a can be estimated from pr ice data on the s e cu r i t i e s subsequent to i s sue . The resu l t of the propos i t ion then i s t e s t a b l e . 3) Propos i t ion 4.6 showed that y is decreasing in PQ<|>. While <|> cannot be measured, PQ is publ ished in the prospectus. Therefore the ana l y t i ca l r e l a t ionsh ip between y and PQ -jS t e s t a b l e . 4) Propos i t ion 4.7 does not appear to have empir ica l content because the entrepreneur 's c o e f f i c i e n t of r i sk aversion cannot be measured. 5) Propos i t ion 4.8 showed that the t rade-of f between a and y 2 as y increases depends upon o . Assuming market r a t i o n a l i t y , y can be estimated from the equ i l ib r ium post-of fe r ing p r i c e . Thus the resu l ts of the propos i t ion appear to be t e s t a b l e . In summary, i f h i s t o r i c a l earnings are used to proxy for y , 2 and i f y and a are estimated from pr ice data , there are several impl i ca t ions of the ana lys is which appear to be amenable to cross-sect iona l empir ica l t e s t i n g . Such empir ical tes ts w i l l be the focus of future research. 126 CHAPTER FIVE RISK SHARING AND VALUATION UNDER MORAL HAZARD INTRODUCTION A second type of asymmetric information between the entrepreneur and investor ar i ses when the entrepreneur manages the f i rm or t ech -nology so that i t s future cash flows are dependent upon his mana-ge r i a l act ions and e f f o r t . In th i s case, i f his act ions are unobservable by i nves to r s , then a moral hazard problem e x i s t s . In the preceding chapter , the d i s t r i b u t i o n of cash flows was exogenous and unobservable; in th i s chapter i t is endogenous and unobservable. Sect ion 1 descr ibes the o r ig ina l formulat ion of the moral hazard problem as a two-person r i sk-shar ing problem. Section 2 reviews recent l i t e r a t u r e which analyzes the moral hazard problem in a market, where f i rm va luat ion depends upon the means of reso lu t ion of the problem. In Sect ion 3, the Leland/Pyle and Jensen/Meckling models are integrated in order to look at the r isk-averse ent repre -neur 's problem under moral hazard. A s p e c i f i c example is analyzed in Section 4 in order to derive a closed-form s o l u t i o n . Empir ical imp l i ca t ions of the analys is are discussed in Section 5. 1. THE PRINCIPAL-AGENT PROBLEM The pr inc ipa l-agent problem was o r i g i n a l l y formulated ( e . g . , Ross (1973) and Holmstrom (1979)) as a two-person r i sk-shar ing problem under moral hazard. 127 Pareto-optimal r i sk sharing between two par t ies under varying assump-t ions about r i sk a t t i tudes was descr ibed in Chapter Four. When both par t i es are r i sk averse, the Pareto-optimal contract spec i f i e s that r i sk is shared so that the ra t io of marginal u t i l i t i e s is a constant for any r i sky outcome, where the ra t io is a funct ion of r isk t o l e r a n -ces and r e l a t i v e bargaining powers. If one party is r i sk neu t r a l , he bears a l l of the r isk of the outcome, and the r isk-averse party receives a f ixed payment. These Pareto-optimal r i sk-shar ing contracts are not a t ta inab le when moral hazard, or unobservabi1ity of a c t i ons , e x i s t s . Condit ions under which such unobservabi1ity pro -h i b i t s e f f i c i e n t contract ing are: (1) Both p r inc ipa l and agent maximize expected u t i l i t y , where (a) the p r i n c i p a l ' s u t i l i t y funct ion U(W) is def ined over wealth and exh ib i ts r isk aversion or r i sk n e u t r a l i t y : U'(W) > 0 u"(w) < 0 (b) the agent 's u t i l i t y funct ion V(W,e) is def ined over wealth and e f f o r t and exh ib i t s s t r i c t r i sk aversion and d i s u t i l i t y of e f f o r t : Vw(W,e) > 0 V e(W,e) < 0 V w w (W,e) < 0 (2) The p r inc ipa l and agent contract to share an observable r i sky outcome from a d i s t r i b u t i o n which (a) has a f ixed support and about which both par t ies have homogeneous b e l i e f s , and 128 (b) depends upon t h e u n o b s e r v a b l e a c t i o n s o r e f f o r t o f t h e a g e n t , such t h a t a h i g h e r l e v e l o f e f f o r t i n c r e a s e s t h e e x p e c t e d v a l u e o f t h e d i s t r i b u t i o n . S i n c e c o n t r a c t s can be w r i t t e n o n l y on i n p u t s , v a r i a b l e s , o r outcomes w h i c h a r e j o i n t l y o b s e r v a b l e , t h e p r i n c i p a l and agen t can c o n t r a c t o n l y on t h e random o u t c o m e . I t w i l l be shown t h a t b o t h p a r t i e s wou ld be b e t t e r o f f i f e f f o r t were o b s e r v a b l e , and t h e r e f o r e c o u l d p r o v i d e a b a s i s f o r c o n t r a c t i n g . Not o n l y does t h e u n o b s e r v a b i 1 i t y o f e f f o r t p r e c l u d e i t s use i n c o n t r a c t i n g , but a b a s i s f o r s h i r k i n g i s p r o v i d e d because t h e agent d e r i v e s d i s u t i l i t y f rom e x p e n d i n g e f f o r t and t h e d e t e c t i o n o f s h i r k i n g i s h i n d e r e d by t h e random v a r i a t i o n i n t h e o u t c o m e . The p r i n c i p a l c anno t d e t e r m i n e , w i t h o u t a d d i t i o n a l i n f o r m a t i o n , whe the r an ex t reme v a l u e o f t h e outcome i s due t o t h e a g e n t ' s e f f o r t o r t o an ex t reme r e a l i z a t i o n o f t h e s t o c h a s t i c v a r i a b l e . The agent can t r a d e o f f t h e g a i n i n e x p e c t e d u t i l i t y f rom h i s s h a r e i n t h e outcome (wh i ch i s i n c r e a s i n g i n h i s e f f o r t s ) a g a i n s t t h e d i s u t i l i t y f rom p r o v i d i n g such e f f o r t s ; w h i l e t h e p r i n c i p a l w i s h e s o n l y t o m a x i m i z e h i s s h a r e o f t h e o u t c o m e . T h e r e f o r e t h e r e i s a c o n f l i c t between t h e o b j e c t i v e s o f t h e p r i n c i p a l and a g e n t . The p r i n c i p a l must s e l e c t a c o n t r a c t wh i ch w i l l m o t i v a t e t h e agent t o p r o v i d e an o p t i m a l l e v e l o f e f f o r t as w e l l as s h a r e r i s k s . The agen t must be s t r i c t l y r i s k a v e r s e f o r t h e p r o b l e m t o e x i s t . I f t h e agent i s r i s k n e u t r a l , t h e o p t i m a l c o n t r a c t i n v o l v e s t h e p r i n -c i p a l r e c e i v i n g a f i x e d s h a r e so t h a t t h e agent bea r s a l l o f t h e c o n -sequences o f h i s a c t i o n s . 129 The usual formulation of the p r i n c i p a l ' s problem is Max Ee{U[x-$(x")]} *(x) ,e s . t . E e {V[$(x) , e]} > V e*(- Argmax E e {V[$(x) , e]} or V w[*(x),e] = V e In the object ive func t i on , the p r inc ipa l se lec ts the agent 's share of the random outcome, $(x) , where the outcome x is condi t iona l on the agent 's e f f o r t e in that more e f f o r t w i l l s h i f t the d i s t r i b u t i o n of x to the r ight in the sense of f i r s t -o rde r s tochas t i c dominance. In the f i r s t cons t r a i n t , V is a minimum level of expected u t i l i t y which must be provided so that the agent w i l l accept the con t rac t . The minimum level of expected u t i l i t y i s determined exogeneously in the market. The second const ra in t is the Nash const ra in t which s t a -tes that the e f f o r t se lected by the p r inc ipa l must be the same leve l of e f f o r t that the agent w i l l se lec t in his own opt imizat ion problem, given $(x) se lected by the p r i n c i p a l . The p r inc ipa l se lec ts $(x) which then induces the agent to se lec t e* in his problem Max E e {v [$ (x) , e]} e 130 The optimal so lu t ion to the p r i n c i p a l ' s problem was derived by Holmstrom: U'[x - *(x)] f (x|e) = k + I — V w [$ (x ) ,e ] f (x|e) where f (x|e ) i s the density funct ion of x condi t iona l on e; and k, z are Lagrangian m u l t i p l i e r s . This so lu t ion can be compared to the Pareto-optimal so lu t ion derived in Chapter Four: U' — = k  VW It is obvious that Pareto-optimal r i sk sharing is unatta inable i f £ 4= 0 s ince f e ( x , e ) + 0 by assumption. Therefore , due to the un-observabi 1 i t y of the agent 's a c t i ons , the agent w i l l expend less e f f o r t and i n e f f i c i e n t r isk sharing w i l l r e s u l t . In the absence of addi t iona l in format ion , reso lu t ion of the agency problem necess i tates that the agent bear some of the r i sk of the outcome for motivat ional purposes. Holmstrom shows that i f some of the noise can be removed from the measurement of x, or information can be provided about e, then r isk sharing can be improved by using the information in con t r a c t i ng . 2. THE PRINCIPAL-AGENT PROBLEM IN A MARKET The owner of a f i rm with a r i sky cash flow can share r i sk in the cap i t a l market. There is no demand for an ind iv idua l agent with whom to share r i sks and therefore an agent must provide some expert ise 131 which the p r inc ipa l does not possess. The d i f f u se ownership s t r u c -ture of a corporat ion creates the demand for agents to manage opera-t ions of the f i r m . The agency problem ar ises under separat ion of ownership and control when the r i sky return to the shareholders/ p r i nc ipa l is dependent upon the unobservable managerial act ions of the manager/agent who i s maximizing his own welfare rather than the welfare of the shareholders . The d i s t r i b u t i o n of cash flows there -fore becomes endogenous where i t was assumed to be exogenous in the asymmetric information problem of Chapter Four. The contract ing problem between owner and manager of a f i rm is more d i f f i c u l t to analyze than the two-person problem analyzed by Holmstrom because addi t iona l complexit ies emerge in a market s e t t i n g . Some of these complexit ies are: 1) The r i sk-shar ing c a p a b i l i t i e s of the cap i ta l market are ava i l ab l e to the p r inc ipa l and agent, and both may be able to use the market to e l iminate the r isk imposed for incent ive purposes. In order to prevent such e l iminat ion of r i s k , var ious assumptions are made, such as: a) The manager has no wealth and cannot borrow or s e l l sho r t . b) The manager's t rading and p o r t f o l i o are observable . c) The manager is not permitted to trade in the f i rm ' s s e c u r i t i e s . 2) Opportunit ies may ex i s t for the manager to reduce the r isk he must bear by a l t e r i n g the variance of cash flows generated by the f i rm ' s cap i ta l investments through his se l e c t i on of investment p ro j ec t s . 132 3) The market value of the f i rm is a funct ion of the d i s t r i b u -t i on of cash flow and therefore is dependent upon managerial act ions and the means used to resolve the moral hazard problem. 4) In addi t ion to the existence of a s e cu r i t i e s market for the r i sky outcome, there is a market for managerial labor which makes endogenous the agent 's reservat ion leve l of expected u t i l i t y which is in fact a market p r i c e . 5) Shareholders represent many p r inc ipa l s and there may be many agents and a hierarchy of agents which make coordinat ion and cont rac t ing c o s t l y . Papers which have addressed these issues w i l l be b r i e f l y d i scussed . Holmstrom showed that information i s valuable i f i t reduces the noise in estimates of the agent 's expenditure of e f f o r t so that more e f f i c i e n t r i sk sharing is a t t a i nab l e . If there is more information about e f f o r t or the draw from the d i s t r i b u t i o n of x ( i . e . , which s ta te of nature occurred ) , less r isk need be imposed upon the r isk-averse agent. Diamond and Verrecchia (1982) look at the problem of using valuable information in contract ing when there are many p r i n -c i p a l s . Top management is considered to be a s ing le r isk-averse agent and the many pr inc ipa ls/shareho lders act as i f they are r i sk neutral because they can d i v e r s i f y r i sk across f i rms . As e a r l i e r shown, in the absence of a moral hazard problem, i t would be optimal to pay the manager a f ixed s a l a r y . However, i f the manager can improve his welfare by s h i r k i n g , he can do so with no cost to himself under a f ixed s a l a r y . There are N iden t i ca l r isk-neutra l share-ho lders , each of whom possesses iden t i ca l information useful in mana-ger ia l contract ing (by d e f i n i t i o n , useful information reduces the 133 noise in estimates of e f f o r t ) . As N grows l a rge , the costs of com-munication and coordinat ion required to d i r e c t l y incorporate the information in a management compensation contract may grow p r o h i b i t i -ve ly large so that the information is not used, even though a l l shareholders would be better o f f i f the information was in the con t r ac t . A low cost way of using the information i s for share-holders to trade in the market on the basis of t h e i r information so that market pr ices r e f l e c t the in format ion . The existence of many p r i n c i pa l s makes d i r ec t contract ing with the agent i n f e a s i b l e ; but due to the existence of a market for the r isky s e c u r i t y , market p r i ce w i l l aggregate the information of the many p r i n c i p a l s . Diamond and Verrecchia use an example to der ive the pr i ce and the optimal incen -t i v e contract when output is a random var iab le whose d i s t r i b u t i o n and r e a l i z a t i o n depend upon a systematic r i sky fac tor with an ex-post observable r e a l i z a t i o n , a f i rm-spec i f i c r i sky fac tor which i s non-observable , and e f f o r t . The manager's compensation is decreasing in the r e a l i z a t i o n of the systematic fac tor and in pr i ce which has impounded the aggregate information about f i rm-spec i f i c r i s k . Therefore pr iva te information about f i rm-spec i f i c r i sk and pub l i c information about systematic r i sk are used in contract ing because they permit ext rac t ion of some r i s k , which in a sense has become observable , so that managerial sh i rk ing becomes more de tec tab le . The r i sk borne by the manager for incent ive purposes has been reduced to a port ion of f i rm-spec i f i c r i s k . Due to the existence of the cap i ta l market, systematic r i sk can be considered to be observable r i sk and therefore the agency problem can be minimized as f i rm-spec i f i c r i sk grows sma l l . (Of course, i t is necessary that the f i rm ' s 3 is not 134 inf luenced by act ions and dec is ions of the manager.) While non-systematic r i sk is i r r e l evan t to cap i ta l budgeting dec is ions in a per fec t market, the magnitude of such r isk becomes important in r i sk sharing under moral hazard and therefore may be quite relevant to cap i t a l budgeting dec is ions when the manager is a r isk-averse agent of the shareholders . The e f f e c t of non-optimal r isk sharing on managerial investment dec is ions a lso i s analyzed by Marcus (1982) when the r isk-averse manager of a f i rm is constrained to hold a spec i f i ed f r a c t i on of ownership in the f i r m . The manager's compensation inc ludes shares in his f i rm ' s stock which he is proh ib i ted from t rad ing on the market. In the two-person agency problem, the agent does not have the oppor-tun i t y to e l iminate r i sk imposed for incent ive reasons. In a market s e t t i n g , i f the r i sk which is borne by the agent is in the form of shares which are tradeable in the market, an addi t iona l const ra in t must be added to the problem: such as that of no t r a d i n g . Marcus imposes the const ra in t and analyzes the e f fec ts on managerial va luat ion of the f i rm ' s shares and managerial investment d e c i s i o n s . The manager values his shares in the f irm at less than market pr i ce because he does not hold a we l l -d i v e r s i f i ed p o r t f o l i o and therefore his r isk premium is for to ta l r i sk where the market's r i sk premium is fo r systematic r i s k . The non-optimal r i sk sharing provides incen -t i ves for the manager to undertake less r i sky investments so as to reduce nonsystematic r isk which he must bear. Since the manager is p roh ib i ted from e l iminat ing f i rm-spec i f i c r i sk through p o r t f o l i o d i v e r s i f i c a t i o n s , he w i l l attempt to e l iminate i t through the i nves t -ment dec is ion he is making for the shareholders of the f i rm and such 135 a search for low-risk investments may be cos t l y to shareholders i f the manager expends resources of the f irm as well as d i ve r t i ng his own e f f o r t s and expert ise to such a c t i v i t i e s . Marcus' resu l t about consequences of investment behavior can be compared to the resu l ts of Diamond and Ve r recch i a . The l a t t e r show that the p r i nc ipa l and agent w i l l be bet ter o f f i f f i rm-spec i f i c r i sk is reduced s ince improved r i sk sharing r e s u l t s . In Marcus' model, the search for r isk-reducing projects may be s u f f i c i e n t l y cos t l y that shareholders are worse o f f while managers are better o f f . Marcus' ana lys is is incomplete for the fo l lowing reasons: 1) The spec i f i ed f r a c t i on of managerial ownership is not de r i ved , but merely assumed. In a more general a n a l y s i s , the manager's share of the r i sky outcome is derived in an op t im i -zat ion problem which is constrained by the need to supply a minimum reservat ion level of expected u t i l i t y to the manager. 2) To analyze such a problem in a f i nanc i a l market without con-s ide ra t i on of the market for managers is a pa r t i a l ana lys is because one determinant of the r i sk imposed on the manager i s the r e l a t i v e bargaining powers. 3) Marcus shows that the manager has an incent ive to underinvest in r i sky p ro j e c t s . He states that the owners of the f i rm must undertake cos t l y monitoring of investment dec is ions or su f f e r the consequences of the suboptimal d e c i s i o n s . Such a statement seems to be al lowing for naivety or i r r a t i o n a l i t y on the part of owners of the f i r m . If investment dec is ions are observable, the manager can be provided with incent ives to undertake the investment projects des i red by the owners 136 through an appropriate forcing contract. If the decisions are not observable, but the available opportunity set of investments is observable, the owners will rationally assume that the manager will select the investment which will maxi-mize his expected u t i l i t y . Since the owners of the firm own the technology and the hired manager is a price-taker, the owners will adjust compensation so that the manager bears the cost of his suboptimal behavior. It then might be in the best interest of the manager to provide monitoring. When the demand for monitoring arises due to the suboptimal incentives of the agent, and the agent is the price-taker, i t would be expected that the agent will bear the monitoring costs in such a scenario. 4) Marcus suggests that in i t i a l underpricing of new equity issues may be explained by the lower valuation placed on shares by the se l l ing entrepreneur. Such a statement implies non-economic behavior of the entrepreneur. If the entrepre-neur values the shares at a lower price than does the market, he would be very happy to sell them at market valuation and receive greater proceeds with which to diversify his port-f o l i o . The Marcus analysis does indicate that the agency problem has added complications when opportunities exist for the agent to diver-s i fy risk and when the agent can alter specif ic parameters of the distr ibution of cash flows by managerial decisions, such as choice of investments. In the two-person problem, the agent must bear r isk . The manager of a firm has available various ways of altering the risk 137 imposed on him and such potent ia l act ions must be p r o h i b i t e d , cons t ra ined , or monitored in contract ing between p r inc ipa l and agent. A d i f f e r en t approach to prov id ing managerial incent ives is used by Beck and Zorn (1982) when they analyze the re l a t ionsh ip between incent ives and share pr i ce when the manager must be motivated to purchase shares in his f i r m . The r i sky return on each share in the f i rm is an increas ing funct ion of the manager's ownership share because managerial incent ives are assumed to be provided through ownership of the f i r m . While i t i s not made e x p l i c i t in the problem, the manager is assumed to be more productive the greater is the pro -port ion of his wealth dependent upon the performance of the f i r m . The manager is r i sk averse and therefore derives d i s u t i l i t y from ownership in his f i rm due to lack of d i v e r s i f i c a t i o n rather than through d i s u t i l i t y of e f f o r t provided to increase r e tu rn . The approach is unusual because the manager/agent and inves tors/ p r i n -c ipa l do not contract to share the r i sky outcome as in the usual pr inc ipa l-agent problem, but rather the agent must purchase his share in the r i sky outcome from the p r i n c i p a l s . It then is the problem of the owner/investor to se lec t a p r i ce and the number of shares to be so ld to the manager in order to maximize expected wealth (assuming r i sk neutral shareholders) such that the number of shares purchased at the se lected pr i ce is the optimal choice of the manager, and the manager receives an exogeneously spec i f i ed minimum reservat ion leve l of expected u t i l i t y of wealth. Since the agent 's d i s u t i l i t y does not der ive from e f f o r t , his u t i l i t y funct ion is defined over wealth. Therefore Beck and Zorn do not re la te f irm value to the moral hazard problem, but focus on incent ive p r i c i ng in which the manager's impact 138 on p roduc t i v i t y and p r o f i t s are endogenous, and the pr i ce charged must be negat ive ly re la ted to the number of shares to be purchased by the manager due to his r i sk ave rs ion . The derived optimal p r i c i ng schedule depends upon the assumption that the manager must receive a reservat ion level of expected u t i l i t y : i f more r i sk i s to be imposed upon the manager, addi t iona l compensation must be provided in order to s a t i s f y the minimum u t i l i t y cons t r a i n t , and the addi t iona l compen-sat ion is provided in the form of a p r i ce reduction for the r i sky shares . The ana lys is is pa r t i a l in that the reservat ion level of expected u t i l i t y is exogenous. An addi t iona l l i m i t a t i o n i s that the manager derives u t i l i t y from his increases in p roduc t i v i t y through ownership in the f i r m . There i s no d i s u t i l i t y to the manager from exert ing add i t iona l productive e f f o r t . The Beck/Zorn model may be cons is tent with some types of management compenation plans in which managers purchase shares below market p r i c e . The Marcus and Beck/Zorn papers focus on the manager's va luat ion of shares in the f i rm which they are constrained to ho ld . The e f f e c t of moral hazard on market va luat ion has been analyzed by Ramakrishnan and Thakor (1982) where the p r i n c i p a l ' s problem is to se lec t mana-ger ia l compensation, managerial e f f o r t and a cos t l y monitoring system in order to maximize the r isk-adjusted present value of net cash flows subject to the two const ra ints of meeting reservat ion leve l of u t i l i t y and s a t i s f y i ng incent ive compa t i b i l i t y . Cash flows can be inf luenced by the manager through his investment and production d e c i -s ions and are reduced by managerial compensation and monitoring c o s t s . The manager is precluded from inves t ing in any asse t s , which e l iminates his a b i l i t y to d i v e r s i f y r isk in the market. Since the 139 manager may provide d i f f e r en t leve ls of e f f o r t under d i f f e r en t moni-to r ing or information systems, to ta l cash flows from production w i l l vary under d i f f e r en t information systems. Therefore f i rm value is dependent not only upon managerial act ions under moral hazard, but a lso upon the means used to resolve the problem. Ramakrishnan and Thakor suggest that the re l a t ionsh ip between accounting information and f i rm value ar ises from the agency problem ex i s t i ng in a cor -porat ion s ince accounting reports are a product of an information system which can be viewed as a monitor of managerial a c t i ons . Campbell and Kracaw (1982) integrate the cap i ta l and managerial labor markets when there is a moral hazard problem between owners and the manager of a f i rm which ar ises because future cash flows depend upon unobservable e f f o r t suppl ied by the manager which may change the expected value of cash f lows. S imi la r to the Ramakrishnan/Thakor a n a l y s i s , f i rm value depends upon managerial act ions because such act ions make endogenous a parameter of the d i s t r i b u t i o n of cash f lows. However, the focus of the Campbel1/Kracaw paper is asset p r i c i n g when managers are a lso investors who may borrow and therefore r i sk sharing can be accomplished d i r e c t l y in the cap i ta l market. Consequently, there ex is ts an optimal investment for the manager to make in his own f irm which is derived in his p o r t f o l i o formation problem. Due to the moral hazard, the labor market imposes r i sk upon the manager through his compensation which is composed of a f ixed payment plus a share in the equity of his own f i r m . If the share imposed on the manager by the labor market exceeds his optimal investment determined in his p o r t f o l i o problem, incent ives are pro -vided through suboptimal r isk sha r ing . The p o r t f o l i o of the manager 140 i s assumed to be observable . Each f i rm has a s ing le manager whose reservat ion level of expected u t i l i t y is exogenous. Investor/ managers in the cap i ta l market solve t h e i r p o r t f o l i o problem while investors in a p a r t i c u l a r f i rm simultaneously solve for optimal mana-ge r i a l compensation. Risk-neutral owners of the f i rm se lec t compen-sat ion in order to maximize t he i r return from the f i rm subject to the incent ive compat ib i l i t y and ind iv idua l r a t i o n a l i t y cons t r a i n t s . Risk-averse investors/managers se lec t investments in a l l f irms and e f f o r t to be expended in t he i r own firms in order to maximize expected u t i l i t y of wealth and e f f o r t , taking as given optimal com-pensation provided by the labor market. Not only is f i rm value a f fec ted by the agency problem, but parameters of the market po r t -f o l i o a lso are a l te red because many investors are managers who must be provided incent ives and who therefore hold nond ive rs i f i ed po r t -f o l i o s . While a manager is not permitted to s e l l his f i rm-spec i f i c cap i t a l in the market, he may attempt to take advantage of r i sk sharing in the cap i ta l market to d i v e r s i f y or e l iminate the r i sk by s e l l i n g short his f i rm ' s secur i t y or invest ing in a hedge p o r t f o l i o with returns negat ive ly cor re la ted with the returns from his f i r m . The manager must be constrained from s e l l i n g short the secur i t y of his own f i r m . If he invests in a hedge p o r t f o l i o he can reduce or e l iminate f i rm-spec i f i c r i sk without reducing or e l iminat ing the incent ive e f f ec t because va r i a t ion in his return w i l l then be due only to his e f f o r t and not to exogenous sources of uncer ta in ty . The analyses summarized attempt to address one or more of the f i v e issues ind icated at the beginning of th i s s e c t i o n . One issue which has not been addressed is that of determination of the agent 's 141 reservation level of expected utility, which is a market price deter-mined in the labor market and which has been assumed to be exogenous. An approach which eliminates the need to determine the market price for managerial expertise is to invert the usual principal-agent for-mulation so that the agent offers an investment contract to potential principals in the market such that he offers that contract which maximizes his expected utility and shareholders accept the contract i f it provides a return equal to that of similar investment oppor-tunities available in the market. Such an approach is used by Atkinson and Feltham (1981). In the Atkinson/Feltham paper, a risk-averse manager is endowed with capital and a productive technology which requires a capital investment in order to generate a return. He offers securities to the market in order to raise external capital, then invests in the capital market and in the productive technology, and both investments earn risky returns. The capital market is complete with respect to systematic risk and therefore such risk can be shared in the market. A moral hazard problem arises because the manager's utility is defined over wealth and effort, and cash flows generated by the pro-ductive investment are dependent upon managerial effort. The contract which the manager offers to potential principals specifies a sharing rule for the risky outcome and a reporting system which he will implement. The focus is similar to that of Ramakrishnan and Thakor in that the manager's return is contingent on information pro-vided by a reporting system and therefore managerial actions will depend upon the monitoring system implemented, and the information 142 system w i l l a f f ec t the welfare of managers and i nves to r s . The moni-t o r i ng system is se lected by the party who se lec ts the cont rac t : the p r i n c i pa l se lec ts the information system in Ramakrishnan/Thakor, while the agent provides i t in Atkinson/Feltham. (Atkinson/Feltham assume that the information provided by the agent 's report ing system is t r u t h f u l . ) Atkinson/Feltham show how the e f f i c i e n c y of r i sk shar ing depends upon the report ing system. If r i s k , e f f o r t , and out-come are reported, then Pareto-optimal r i sk sharing is a t t a i nab l e . At the other extreme, i f there is no information about r i s k , e f f o r t , or outcome, a l l f i rm-spec i f i c r i sk is borne by the agent. Ex-post report ing systems between the two extremes are analyzed as to t he i r e f f e c t s on r i sk sharing and incent ives in a cap i ta l market. A report ing system provides a basis for e f f i c i e n t shar ing of non-systematic r i sk i f the report is cor re la ted with the f i rm ' s output, and can be used to provide managerial incent ives i f i t reports agents' act ions and thus serves as a basis for performance-contingent compensation. Therefore , Pareto-optimal shar ing of systematic market r i sk can be achieved in the cap i ta l market and the degree to which nonsystematic f i rm-spec i f i c r i sk can be e f f i c i e n t l y shared under moral hazard depends upon the. informativeness of the report ing system provided by the agent. An approach s im i l a r to that of Atkinson and Feltham is that of Jensen and Meckling (1976). A r isk-neutra l owner/manager of a f i rm is endowed with a productive technology and has an i n s u f f i c i e n t wealth endowment to f inance the cap i ta l investment necessary to r e a l i z e a return from the technology. He therefore seeks to ra ise cap i t a l in the market. A moral hazard problem ar ises because mana-ge r i a l act ions are not observable and the manager can d ive r t assets 143 of the f irm for his personal consumption. Jensen and Meckling descr ibe the suboptimal (from the viewpoint of shareholders) behavior as consumption of p e r q u i s i t e s . However, such behavior is in e f f ec t the same as sh i rk ing or reducing e f f o r t expenditure in that both reduce the expected value of cash flows and both are unobservable. When the owner/manager owns 100% of the equity in his f i r m , he receives 100% of the benef i ts of pe rqu i s i t e consumption and bears 100% of the cos t . As his proport ion of ownership d e c l i n e s , he bears less than 100% of the cost of his behavior while cont inuing to receive a l l the bene f i t . Non-managing prospect ive shareholders know the manager's u t i l i t y f unc t i on , can r a t i ona l l y i n f e r his behavior as his ownership dec l i n e s , and w i l l p r i ce the equity accord ing l y . The manager se lec ts his proport ion of ownership in his f i rm in order to maximize his return where the market va luat ion of the equity so ld is increas ing in his proport ionate ownership and his pe rqu i s i t e consump-t i on is decreas ing . Jensen and Meckling suggest that monitoring or bonding a c t i v i t i e s can be used to control the manager's behavior . Monitor ing and bonding through control systems and preparat ion of audited f i nanc i a l statements represent use of information systems to reduce the noise in e f f o r t measurement s im i l a r to those a c t i v i t i e s analyzed more formal ly by Atkinson/Feltham and Ramakrishnan/Thakor. The costs of monitoring are borne by the manager s ince market par-t i c i p a n t s pr i ce s e cu r i t i e s r a t i o n a l l y . Jensen and Meckl ing 's manager i s r i sk neutral and therefore the real cost of his owning a propor-t i on of his f i rm is not apparent. Jensen and Meckling state that t he i r approach d i f f e r s fundamen-t a l l y from the agency theory descr ibed e a r l i e r in th i s s e c t i o n . 144 However the two approaches are not substantially different i f risk aversion is added to the Jensen/Meckling model and it is compared to the Atkinson/Feltham model. When the agent is risk averse, his ownership in his own firm clearly represents suboptimal risk sharing which he accepts in order to communicate his behavior to the market. Jensen and Meckling are indirectly determining an optimal compen-sation contract in which a portion of the manager's compensation con-sists of returns from his own firm which is a nontradeable asset and which imposes risk on him in order to motivate him to act in the best interests of the owners of his firm. The manager chooses to substi-tute compensation in the form of unobservable nontradeable riskless perquisites for observable nontradeable risky shares in order to maximize his expected utility. In the next section, the Jensen/Meckling problem of an owner/manager seeking external equity capital will be formulated under risk aversion. It will be seen that the implications of the model for managerial behavior under moral hazard are the same as those in agency models in which the principal offers a contract to an agent in order to share risks and provide incentives. 3. RISK SHARING AND VALUATION WITH MORAL HAZARD The problem of an entrepreneur seeking to raise funds to finance a capital investment will be analyzed where all market particpants have homogeneous beliefs about the exogenous distribution of future cash flows to be generated by the capital investment. The entrepreneur/owner will manage operations of the firm and can alter the distribution of cash flows through his actions which are unobser-vable by outside investors in the project or firm. It was shown in 145 Sect ion 1 of Chapter Four that Pareto-optimal r i sk sharing resu l ts when the r isk-averse entrepreneur s e l l s a l l of the equity in the cash flows generated by the project because systematic market r i sk can be opt imal ly shared in the cap i ta l market and the market is r i sk neutral as to nonsystematic f i rm-spec i f i c r i s k . This Pareto-optimal resu l t i s a t ta inab le in a per fect market, but was shown to be unatta inable when there ex i s t s a market imperfect ion such as asymmetric i n f o r -mation about the expected value of future cash f lows. A s im i l a r market imperfect ion which precludes attainment of e f f i c i e n t r isk, shar ing ex is ts when the manager can reduce the expected value of future cash flows through his unobservable act ions in order to maxi-mize his expected u t i l i t y . Since the manager se lec ts his act ions the informational asymmetry is in e f f ec t the same as that of Chapter Four: the entrepreneur has ins ide information about f i rm va lue . The entrepreneur chooses his ownership in his f i r m , a, and his act ions in order to maximize his expected u t i l i t y of wealth. He can reduce cash flows in every state by: (a) s h i r k i n g , or reducing the amount of e f f o r t expended in manag-ing the f i r m , and (b) taking non-pecuniary bene f i t s , or d i ve r t ing assets of the f i rm to his personal use ( e . g . , supplying himself with a com-pany ca r , or using the corporate j e t for recreat iona l t r a v e l ) . Sh i rk ing w i l l resu l t in reduced cash flows to the extent that they are dependent upon managerial a c t i ons . Perqu is i tes reduce cash flows by t he i r co s t . The reduction in cash flows in every s tate due to sh i rk ing and perqu i s i t e consumption w i l l be denoted F. Perqu is i tes a f f e c t only the expected value of cash flows and therefore are 146 riskless to the entrepreneur. When a is equal to the Pareto-optimal value of zero, the manager will receive 100% of the benefits of F while the firm's shareholders will bear 100% of the cost. When a > 0, the manager continues to receive 100% of the benefits of F, but also bears a proportion of the cost. Therefore as a increases, the manager's propensity to consume perquisites should decrease. In the problem at hand, a linear sharing rule is being assumed to simplify the analysis. A linear sharing rule is not likely to be optimal when a moral hazard problem exists. Therefore a loss in generality is being accepted so that a solution can be derived and analyzed. The problem of the entrepreneur is to select a, 3, F in order to maximize expected utility of end-of-period wealth. Max E{U(W\,F)} (5.3.1) a,!*,F where = o(x - F) + 3M + (l+r)Y (5.3.2) s.t. WQ + (l-o)V(o) - I - 3Vm - Y = 0 (5.3.3) V(«*) - P ' [if] ~ X = y - X = V (5.3.4) End-of-period wealth in expression (5.3.2) is reduced by the propor-tion of the cost of the perquisites actually consumed by the entrepreneur which he will bear, o f . In the budget constraint (5.3.3), the market pays (1-a) times the value which it infers from observation of a for (1-a) of equity in future cash flows generated by the investment I. Expression (5.3.4) is the market rationality 147 const ra in t that the market's inference is correct in equ i l i b r i um . Firm value is reduced by F through the reduction in expected value of future cash f lows. In the entrepreneur 's object ive funct ion (5.3.1) perqu is i t es F is shown separate from wealth W .^ U t i l i t y is derived from the use of assets consumed as perqu is i tes or from s h i r k i n g , and both are nonmarketable bene f i t s . There are a l t e rna t i ve ways of f o r -mulating the object ive f unc t i on . As shown in Section 1, in a two-person agency problem the agent 's u t i l i t y i s add i t i v e l y separable in wealth and e f f o r t and can be represented with two u t i l i t y funct ions ( e . g . , U(W) - G(e) ) . In the problem at hand, a separate u t i l i t y funct ion for perqu is t i es could be def ined so that the object ive func-t i on becomes max E{U(W^) + V(F)}. The approach to be taken i s to transform the benef i ts of F into do l l a r s of wealth so that the s i m p l i f i c a t i o n of the object ive funct ion made poss ib le by combining the normal d i s t r i b u t i o n and negative exponential u t i l i t y funct ion can be used. The transformation of F into do l l a r s of wealth w i l l be accomplished by def in ing a transformation funct ion T(F) which must s a t i s f y the fo l lowing cond i t ions : ( i ) T(0) = 0 ( i i ) T(F) > 0 for F > 0 because benef i ts are derived from any pos i t i v e level of perqu is i t es or s h i r k i n g . ( i i i ) 0 < T ' (F ) < 1 since more perqu is i tes are preferred to less and they are not t radeab le . ( iv ) T"(F) < 0 (v) T " ' ( F ) > 0 148 Conditions (iv) and (v) impose sufficient regularity on T(F) necessary for the following analysis. Thus T(F) is a type of ' u t i l i -ty' function which transforms F to dollars of wealth rather than utiles. Figure 5.1 depicts an acceptable transformation function. Figure 5.1. Perquisite Transformation Function T(F) is measured in the same units as wealth and can therefore be entered into the utility function defined over wealth as: - , -b(W, + T(F)) U(W1,F) = -e 1 It was proved in Chapter Four that arg Max E{U(WX)} = arg Max {W^  - j aj} Therefore, because F is riskless, the entrepreneur's objective func-tion (5.3.1) can be rewritten as: 149 Max GfRj - £ a. 2+ a,B,F w T(F)} Let H(a,B,F) b 2 . 2 aw + T(F) To solve the entrepreneur 's problem, subs t i tu te for Y in ( 5 .3 .2 ) , using (5.3.3) Wj = a(x - F) + W + (1+r) [W0 + (l-a)V(a) - I - BVJ (5.3.5) A f te r subs t i tu t ion for V(a) using 5.3.4 and s i m p l i f i c a t i o n , (5.3.5) becomes: = a[x - F - y + F(o) + X] + 0[M - ( l+r )V m ] (5.3.6) + y - F(o) - X + (l+r)(W Q - I) Recall from Chapter Four that M - (l+r)V X = £ ~ • Cov(x,M) °m The expected value and variance of 5.3.6 are: Wj_ = o[y - F - y + F(o) + X] + B[M - ( l - r jVJ (5.3.7) + y - F(a) - X + (l+r)(Wn - I) a 2 = a2a2 + 02 a2 + 2 a 0 Cov(x.M) (5.3.8) m The f i r s t order condi t ions to the problem are : 150 i H = M _ F _ u + F(a) + X + ( a - l ) F - aba 2 - 0 b Cov(x,M) = 0 | | = M - ( l+r )V m - 3ba m 2 - a b Cov(x,M) = 0 (5 .3 .9) (5.3.10) |» = _ a + T ' ( F ) = 0 (5.3.11) In order to e l iminate 3 from the problem, (5.3.10) i s solved for 3b and then subst i tu ted in to ( 5 . 3 . 9 ) : -F * F ( « ) • ( » 1 ) F - ob [ ° 2 ^ ' C ° , ( X ' ' W " ) 2 ] - 0 (5.3.12) m The market r a t i o n a l i t y cond i t ion (5 .3 .4) i s combined with (5.3.12) to a r r i v e a t : r ° 2 ° m " Cov(x.M) 2 n ( a - l ) F a = ab [ — — ' 1 (5.3.13) am Equation (5.3.11) i s rewritten as: T ' ( F ) = a (5.3.14) Equations (5.3.13) and (5.3.14) are the necessary e q u i l i b r i u m c o n d i t i o n s , each equating marginal benef i t and marginal cost for a choice v a r i a b l e . In ( 5 . 3 . 1 3 ) , s ince ( a - l ) < 0 , then F Q < 0 because the r ight-hand s ide i s p o s i t i v e . The marginal benef i t of a i s the increase in proceeds, ( a - l ) F a , and the marginal cost of a i s the bearing of f i r m - s p e c i f i c r i s k . The marginal benef i t of F i s T * ( F ) , 151 or the marginal increase in the wealth-equivalent of perqu is i tes and the marginal cost of F i s a, the entrepreneur 's share of the cost of F. F igure 5.2 i l l u s t r a t e s how the entrepreneur s e l e c t s his act ions on the basis of a. Therefore , the market i n f e r s F from observat ion of a and the entrepreneur does indeed s e l e c t F based upon a which i s se lected according to (5.3.13). F F*(a*) Figure 5.2. Choice of F(a*) Since 0 < a < 1, 0 < T*(F) < 1 which i s cons is tent with Figure 5.1 and the condi t ions on T ( F ) . It was suggested e a r l i e r in t h i s sect ion that the manager's pro-pensity to consume perqu is i tes or sh i rk should decrease as a i n c r e a s e s . In order to v e r i f y t h i s conjecture , t o t a l l y d i f f e r e n t i a t e (5.3.14) with respect to F and a: 152 T"(F)dF = da or dF _ 1 da = T T F J < 0 (5.3.15) from cond i t ion ( i v ) on T(F) Therefore i t i s t rue that F i s decreasing in a. The choice of F as a funct ion of a i s i l l u s t r a t e d in F igure 5 . 3 . Convexity i s proved by d i f f e r e n t i a t i n g (5.3.15) with respect to a: 1 d 2 F _ da' [T"(F)J T T ' " ( F ) F > 0 2 a (5.3.16) fol lows from T ' " > 0 F a < 0 Figure 5 . 3 . The Entrepreneur 's F(a) Choice 153 Since the market's inference i s assumed to be r a t i o n a l , the market's inference schedule w i l l a lso look l i k e Figure 5.3 and (5.3.15) can be subst i tu ted in to (5.3.13) to a r r i v e at the s i n g l e necessary e q u i l i b r i u m c o n d i t i o n . (g-1) _ . r ° 2 % - Cov(x,M) 2 . , T « / p \ = ab [ p ] (5.3.17) a m which has replaced the market's inference F a with the entrepreneur 's choice F = J . Equation (5.3.17) r e la tes choices of a and F to exoge-a T (F) nous parameters. A proof that second-order condi t ions are s a t i s f i e d appears in Appendix 5-A. Propos i t ion 5.1. An increase in f i rm s p e c i f i c r i s k w i l l r e s u l t in a * * decrease in equ i l i b r ium a and a corresponding increase i n F . Proof . It was shown in Chapter Four that o 2 a m 2 - Cov(x",M)2 2 2 = o £ , f i rm s p e c i f i c r i s k Rewrite (5.3.13), rep lac ing [•] with a ( a - l ) F = aba 2 (5.3.18) 154 The to ta l de r i va t i ve of (5.3.18) with respect to a and a £ i s : 2 2 ( a - l ) F da + F da = ba da + ab da x aa a e e or = < 0 (5.3.19) d a 2 (a-l)F + F - b a 2 e aa a e since (a-l) < 0 F > 0 aa F < 0 a b a 2 > 0 e Q.E.D. If f i rm-spec i f i c r isk inc reases , then ' s i g n a l i n g ' with a becomes more cos t l y and therefore the entrepreneur i s better o f f exchanging r i sky a for r i s k l e s s F. Propos i t ion 5.1 can be compared to resu l ts of the papers descr ibed in Section 2. Systematic r isk is 'observable ' and there -fore can be shared opt imal ly in the cap i ta l market. In the absence of moral hazard, non-systematic r i sk is borne by the r isk-neutra l p r i n c i p a l / i n v e s t o r s , as proved in Chapter Four. Due to the need to provide incent ives to the r isk-averse agent/manager, f i rm-spec i f i c r i sk is imposed on him. In the model here, the agent se lec ts the f i rm-spec i f i c r i sk that he w i l l bear in order to s ignal his act ions to the market. If f i rm s p e c i f i c r i sk inc reases , the level of pe rqu is i t es se lected w i l l increase because the manager subst i tu tes a 155 riski ess return from his firm for the risky return. To the manager perquisites serve as insurance against increases in risk. Proposition 5.2. An increase in the risk aversion parameter b will * result in a decrease in equilibrium a and a corresponding increase * in F . Proof. The total derivative of (5.3.18) with respect to a and b is: (o-l)F da + F da = b a 2 da + aa 2 db aa a e e 2 A aa„ da _ e , n or - J T s o — < 0 d b (a-l)F + F - b a 2 aa a e Q.E.D. This result is similar to Proposition 5.1. If b increases, com-municating through a becomes more costly and therefore risky a is exchanged for riskless F. Many of the studies described in Section 2 show how the manager may be motivated to reduce the variance of cash flows through his investment policy in order to reduce the risk which he bears. Diamond and Verrecchia describe systematic risk as being 'observable' and conclude that reduction of firm-specific risk should result in improved risk sharing between a risk-averse agent and risk-neutral principal because effort is more easily detectable. It can be seen from (5.3.17) that firm-specific risk can be reduced i f a is 2 decreased or Cov is increased. The following proposition formalizes the Diamond/Verrecchia conjecture. 156 Proposition 5.3. A reduction in firm-specific risk achieved through a reduction in a results in a greater expected utility for the entrepreneur and an increase in market value of the firm, for a given  covariance. Proof. (a) It was earlier shown that Arg Max E{U} = Arg Max G{H} = Arg Max H since G' > 0 T K a B d E {U} _ r>tu\ dH  T n e n ' d(parameter) " G ( H ) d(paramete7T , . d E{U| _ dH a n a s i g n d(parameter) " d(parameter) as long as the parameter is not b which appears in G. * * * * Let H (a , 3 F ) be the maximal value function. Then dH*. _ _9H*_ _9H*_ _9a_ + _9H*_ _9F 9a . 2 ~ 2 9a " 2 9 F * 9 a * 2 da 9a 9a 9a * 9H 2~ by envelope theorem. 9 a Using (5.3.8) dH da 2 4 a 2 < 0 157 2 2 A decrease in a reduces a and therefore improves the welfare w l of the entrepreneur in that the cost of communicating F by a has decreased. (b) To show that the market value increases, differentiate V(a) in p (5.3.4) with respect to a : dV ( c t ) _ 8V 8F 8 a , n . . . „ n — o " T F * * — o < 0 since each term < 0 j c. 8 r 8 a „ c do 8a Q . E . D . Market valuation increases because F(o) decreases as a result in a 2 decrease in a . In a perfect market, firm value is a function of systematic risk and changes in firm specific risk should have no effect on valuation. However, when moral hazard is present and the manager must bear firm-specific risk as an agency cost, changes in that risk result in changes in his behavior and therefore in firm valuation which depends upon his behavior. Therefore, more efficient risk sharing does result when firm-specific risk is reduced such that both shareholders and manager are better off. Shareholders are indifferent to the value of and changes in 2 a ex ante because they correctly infer managerial behavior and value the firm based upon observation of a; while the manager does gain by 2 ex ante reduction in a as shown in part (a) of the proof. On the 2 other hand, ex post reduction of a does benefit shareholders as well as the manager because the value of the firm will increase despite no changes in the expected value and systematic risk of cash flows. 158 As a £ becomes very small, it is seen from (5.3.18) that a approaches the value of 1 because the market knows that the cost of a to the entrepreneur is very small. It was shown in Chapter Four that 2 i f cr = 0, the firm's cash flows are prefectly correlated with those of the market portfolio so that the entrepreneur's investment in his own firm is a perfect substitute for an investment in the market. 2 Therefore no moral hazard problem will exist i f a£ =0: the entrepreneur will own 100% of the equity in future cash flows, will hold an investment in the market portfolio which complements the systematic risk in his firm, and hence will bear 100% of the cost of his behavior. Therefore it is indeed true that the agency problem is minimized i f firm-specific risk is very small. Proposition 5.4. A decrease in Cov(x,M) results in greater expected utility for the entrepreneur even i f i t results in greater firm-2 specific risk, given constant a . The effect on market value depends upon the sign of the covariance. (a) By use of the envelope condition as in the proof of Proposition Proof. 5.3: * * 3 H 3 Cov dH d Cov = X°(o-l) - a b 3 < 0 fl - (l+r)V, m where X = 2 is market price of risk. 159 I f Cov (x ,M ) d e c r e a s e s , t h e e n t r e p r e n e u r ' s e x p e c t e d u t i l i t y i n c r e a s e s because t h e v a l u e o f t h e f i r m has i n c r e a s e d . The f i r s t -o r d e r c o n d i t i o n ( 5 . 3 . 1 0 ) s i m p l i f i e s t o : 3 = £ - - < * Cov (x .M ) ( 5 . 3 . 2 0 ) I t was shown i n C h a p t e r Fou r t h a t t h e o p t i m a l c h o i c e o f a and e i n a p e r f e c t marke t a r e : 0 - n a - U s ° i s t h e o p t i m a l i n v e s t m e n t i n t h e marke t p o r t f o l i o o f an i n v e s t o r w i t h a c o e f f i c i e n t o f r i s k a v e r s i o n b i n o r d e r t o b e a r an o p t i m a l amount o f s y s t e m a t i c marke t r i s k . I f Cov (x ,M ) = 0 , t h e n 3* = 3° r e g a r d l e s s o f t h e l e v e l o f a . S i n c e t h e f i r m i s u n c o r r e c t e d w i t h t h e m a r k e t , t h e e n t r e p r e n e u r w i l l b ea r t h e o p t i m a l amount o f s y s t e m a -t i c r i s k t h r o u g h h i s i n v e s t m e n t i n t h e marke t p o r t f o l i o . I f Cov (x ,M ) > 0 , some s y s t e m a t i c r i s k i s h e l d t h r o u g h t h e i n v e s t m e n t a i n h i s own f i r m and t h e r e f o r e t h e e n t r e p r e n e u r r educes h i s i n v e s t m e n t i n t h e marke t by <xCov(x,M). I f Cov (x ,M ) < 0 , t h e e n t r e p r e n e u r i s ' s e l l i n g s h o r t ' s y s t e m a t i c r i s k t h r o u g h h i s i n v e s t m e n t a and t h e r e -f o r e he i n c r e a s e s h i s i n v e s t m e n t i n t h e marke t so as t o a c q u i r e t h e d e s i r e d amount o f marke t r i s k . T h e r e f o r e t h e c h o i c e s o f 3* i n t h e p r e s e n t p r o b l e m a r e : 3* < 3 ° i f Cov (x ,M ) > 0 3* > 3° i f Cov (x ,M ) < 0 3* = 3° i f Cov (x ,M ) = 0 160 2 If the covariance changes, while a is constant, firm-specific risk changes and therefore a will change. As both Cov and a change, the entrepreneur will adjust 3* so that he continues to hold the optimal amount of systematic risk. If Cov(x,M) > 0, a decrease in Cov(x,M) has the following effects: 9 Increase in o -»• decrease in a* e because the signal a has become more costly. Decrease in Cov] (• increase in 3* Decrease in o j because less market risk is held through a. Less wealth is,invested in a non-tradeable asset with systematic risk and therefore a greater investment will be made in the market so that 3° is reattained. Increase in E{ll} because the value of the firm has i ncreased. If Cov(x,M) < 0, a decrease in Cov(x,M) has the following effects: 2 Decrease in a •»• increase in a* e because the signal a has become more costly. -»• increase in 3* Decrease in Cov^ Increase in a 161 Because of the negative c o r r e l a t i o n , not only does a decrease in covariance mean that less market r i sk is he ld , but a lso the increase in a means that more ' s o l d s h o r t ' . Therefore a greater investment is made in the market. Increase in E{U} because the value of the f i rm has inc reased . (b) In order to prove the e f f e c t on market va lue, (5.3.4) is rewri t ten as: dV _ 3V 9V . 3F . 3a (5 3 22) d Cov 3 Cov T F 3a 3 Cov KO.O.CC) A l l of the above pa r t i a l der i va t i ves are negat ive, with the exception of 3a/3 Cov which was shown in part (a) of th i s proof to depend upon the sign of the covar iance, where: V ( 0 ) - M - F ( a ) - X° Cov(x,M) (5.3.21) which is then d i f f e r e n t i a t e d with respect to Cov(x,M). < 0 > 0 i f Cov J > 0 < 0 Therefore : dV < 0 i f Cov < 0 d Cov < > 0 i f Cov > 0 162 The change in value in (5.3.22) has two terms: one representing an exogenous effect which is a change in the risk priced by the market, the second an endogenous effect resulting from managerial behavior. In a perfect market, only the first effect would result from a change in the covariance. If Cov(x,M) > 0, a decrease in Cov(x,M) has the following effects: Increase in aQ •*• decrease in a -»• increase in F > lower value Decrease in risk adjustment •*• higher value If Cov (x,M) < 0, a decrease in Cov(x,M) has the following effects: Decrease in a E -*• increase in a -»• decrease in F > higher val ue Decrease in risk adjustment > higher value. Therefore the effect on firm value i f Cov(x,M) < 0 depends upon the relative sizes of the exogenous and endogenous changes. Q.E.D. Propositions 5.3 and 5.4 illustrate the complexity of the principal-agent problem in a market in which the agent may make deci-sions other than how much effort to expend or perquisites to consume. Proposition 5.3 shows that all market participants are better off if the variance of cash flows is reduced. Proposition 5.4 shows that the manager can reduce his risk through adjustment of his personal investment portfolio as well as through the firm's investment policy. Investors in the market are assumed to be rational and can infer that the manager will undertake any feasible action that maximizes his 163 wel fare . Therefore secu r i t i e s w i l l be pr iced r a t i ona l l y and the entrepreneur w i l l bear the costs of his a c t i ons . Since the manager must bear f i rm-spec i f i c r isk and w i l l be assumed to se lec t i nves t -ments to maximize his we l fare , he may be motivated to ( i ) o f f e r an a l t e rna t i ve bonding system so that he can reduce his r i sk and ( i i ) provide a system which monitors his investment p o l i c y . 4. AN EXAMPLE The so lu t ion to the entrepreneur 's problem in Section Three was in the form of an i m p l i c i t funct ion of a. A closed form so lu t ion is not a t ta inab le without a s p e c i f i c a t i o n of the form of T ( F ) . Necessary c r i t e r i a which T(F) must s a t i s f y were descr ibed as: ( i ) T(0) = 0 ( i i ) T(F) > 0 for F > 0 ( i i i ) 0 < T ' (F ) < 1 ( iv ) T"(F) < 0 (v) T " ' ( F ) > 0 A funct ion which s a t i s f i e s these c r i t e r i a i s the negative exponen-t i a l funct ion T(F) = 1 - e ' F (5.4.1) A parameter in an i n d i v i d u a l ' s u t i l i t y funct ion is the c o e f f i c i e n t of r i sk aversion which describes the a t t i tude of the ind iv idua l toward r i s k . A useful parameter in an i n d i v i d u a l ' s pe rqu i s i t e t r a n s f o r -mation funct ion would be a c o e f f i c i e n t which would descr ibe the a t t i -tudes of the ind iv idua l toward sh i rk ing or consumption of p e r q u i s i t e s . Such a parameter w i l l be included in T(F) as: 164 T(F) = i - ^ e ' Y F (5.4.2) where y > 0 is the coefficient of the propensity to consume perequisites. To show that (5.4.2) satisfies the five criteria listed above, ( i ) T ( F ) = 4 " = 0 w n e n F=0 (ii) T(F). > 0 for F > 0 Since ^  [ l - e " y F ] > 0 -YF follows from e 1 < 1 for y¥ > 0 (i i i ) T'(F) = e" y F = 1 when F=0 T'(F) > 0 since e~ y F > 0 T'(F) < 1 since e" Y p < 1 for yF > 0 (iv) T"(F) = -Ye"YF < 0 (v) T'"(F) = y 2e" y F > 0 The equilibrium conditions which were derived in Section Four are: T'(F) = a (5.3.14) (a-l)Fa = ab^ 2 (5.3.18) To solve for F*, substitute for T'F in (5.3.14) e" y F = a (5.4.3) Taking logarithms of (5.4.3): -YF = In a or F* = - l"-25 > 0 Since 0 < a < 1 (5.4.4) and F a = - < 0 (5.4.5) 165 and F = ^ — - > 0 ( 5 . 4 . 6 ) Y Y Expressions ( 5 . 4 . 4 ) - ( 5 . 4 . 6 ) describe the entrepreneur's choice of F as decreasing in a and increasing in y . From ( 5 . 4 . 4 ) it is seen that lim F = °° a+0 and lim F = 0 a + l The manager will consume zero perquisites i f he owns the entire firm because he bears all the cost and his benefit is less than cost (from T(F) < F). If no equity in the firm is held, he will consume all cash flows, and therefore investors will not purchase 100% of the equity in the project. The market knows the manager's perquisite transformation func-tion, observes a * , and can perfectly infer F*. F (a* ) = F* ( 5 . 4 . 7 ) Substituting for F* from ( 5 . 4 . 4 ) , ct *\ - 1 n a F ( a* ) = — In order to derive a * , substitute for Fa in ( 5 . 3 . 1 8 ) , using a ( 5 . 4 . 5 ) d ^ l l - a b a 2 a y e or a 2yba £ 2 + a - 1 = 0 ( 5 . 4 . 8 ) The solution to ( 5 . 4 . 8 ) is: 166 -1 + /l + 4yba 2 a * = ~ - (5.4.9) 2yba £ Market va luat ion of the f i rm obtains by subs t i t u t i ng for F ( a ) in the va luat ion funct ion v/a) - v - F(a) - X° Cov(x.M) 1+r w +JLIL2. x ° Cov(x\M) so that V(a) = y 1 + r (5.4.10) Both a and y enter into va luat ion because both are determinants of F . Propos i t ion 5 . 5 . An increase in the propensity to consume p e r q u i s i -tes y w i l l resu l t in a decrease in a . Proof . Proposi t ions 5 . 1 and 5 . 2 ind icated that increases in b or o a £ would resu l t in a decrease in a . In expression ( 5 . 4 . 9 ) , 2 Y , b , a £ appear m u l t i p l i c a t i v e l y . 2 T o t a l l y d i f f e r e n t i a t e ( 5 . 4 . 8 ) with respect to a and ( yba £ ) . a 2 d ( y b a £ 2 ) + 2 a ( y b a £ 2 ) da + da = 0 , 2 da a , n or 5— = 5 < 0 d(yba d) 2a ( yba + 1 £ £ Q.E.D. 2 a* decreases i f b or a increase because a becomes a more e cos t l y s ignal of F . 167 a* decreases if y increases because F increases with y and a and F are inversely related. Proposition 5.6. The choice of a* will always be such that 0 < a < 1. Proof. (a) Verification that a > 0: From (5.4.9) it is clear that a* > 0 since 4Yba e 2 > 0 (b) Verification that a < 1: To be proved: -1 + / l + 4yba 2 < 2yba 2 or / l + 4yba e < 1 + 2yba^ Squaring both sides, 1 + 4yba £ 2 < 1 + 4yba £ 2 + 4(yba e 2) 2 2 2 which is clearly true since 4(yba e ) > 0 Q.E.D. In the example analyzed in this section, firm valuation is a function of an observable managerial action, a, and an individual managerial behavioral parameter, y. Investors know that cash flows are reduced by perquisites and that the level of perquisites is determined by a and y. 168 5. EMPIRICAL IMPLICATIONS The information set ava i l ab le to investors for va luing a new secu r i t y was b r i e f l y descr ibed in sect ion 4 of Chapter Four. In 1977, the SEC issued Secur i t i es Act Release No. 5856 which expanded the mandatory d i sc losure in r eg i s t r a t i on statements to include i n f o r -mation about managerial nonpecuniary compensation. D isc losure of remuneration i s mandatory for the three highest paid o f f i c e r s and any o f f i c e r whose d i r ec t remuneration exceeds $40,000. In spec i f y ing what is to be considered d i rec t remuneration, "The Release d iv ides d i r ec t remuneration into two ca tegor i es , namely ' s a l a r i e s , f ees , bonuses and other payments' (which have t r a d i t i o n a l l y been deemed covered by the ex i s t i ng d i sc losure requirements) and the 'personal bene f i t s ' received by management a euphemism for p e r q u i s i t e s . " [ P r ac t i s i ng Law Ins t i tu te (1977), p. 504] There are three categor ies of personal b e n e f i t s . A. Benef i ts which must be reported as remuneration are those payments made by the company f o r : 1. home repairs and improvements; 2. l i v i n g expenses; 3. the personal use of company property such as automobi-l e s , yachts , or vacation houses; 4. personal t rave l expenses; 5. personal entertainment expenses; and 6. legal and accounting fees unrelated to company bus iness . B. Benef i ts which may be reported as remuneration are 1. the manager's a b i l i t y to obtain favorable bank loans or s i m i l a r benef i ts because the company compensates the t h i r d par ty , and 169 2. the use of corporate staff for personal purposes. C. Benefits which are not considered to be remuneration are: 1. directly related to job performance (e.g., use of a parking space), or 2. necessary to the conduct of the company's business (e.g., an expense account). The total pecuniary and nonpecuniary remuneration received by top management therefore is disclosed to some extent and can be used as a measure of riskless F in empirical tests of the predictions from the analysis in the preceding section. The principal empirical prediction of both the adverse selection model in Chapter Four and the moral hazard model in Chapter Five is that firm value will be positively related to a. The empirical tests discussed in Section 4 of Chapter Four found such a positive rela-tionship. Since there are two different explanations for the posi-tive relationship, it would be desirable to design an empirical test which could differentiate between the adverse selection and the moral hazard explanations. Such a test may be possible due to the existence of data about perquisites. Both Proposition 4.4 and Proposition 5.1 show that an increase in o £ will result in a decrease in a, which is empirically testable. However, Proposition 5.1 also adds that an increase in c r will result in an increase in F, which also is empirically testable since F is measurable. If a negative relationship between <r and a is found empirically, and there is no change in remuneration, then empirical support for the model of Chapter Four is provided. If however, 2 there is also found a positive relationship between a and F, then 170 the empirical evidence supports the moral hazard model (perhaps in addition to the adverse selection model). The analytical result that there will be a negative relationship between a and F is testable. According to the capital asset pricing model, firm value should depend upon systematic risk and be independent of firm-specific risk. Proposition 5.3 shows that under moral hazard, firm value will change i f firm-specific risk changes while the covariance is constant. Since a and Cov(x,M) can be estimated from price data, then the prediction of Proposition 5.3 is testable. Firm value is decreasing in Cov(x,M) according to the capital asset pricing model. Proposition 5.4 indicates that firm value may be increasing in covariance due to the agency problem and the effects of changes in risk on the choice of a. The prediction of this propo-sition therefore is testable. 2 In summary, since F and a are disclosed in the prospectus and a £ and Cov(x,M) can be estimated from a time series of price data, there are implications of the analysis in this chapter which can be empiri-cally tested. 171 CHAPTER SIX RISK SHARING AND VALUATION UNDER ADVERSE SELECTION AND MORAL HAZARD INTRODUCTION This chapter integrates the results of risk sharing and valuation under adverse selection from Chapter Four and under moral hazard from Chapter Five. The entrepreneur employs two signals to communicate his information about both the exogenous parameters of the distribu-tion of cash flows and his endogenous behavior. While a complete solution to the problem cannot be derived due to a mathematical dif-ficulty, the formulation and partial solution indicate how the adverse selection and moral hazard problems are in fact variations of one basic informational problem of unobservabi1ity, and how sensitive a solution will be to the nature of the interaction of the signals. AN INTEGRATION OF THE ADVERSE SELECTION AND MORAL HAZARD PROBLEMS The informational asymmetry which exists in the integrated model arises from the ex ante unobservabi1ity of the expected value of cash flows and the ex post unobservabi1ity of managerial effort. As in Chapter Four, it is assumed that the firm's cash flows are uncorre-cted with those of the market. In a perfect market, the value of the firm then is a function of the expected value of future cash f1ows: V = T £ f (6.1) 172 The entrepreneur knows the parameters of the distribution of future cash flows while investors do not. The entrepreneur also expends effort in managing the firm and can reduce the expected value of cash flows through his unobservable consumption of perquisites and shirking. The end-of-period realization of cash flow is a random variable observable by investors and the entrepreneur. The problem of the entrepreneur is to select ownership in his firm, perquisite consumption, and a disclosure about value so as to maximize his expected utility. In the absence of asymmetric infor-mation, investors know firm value, there will be no disclosure and the entrepreneur will sell 100% of the equity in his firm. In the problem of Chapter Four, two costly signals were supplied by the entrepreneur to the market to communicate information about \i 2 because the costs of both signals are functions of a about which there is asymmetric information. In the moral hazard problem of Chapter Five, the entrepreneur selected his ownership in his firm in order to communicate information about his behavior. In the integrated problem in this chapter, the entrepreneur selects ownership in his firm and disclosure when the market does not know 2 p or 0 and cannot observe F. There is sufficient separability in the problem as formulated that investors can infer F from a alone. The entrepreneur selects y in order to disclose his information about \i. However, since the choice of a affects the marginal benefits of the signal y, it is also used by investors to infer y. The market rationality conditions to the integrated problems then are: F(o*) = F* (6.2) 173 x(a*,y*) = y (6.3) The market observes a* and correctly infers endogenous managerial behavior; and also observes y and correctly infers the exogenous parameter y. Since the result of the entrepreneur's behavior is a reduction in cash flows, inferred firm value is V(a* > y * ) = X ( a * » y * ) - F t « *> (6.4) The problem of the entrepreneur is Max E{U(W)1)} = Max H (6.5) o.P.F,y o,0,Fty s.t. WQ + (l-a)V(o,y) - C(y) - I - 0Vm = Y (6.6) V(a*,y*) = "x(a*»yVr F ( a * } = TTr" = V <6'7) where H = ^ - | a 2 + T(F) (6.8) wx = a(x-F) + 3M + (l+r)Y (6.9) The problem is constrained by the budget constraint (6.6) and the market rationality constraint (6.7) which follows from (6.2), (6.3), and (6.4). In order to derive expression (6.8), substitute (6.6) into (6.9) Wj_ = o(x-F) + 3M + (1+r) [WQ + (l-o)V(o.y) - C(y) - I - fSVj (6.10) After substitution of (6.4) and rearrangement, (6.10) becomes Wx = a [x - F - x(a,y) + F(o)] + B[M - ( l + r ) V j + x(a,y) - F(a) + (l+r)[WQ - C(y) - I] (6.11) 174 The expected value and variance of (6.11) are Wj_ = a[y - F - x(a.y) + F(o)] + p[M - U+rJVj + x(a,y) F(a) + (1+r) [WQ-C(y)-I] (6.12) a 2 = a a2 + g 2 a 2 (6.13) First-order conditions to (6.5) are: ~ = M - F - x(a,y) + F(a) + (l-a)x + (a-l) F - aba2 = 0 dot ot oc (6.14) | H = M . ( 1 + r ) V m . g b a 2 = 0 ( 6 > 1 5 ) |[i = -a + T'(F) =0 (6.16) -fy = (l -a)x y - (l+r)Cy = 0 (6.17) Due to the separability in these first-order conditions, the choices of s and F can be isolated from the choice of a and y. The separability results from assuming Cov(x,M) = 0, a T(F) function independent of 8 or y, and C(y) function independent of 3 or F. The choice of 8 can be derived from (6.15) as: 175 M-(l+r)V U s i n g A = g-a m It was shown in Chapter Five that A 0 3 * = F~~ aCov(x,M) In the problem at hand when Cov(x,M) = 0 , the entrepreneur holds the optimal amount of market risk through his investment in the market portfolio since ownership in his firm imposes only firm-specific risk on him. In order to derive the choice of F, equation ( 6 . 1 4 ) is combined with ( 6 . 2 ) and ( 6 . 3 ) ( a - l ) F a = a b a 2 ( 6 . 1 8 ) Equations ( 6 . 1 6 ) and ( 6 . 1 8 ) are identical to the first-order condi-tions of the moral hazard problem in Chapter Five. In order to derive an explicit solution for F ( a ) , the perquisite transformation function adopted in section four of Chapter Five will be employed here. -yF Assume T(F) = ^  - e ( 6 . 1 9 ) Differentiate ( 6 . 1 9 ) and use ( 6 . 1 6 ) -YF T'(F) = e = a or - yF = In a and F* = - -1^ -2 ( 6 . 2 0 ) 176 In (6.20), both a and y are observable. The optimal selection of perquisites is unchanged by the additional asymmetric information 2 2 about p and a . The market, however, now can infer CK from obser-vation of a above since, from (6.18), (6.21) can be substituted into (6.18). a-l _ u 2 = a b a ay or a 2 inferred =-g-—. (6.22) a by The entrepreneur selects F so that T'(F) = a where the marginal bene-f i t and marginal cost of F are equal. Given the assumed negative exponential form of T(F), he selects F according to (6.20) as a func-tion of a and his propensity to consume perquisites y. Since they understand the entrepreneur's problem, investors know y, observe a, 2 2 and correctly infer F and a . While a is irrelevant for firm valuation, i t is a parameter which is necessary to infer p from y. The entrepreneur therefore chooses and F* = a i c -1 + /I + 4byo2 ( 6 > 2 3 ) 2bya from (6.22) -In a The market infers 177 F(o*) = F* = •ln a* 2, 1 - a* 2 a (a*) = — £ = a a* by 2 ? To show that the market s inference o~:{a*) is equal to the true a , subs t i tu te for a*, using (6.23) in the inference f unc t i on . a 2(a*) •1 + / l + 4bya 2byo by r - l + •! + 4bya  L 2 2bya CT2 a f te r s i m p l i f i c a t i o n In order to derive y* , i t is necessary to derive the market's inference schedule x (o , y ) . The cost funct ion for y which was assumed in Chapter Four w i l l be assumed here: C ( y ;u ,o ) = (l+r)y<* (6.24) and C. 3Pl (l+r)ua (6.25) 2 As in Chapter Four, a is i r r e l evan t to investors in valuing the f i rm 2 in a per fect market. However, s ince the cost of y depends upon a , 2 investors must know or be able to i n f e r a in order to in te rpre t y . Equation (6.25) is subst i tu ted into (6.17): 178 ( l - a ) x y = 3 P y l ( 6 ^ 2 6 ) ya The market rationality condition (6.3) is substitution into (6.26) in equilibrium 2 (l-a)xyx(o,y) = ^ f - (6.27) y a Condition (6.3) is also substituted into (6.14): (l-a)x o + («-l)Fa - aba 2 = 0 (6.28) Expression (6.21) for F a is substituted into (6.28): (l-a)x + l l 2 _ aba 2 = 0 (6.29) a ay The market's inference schedule is the solution to the simultaneous partial differential equations: 2 (l-o)x x - ^ f - = 0 (6.27) a (l"«)xa + ^ - aba 2 = 0 (6.29) The method of separation of variables which was used in Chapter Four cannot be used to solve the system because the solution does not appear to be of the form x(ct,y) = g(a)h(y) as was conjectured in Chapter Four. The -^—t term in (6.29) prohibits separation. In 2 Chapter Four, a provided information about a so that y could be inferred. In the problem at hand, a provides information about perquisites and, in a sense, affects how much information is provided 179 by the disclosure y. As a approaches zero, F becomes very large and investors know that the firm has l i t t l e value without observing y. As a approaches one, F becomes very small and investors now that the firm value is - j — and therefore must observe y to infer value. More formally, As o + 0, F ->• x and E(x-F) > 0 and V ^  0 As a + 1, F + 0 and E(x-F) •»• y and V - ^ The speculated interaction between a and y is that, for a fixed y, i f a is very small, investors can infer value without y and less y will be provided by the manager because it is costly. If a is very large, investors cannot infer value without y and therefore the marginal benefits of y increase, resulting in a choice of a high y. A second type of interaction is seen in (6.27) in the (l-a)x yx term which indicates how the marginal benefit of y depends upon a. The conjec-tured form of the inference schedule then is x(a,y) = b(y) + g(a)h(y) where the multiplicative term captures the interaction between the two signals. The exact solution of the inference schedule will be addressed in future research. 180 When the problem as formulated in this Chapter is compared to those in Chapters Four and Five, it is clear that the adverse selec-tion and moral hazard problems are variations of one basi*c infor-mational problem of unobservabi1ity of value, or quality, where value is exogenous in one case and endogenous in the second. The mathema-tical difficulty which prohibits the solution of the integrated problem of this Chapter at this stage is not created by the com-bination of adverse selection and moral hazard into one problem; rather it is due to the inability to conjecture an appropriate func-tional form which permits a solution. Based upon the analysis in this dissertation, it appears that the existence of a fully-revealing signaling equilibrium in a multivariate signaling model will depend upon the nature of the interactions of the signals. There also must be a sufficient amount of separability among the choice variables in order for a solution to be tractable. 181 BIBLIOGRAPHY Atkinson, A.A. and G.A. Feltham. "Information in Capital Markets: An Agency Theory Perspective." University of British Columbia Working Paper, 1982. Akerlof, George. "The Market for 'Lemons': Qualitative Uncertainity and the Market Mechanism." Quarterly Journal of  Economics 89 (August 1970), 488-500. Baron, David P. "The Incentive Problem and the Design of Investment Banking Contracts." Journal of Banking and Finance 3 (1979), 157-75. Baron, David P. "A Model of the Demand for Investment Banking Advising and Distribution Services for New Issues." The  Journal of Finance 37 (September 1982), 955-76. Baron, David P. and Bengt Holmstrom. "The Investment Banking Contract for New Issues Under Asymmetric Information: Delegation and The Incentive Problem." The Journal of Finance 35 (December 1980), 1115-38. : Beaver, William H. Financial Reporting: An Accounting Revolution. Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1981. Beck, Paul J. and Thomas S. Zorn. "Managerial Incentives in a Stock Market Economy." The Journal of Finance 37 (December 1982), 1151-67. Bhattacharya, Sudipto. "Imperfect Information, Dividend Policy, and 'the Bird in the Hand' Fallacy." The Bell Journal of  Economics 10 (Spring 1979), 259-70. Bhattacharya, Sudipto. "Nondissipative Signaling Structures and Dividend Policy." The Quarterly Journal of Economics 95 (August 1980), l-ZT. Borch, Karl. "Equilibrium in a Reinsurance Market." Econometrica 30 (July 1962), 424-44. Boyce, William E. and Richard C. DiPrima. Elementary Differential  Equations and Boundary Value Problems. Second edition. John Wiley & Sons, Inc., New York, 1969. 182 Campbell, Tim S. and William A. Kracaw. "Information Production, Market Signalling, and the Theory of Financial Intermediation." The Journal of Finance 35 (September 1980), 863-82. Campbell, Tim S. and William A. Kracaw. "The Market for Managerial Labor Services and Capital Market Equilibrium." University of Utah Working Paper, 1982. Cass, D. and J.E. Stiglitz. "The Structure of Investor Preferences and Asset Returns, and Separability in Portfolio Allocation: A Contribution to the Pure Theory of Mutual Funds." Journal of Economic  Theory 2 (June, 1970), 122-60. DeGroot, Morris H. Optimal Statistical Decisions. McGraw-Hill Book Company. New York, 1970. Diamond, Douglas W. "Financial Intermediation and Delegated Monitoring." Forthcoming, Review of Economic Studies, 1984. Diamond, Douglas and Robert Verrecchia. "Optimal Managerial Contracts and Equilibrium Security Prices." The Journal of  Finance. 37 (May 1982), 275-87. Downes, David H. and Robert Heinkel. "Signaling and the Valuation of Unseasoned New Issues." The Journal of  Finance. 37 (March 1982), 1-10. Fama, Eugene and Merton Miller. The Theory of Finance. Dryden Press. Hinsdale, Illinois. 1972 Feltham, G.A. and John S. Hughes. "Communication of Private Information in Capital Markets: Contingent Contracts and Verified Public Reports." University of British Columbia working paper, 1983. Friend, Irwin and Longstreet, Mendelson, Miller, and Hess. Investment Banking and the New Issues Market. The World Publishing Company. New York, 1967. Gonedes, Nicholas. "Corporate Signaling, External Accounting and Capital Market Equilibrium: Evidence on Dividends, Income, and Extraordinary Items." Journal of Accounting Research 16 (Spring 1978), 26-79. Grossman, Sanford J. "The Informational Role of Warranties and Private Disclosure About Product Quality." The Journal of  Law and Economics 24 (December, 1981), 461-83. Harrison, Tom. "Different Market Reactions to Discretionary and NonDiscretionary Accounting Changes." Journal of Accounting Research 15 (Spring 1977), 84-107. 183 Heinkel, Robert. "Dividend Policy as a Signal of Firm Value." from "Essays on Financial Markets with Imperfect Information." Ph.D. dissertation, University of California, Berkeley, 1978. Heinkel, Robert. "Uncertain Product Quality: The Market for Lemons with An Imperfect Testing Technology." The Bell Journal of Economics 12 (Autumn 1981), 625-36. Holmstrom, Bengt. "Moral Hazard and Observability." The Bell  Journal of Economics 10 (Spring 1979), 74-91. Ibbotson, Roger G. "Price Performance of Common Stock New Issues." Journal of Financial Economics 2 (1975), 235-72. Jensen, Michael C. and William H. Meckling "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure." Journal of Financial Economics 3 (1976), 305-60. Leland, Hayne E. "Quacks, Lemons, and Licensing: A Theory of Minimum Quality Standards." Journal of Political Economy 87, No. 6 (1979), 1328-46. Leland, Hayne E. and David H. Pyle. "Informational Asymmetries, Financial Structure, and Financial Intermediation." The  Journal of Finance 32 (May 1977), 371-87. Logue, Dennis E. "On the Pricing of Unseasoned Equity Issues: 1965-1969." Journal of Financial Quantitative Analysis 8 (January 1973), 91-103. Mandelker,Gershon and Artur Raviv. "Investment Banking: An Economic Analysis of Optimal Underwriting Contracts." The  Journal of Finance 32 (June 1977), 683-94. Marcus, Alan J. "Risk Sharing and the Theory of the Firm." The  Bell Journal of Economics 13 (Autumn 1982), 369-78. McDonald, J.G. and A.K. Fisher. "New-Issue Stock Price Behavior." The Journal of Finance 27 (March 1972), 97-102. Mossin, J. Theory of Financial Markets. Prentice-Hall, Englewood Cliffs, N.J., 1973. Patell, James. "Corporate Forecasts of Earnings Per Share and . Stock Price Behavior." Journal of Accounting Research 14 (Autumn 1976), 246-76. Penman, Stephen H. "An Empirical Investigation of the Voluntary Disclosure of Corporate Earnings Forecasts." Journal of  Accounting Research 18 (Spring 1980), 132-60. 184 Practising Law Institute Corporate Law and Practice Course Handbook Series, Number 262, "Preparation of Annual Documents Disclosure," Practising Law Institute, New York City, 1977. Ramakrishnan, Ram I.S. and Anjan V. Thakor. "Moral Hazard, Agency Costs, and Asset Prices in a Competitive Equilibrium." Journal of Financial and Quantitative Analysis 17 (November T9~82), 503-52". Reilly, F.K. and K. Hatfield. "Investor Experience with New Stock Issues." Financial Analysis Journal 25 (1969), 73-80. Ricks, William E. "The Market's Response to the 1974 LIFO Adoptions." Journal of Accounting Reseach 20 (Autumn 1982), 367-87. Riley, John G. "Informational Equilibrium." Econometrica 47 (March, 1979), 331-59. Ritter, Jay R. "Inside Holdings and the Pricing of Initial Public Offerings." working Paper, Wharton School, University of Pennsylvania. February, 1982. Ritter, Jay R. "The 'Hot Issue' Market of 1980." Working Paper, Wharton, School University of Pennsylvania. 1983. Robinson, Gerald J. and Klaus Eppler. Going Public. Securities Law Series, Volume 1. Clark Boardman Company, Ltd, 1978. Rock Kevin. "Why are New Issues Underpriced?" Working Paper, University of Chicago, 1982. Ross, Stephen A. "The Economic Theory of Agency: The Principal's Problem." The American Economic Review 63 (May 1973), 134-39. Ross, Stephen A. "Mutual Fund Separation and Financial Theory - The Separating Distributions." Journal of Economic Theory. (April, 1978). Ross, Stephen A. "The Determination of Financial Structure: The Incentive Signalling Approach." The Bell Journal of Economics 8 (Spring 1977), 23-40. Spence, Michael. "Job Market Signaling." Quarterly Journal of  Economics 87 (August 1973), 355-74. Spence, Michael. "Competitive and Optimal Responses to Signals: An Analysis of Efficiency and Distribution." Journal of  Economic Theory 7 (1974), 296-332. Spence, Michael. "Informational Aspects of Market Structure: An Introduction." Quarterly Journal of Economics 90 (November 1976), 591-97. 185 Stiglitz, Joseph E. "Information and Capital Markets." Financial  Economics: Essays in Honor of Paul Cootner. Edited by William F. Sharpe and Cathryn Cootner. Prentice-Hall. Englewood Cliffs, New Jersey. 1982. Talmor, E l i . "Asymmetric Information, Signaling, and Optimal Corporate Financial Decisions." Journal of Financial and  Quantitative Analysis 41 (November 1981), 413-38. Thakor, Anjan V. "An Exploration of Competitive Signalling Equilibria with 'Third Party' Information Production: The Case of Debt Insurance." The Journal of Finance 37 (June 1982), 717-39. U.S. Government Printing Office. Laws Relating to Securities Commission Exchanges and Holding Companies. Washington, D.C, 1976. ~ 186 APPENDIX APPENDIX 1 The Portfolio Problem of the Underwriting Syndicate The risk-averse investment banker can reduce risk-bearing costs by dividing risk with other bankers. Assume that n identical risk-averse bankers underwriter the issue so that each buys 1 of the shares sold by the entrepreneur. The problem of each banker i becomes:* Max E (U^.)} i = 1 n (Al.l) V B i where W]. = a. + 0. M + (l+r)Yi (Al .2) s.t. W0. + ( l - a i ) 1- B l Vm - Y = o (A1.3) where V= (Al .4) 1+r The portfolio problem of the underwriter is similar to that of the entrepreneur. Each individual banker in the group selects , how much of his equity of ^  to retain in the entrepreneur's security, and 3.j and Y^ , his investments in the market portfolio and the riskless asset. 187 Assuming a negative exponential utility function with risk aversion parameter b and normally distributed cash flows, the maxi' mization of(Al.l), as shown in Chapter Four can be simplified to: MaxH = w - b 2 V *i i where, using substitutions as in Chapter Four x . ~ „ x r i l (1-OL.) (y-X) W H = ^  - + e. M + (Hr) [Woi Si \ = ^ X + X + p1 [M - (l+r)V m] + + (Hr) WQi (A1.5) The expected value of (A1.5) is: " l i = a i r7 + B i [^ " ( 1 + r ) Vm ] + — + O+r) WQi (Al .6) The variance of (A1.5) is: 2 2a.3. CTWi = a i " T + 3 i 2 am2+ n-2- Cov(*»M~) (A1.7) n The first-order conditions to the problem are: 9H = X a,ba2 p.b 3H," n " "V'-n- C o v = 0 <A1'8) 9H _ 2 ou b „ „ — = M - (Hr)V m - B . b o m - — Cov(x,M) = 0 (Al .9) 90.. x ' m I m n 188 The single necessary condition is derived from the combination of (AT.8) and (A1.9): «. b ro 2 - CovU.M)^ , Q ( A 1 J Q ) 2" 2  n °m mFeasible solutions to (Al .10) are = 0, risk neutrality, and zero firm-specific risk, as discussed in section one of Chapter Four. However, in a group of n risk-averse individuals, a fourth feasible solution is n •*• ». Therefore the cost of Oj > 0 is decreasing in n. The larger is the underwriting syndicate, the lower is the cost to the group of the risk of not selling the entire issue. The risk premium charged by a group of more than one investment bankers is less than that of an individual and therefore one of the conditions necessary for viable intermediation described in Chapter Three is satisfied: the entrepreneur earns a return at least as great as he would by contracting directly with the market. Since the risk borne becomes very small with large n, a large underwriting group behaves as i f it were risk neutral. Footnote to Appendix 1: ^ The notation for this appendix is developed in chapter Four although the reference to the appendix appears in Chapter Three. 189 APPENDIX 2 Second-Order Conditions To The Bi van" ate Signaling Model A sufficient condition for a maximization of the objective function is that the Hessian matrix of second-order partial deriva-tives is negative definite. Since the choice of s was eliminated from the problem, the Hessian matrix is composed of the second-order partial derivatives of the objective function with respect to a and y. The Hessian matrix 1 H H w aa ay H«y Hyy is negative definite i f (1) H < 0 aa (2) H y y < 0 (3) H H v ' aa yy H u > 0 ay Values for the second-order partial derivatives are derived from (4.3.13) and (4.3.15): H = (l-a)x - 2x - b tf aa aa a (A2.1) "y " """Ny " <1+r)cyy (A2.2) (A2.3) I. Proof that H < 0 aa The following equilibrium relationships were derived in Chapter Four. 190 Py3 ( D C - "—2— <4-3-7) (1+r)ya Then (Hr) C y y = ( A 2- 4) ua (ii) x = {9bPy3L}1/3 (4.3.39) Letting L = ^  + 1 n ^ <A2'5) I - « (A2.6) a 2 (1-a)' L = I ]±2 ) (A2.7) aa ~ ~T (1-a) or x3 = 9bPy3L (A2.8) (i i i ) a + (1-a) ln (1-a) = -*L— (4.3.45) 3ba or (l-a)L ( A 2' 9) 3bo 2 2 1/3 ( 1 v ) y = { l l l « L u _ ? _ } (4.3.46) 3P (v) x = y (4.3.6) 191 Equations (ii) - (v) must hold in equilibrium and therefore can be used in determining whether the second-order conditions hold at equilibrium. Totally differentiate (A2.8) with respect to a: 3 x 2 x a = 9bPy3 l _ a (A2.10) Substitute for L q using (A2.6): v - 3 a b Py3 (A2.ll) a " 2 2 (1 -a ) X Expression (A2.ll) is simplified by substituting for y from (4.3.46) and for x from (4.3.6). 2 2 (1-a) y 3P - = 3 a bP ( l - a ) y a a 2~2 2 Then x = a. b f which is the first-order condition (4.3.17) a (1-a) v ' To derive x^, totally differentiate (A2.10) with respect to a. 2 3 x 2 x + 6 x x = 9 b Py3 L aa a aa 192 3 b Py3 L - 2 x x 2 ... ... or X = i - , - 2 2 2 - ( A 2 J 2 ) aa 2 X Expression (A2.12) is simplified by substituting for laa from (A2.7) and x from (4.3.6). 3bPy3(1 + g) - 2 y x 2 _ ( l - a ) x aa 2 y which is further simplified by substituting for x a from (4.3.17) and y from (4.3.46). 2 3bP(1 + a) . (1-g) y2 a2 - 2y ]~g b a2 ~j 3 3P L(l-a)J which is further simplified by substituting for X Q from (4.3.17) and y from (4.3.46). 193 or x a a b ( l + a) y g - 2 ( a b a ) 2 ( l - « ) y (A2.13) The expressions for x a a and x a are substituted into ( A 2 . 1 ) H = ( l - a ) a a v ' P M l + a) y a 2 - 2 ( a b g 2 ) 2~[ 2 a b g 2 _ 2 ( 1 - a ) y T i ^ a T b ( l + a) y g 2 - 2 ( a b g 2 ) 2 T N a T - 2 a b g 2 - b a 2 b ( l + a ) y g 2 - 2 ( a b g 2 ) - 2 a b g 2 y - ( 1 - a ) b g 2 y ( 1 - a ) y b y g 2 ( 1 + a - 1 + a) - 2 a b g 2 ( y + a b a 2 ) n ^ a T i 2 a b y g 2 - 2 a b g 2 ( y + ab g 2 ) ( 1 - a ) y 2 q ) <0 ( 1 - a ) y ( A 2 . 1 4 ) Q.E.D. II. Proof that H < 0 It was shown in equation (4.3.41) is Chapter Four that 194 1/3 x = { 9 b P [ T2_+ ln (1-a)]} Then x = 0. yy The expressions for x y y and C y y from (A2.4) are substituted into (A2.2): H y y « (1-) (0) -1£ < 0 (A2.15) ya Q.E.D. 2 III. Proof that H H - H > 0 a a yy o& 2 H a a H y y " H a y c a n b e rewritten: H a a Hyy " X a y " xy } u s i n 9 <A2'3) To derive x , totally differentiate (A2.8) with respect to y: 3 x2 xy = 27bPy2L 9 b Py2 L or x = which differs from (4.3.41) because the ( A2.16) y - 2 2 x(a,y) term has not been substituted This expression is simplified by substituting for L from (A2.9) and for x from (4.3.6). - = 9b Py2 . y 2 2 y 3b a (1-a) 195 2 3Py or x = — -= 1 which is the first-order condition (4.3.18) y ( l - a ) y a 2 To derive x , totally differentiate (A2.10) with respect to y. 3 x2 x + 6 x x x = 27bPy2 L ay a y J a , - 2 ; (A2 . U ) ay 2 x Expression (A2.17) is simplified by substituting for L q from (A2.6), x from (4.3.6), x from (4.3.17), and x from (A2.16). a y r 2 - 2 y a b a 9bPy a - (1-a) i i l - a ) J L n -a )yq . Ill ay 9 a b P y - 6 a b P y 2 2 (1-a) y or x ay 3 a b P y 2~T (1-a) v (A2.18) 196 Substitute (4.3.18) and (A2.18) into (A2.3): ? 2 u = (l-a)3abP/ - 3 Py ay 2 2 2 (1-a) y (1-a) pa = 3 a b P.y2 a 2 - 3 Py2 u 2 2 (1-a) y a = 3Py2 { a b g 2 I \) (A2.19) (1-a) y a After substitution for y using (4.3.46), (A2.19) becomes: u _ -^nfCl-a) V 2 g 2 1 2/3 faba 2 - y 1 ay " ^ 1 3P J i 2 2' (1 - a) y a ( l - a ) y 2 a 2 4/3 a b a 2 - y 2 and H a y = (3P)'{ } { ^-T^ 3P (1-a) y a 2 o p 2/3 9 2 or H a y ={ \ 2 } (ab a^ - y) (A.2.20) (1 - a) y a Using (A2.14) and (A2.15) u u -2(abo 2) 2 -6Py H a a Hyy ~ 2 ~ (1-a) y ya 197 A f t e r s u b s t i t u t i o n f o r y f rom (4.3.46), 2 1 / 3 H H = {12 ( a b q 9 ) 2 p} {^'a ) 2 a } aa yy 1 2 2J 1 ' (1-a) y a 3P |3P» 4(aba)2j ^(1-a) y 2 g 2 j 1 / 3 (1-a) y 2 o2 3P o r 2,2 3 P 2 / 3 Haa Hyy = « < * > < ? ) { 2"2> ( A 2 ' 2 1> (1-a) y a Haa Hyy" Hay 2 i s s i m P 1 i f i e d u s i n 9 (A.21) and (A2.20) H H w - H 2 aa ay ay 2/3 2/3 = 4 (aba 2) 2{—3P } -{-JZ } [ a b a 2 - y] 2 2 2 2 2 ( l - a ) y a (1-a) y a 2/3 = { 3 P g 2 } {4(aba)2 - [aba2 - y]2} (1-a) y a The f i r s t t e r m i s > 0. T h e r e f o r e t h e t h i r d s e c o n d - o r d e r c o n d i t i o n i s s a t i s f i e d i f 4(aba2)2 - [aba2 - y] 2 > 0 198 Expansion of the expression results in: 4(aba 2) 2 - (abo 2) 2 + 2 aba 2 p - p 2 • 3(aba 2) 2 + 2aba2 p - p 2 > 0 i f 3(aba 2) 2 + 2aba2 p > p 2 (A2.22) It is known that a > — ^ from (4.3.45) since (1-a) In (1-a) < 0. 3ba Then 3aba2 > p (A2.23) It follows from (A2.23) that 9(oba 2) 2 > p 2 2 or 3(aba 2) 2 > (A2.24) It follows from (A2.23) that 2 2 2 . 3 aba p > 2 p or 2 a ba 2 p > 2 p 2 (A2.25) 3 Adding together (A2.24) and (A2.25): 2 2 2 2 + 2 2 3 ( ab a 2) + 2 ab a 2 p > + -2-^ — = p 2 Q.E.D. 199 APPENDIX 3 Second-Order Conditions to the Moral Hazard Problem A sufficient condition for a maximization of the objective function is that the Hessian matrix of second-order partial deri-vatives is negative definite: Since the choice of 3 was elimi-niated from the problem, the Hessian matrix is composed of the second-order partial derivatives of the objective function with respect to a and F. The Hessian matrix = Tfl Hp a a a r ' a F FF is negative definite i f H a a < 0 (2) H F F < o (3) H H c c - H rr > 0 aa FF aF Values for the second-order partial derivatives are derived from (5.3.12) and (5.3.14): H = 2 F + ( a - l ) F - ba a a a a a e H F F = T"(F) H a F = - 1 (A3.1) (A3.2) (A3.3) 200 I. Proof that H < 0 aa H < 0 follows from (A3.1) aa F < 0 from (5.3.15) a (a-l) < 0 F > 0 from (5.3.16) aa 2 b a > 0 e II. Proof that Hri- , n T" (F) < 0 by assumption Q.E.D. 2 III. Proof that H Hzc - H c > 0 aa FF aF Expressions (A3.1), (A3.2) and (A3.3) are substituted. To be shown: 2 [ 2F a + (a-l)F a a - b a £ ] [T" (F)] - 1 > 0 (A3.4) The following substitutions will be made to simplify (A3.4): F Q = yn- < 0 from (5.3.15) T . . . F = 5- F from (5.3.16) aa c a (T") 201 T"' 2 using (5.13.15) (T") Then A3.4 becomes: T" / i \ T''' - (a-') T - bo T" -1 L e (T") 1 - (a-l) (T") bo T" > 0 e Since (a-l) < 0 T'" > 0 T" < 0 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0096410/manifest

Comment

Related Items