Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A two-period model of signaling with ownership retention Courteau, Lucie 1992

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

Item Metadata

Download

Media
831-ubc_1992_fall_courteau_lucie.pdf [ 4.91MB ]
Metadata
JSON: 831-1.0086536.json
JSON-LD: 831-1.0086536-ld.json
RDF/XML (Pretty): 831-1.0086536-rdf.xml
RDF/JSON: 831-1.0086536-rdf.json
Turtle: 831-1.0086536-turtle.txt
N-Triples: 831-1.0086536-rdf-ntriples.txt
Original Record: 831-1.0086536-source.json
Full Text
831-1.0086536-fulltext.txt
Citation
831-1.0086536.ris

Full Text

A T W O - P E R I O D M O D E L O F S I G N A L I N G W I T H O W N E R S H I P R E T E N T I O N B y Lucie Courteau B.Sc .adm. , Université Lava l , 1980 L ie . Sc.compt., Université L a v a l , 1981 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L 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 T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S C O M M E R C E We accept this thesis as confçrming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A October 1992 © Lucie Courteau , 1992 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of (2&^ fy^iS^CC^ The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract This dissertation is an extension of Le land and Pyle 's (1977) signaling model . It introduces the length of the retention period to which the entrepreneur commits i n the prospectus as a signal of f i rm value, i n addit ion to the retention level. The analysis uses concepts of game theory to examine a two-period model where an entre-preneur seeks to issue shares on the market and invest i n a productive project that generates outcomes which are publ ic ly announced at the end of the next two periods. The entrepre-neur can retain some of her firm's shares and trade them later on the secondary market, after information has been released about the outcomes. The length of the retention period is found to be a signaling mechanism that complements ownership retention. Depending on the information structure of the f i r m , a longer retention period may reduce or increase the retention level necessary for separation. The model also shows that there are realistic situations i n which entrepreneurs prefer to retain a port ion of their f irm's shares for longer than the m i n i m u m retention period imposed by regulations, and others i n which she prefers the shortest period possible. The opt imal combination of under-diversification and commitment is shown to depend on the information structure and the probabi l i ty d istr ibut ion of outcomes of the f i rm. The empir ical implications of the model are tested on the set of firms that made an in i t ia l publ ic offering i n 1981. A l t h o u g h the results of the tests are generally consistent wi th the predictions of the model , they are not strong enough to reject the nu l l hypotheses. Table of Contents Abstract ii List of Tables v i List of Figures vi i Acknowledgement vii i 1 Introduction 1 2 Review of the Literature 4 2.1 Signaling 4 2.1.1 Ownership Retention 4 2.1.2 Underpr ic ing 7 2.1.3 Commitment 8 2.1.4 E q u i l i b r i u m 11 2.2 E m p i r i c a l Studies 14 2.2.1 E m p i r i c a l Investigations of Signal ing Models 14 2.2.2 Marlcet React ion to Earnings Announcements 16 3 T h e M o d e l 20 3.1 Description of the M o d e l 21 3.1.1 Timel ine 22 3.1.2 Assumptions 23 3.2 Two-Per iod Mandatory Retention 25 3.3 One-Per iod M a n d a t o r y Retention 27 3.4 O p t i m a l Strategies 29 3.4.1 Comparison of Mandatory Hold ing Periods 29 3.4.2 Choice of Strategy 31 3.5 Random Revelation of F i r m Value after One Period 33 3.5.1 Two-Per iod Mandatory Retention 33 3.5.2 One-Period Mandatory Retention 35 3.6 Special Cases 36 3.6.1 Information Structure 37 3.6.2 Outcome Structure 38 3.7 E m p i r i c a l Implications 44 3.8 Conclusion 45 4 E m p i r i c a l Analysis 47 4.1 Sample Description 47 4.2 Valuat ion M o d e l 53 4.3 Association between Ownership Retention Level and Length 55 4.4 Associat ion between F i r m Value and Length of Retention Per iod 61 4.4.1 Scaled F i r m Values 63 4.4.2 Matched Samples 67 4.5 Associat ion between Time-Series Behaviour of Earnings and Ownership Reten-t ion Per iod 69 4.5.1 Earnings Response Coefficients 70 4.5.2 Al ternat ive React ion Measures 72 4.6 Conclusion 77 A List of Variables 85 B Proofs 87 B . l Proposi t ion 1 87 B.2 Propos i t ion 2 93 B.3 Proposi t ion 3 B.4 Proposi t ion 4 100 B.5 Proposi t ion 5 B.6 Propos i t ion 6 B.7 Propos i t ion 7 106 B.8 Proposi t ion 8 106 B.9 Propos i t ion 9 10^ B.IO CoroUary 1 B . l l Coro l lary 2 109 B.12 CoroUary 3 H O B.13 CoroUary 4 H O C List of Sample F i r m s m List of Tables 4.1 Issue Dates 48 4.2 Dates of F irs t Earnings Announcement 50 4.3 Dates of F irs t Yearend Earnings Announcement 51 4.4 Descriptive Statistics 52 4.5 Regression of F i r m Value on Retention 56 4.6 Retention Levels for Long and Short M a n d a t o r y Retention Periods 57 4.7 Test of Retention Level and M a n d a t o r y Retention Length 59 4.8 Choice of Retention Per iod 61 4.9 Test of Scaled F i r m Value and Voluntary Retention Length 63 4.10 Test of Scaled F i r m Value and M i n i m u m vs. Long Retention Period 65 4.11 Test of Scaled F i r m Value and Short vs. Long Retention Per iod 66 4.12 Test of Scaled F i r m Value and Retention Length i n Matched Samples 68 4.13 Test of Pr i ce React ion to F i r s t Earnings Announcements and Voluntary Reten-t ion Length 74 4.14 Test of Pr i ce React ion to F irs t A n n u a l Earnings Announcement and Voluntary Retention Length 75 4.15 Test of Pr i ce React ion to F i r s t Earnings Announcements and Retention Length . 76 4.16 Test of Pr ice React ion to F irs t A n n u a l Earnings Announcement and Retention Length 78 C . l L i s t of Sample firms 112 List of Figures Timel ine Acknowledgement I wish to thank Jerry Fe l tham for his patience and his continued support. I have greatly benefited from his insight and his t imely comments. Wi thout h i m , this project would not have been completed. I am also deeply grateful to Jack Hughes for his continued interest and his opt imism that kept me going. I owe an enormous debt of gratitude to my fami ly : my parents who encouraged and sup-ported me al l these years; my husband Jean-Miche l who shared my tr iumphs and my agonies; and my chi ldren, Isabelle and Jean-Christophe, who have been involved i n this project for the greater part of their lives. T h i s dissertation is dedicated to Jean -Miche l , Isabelle, and Jean-Christophe. C h a p t e r 1 Introduction The classical theory of efficient pr ic ing of securities assumes that capi ta l markets are perfect; al l agents are price-takers w i t h perfect and homogeneous information. W h i l e this simplifying assumption was very useful to model and understand the basic funct ioning of financial markets, i t is necessary to abandon it i n order to examine some phenomena that are inconsistent wi th the theory. Recent research has investigated the relative influence inst i tut ional investors may have on market prices of securities, as wel l as different forms of information asymmetry between the various market partic ipants . Th i s study concentrates on information asymmetry between security issuers and other market partic ipants. T h e dissemination of f inancial information is one of the most important prerequisites for efficient operation of capital markets. In order to make investment, product ion , and allocation decisions, investors and entrepreneurs need reliable information about the firms whose securities are available on the market . T h e m a i n source of firm-specific information is the firm's top management. It is important to examine how this information can be communicated to other market partic ipants. The problem is most significant when a firm makes a first public issue since, at this t ime, the asymmetry is at its highest point i n the firm's life. Various communication mechanisms have been studied i n connection wi th i n i t i a l public offerings. T h i s study concentrates on signaling based on the percentage of ownership retained by the current shareholders after the issue, following Le land and Py le (1977). Often associated wi th ownership retention is a commitment by the owner(s) of the issuing firm to a certain holding period for the shares they keep. Security regulations even contain provisions requiring a m i n i m u m retention period after the issue, for current shareholders of a firm. Whi le other researchers have ignored this commitment , the model here attempts to explain it in the context of information communicat ion. The analysis is done in the context of an investment game similar to one used by Datar , Fe l tham, and Hughes (1991). The owner of a private f i rm (hereafter called the entrepreneur) possesses private information about the value of her firm and plays first by offering a contract to a group of uninformed players, the prospective investors. The contract is contained in a prospectus that the entrepreneur distributes to investors and which contains information about the percentage of her firm's shares she wants to sell , the issue price and the length of time she intends to retain her remaining shares i n the firm. The investors then play by either accepting or rejecting the contract offered to them. Nature gets the last move and randomly chooses the ex post value of the firm, which is divided between the entrepreneur and the investors, each according to his share of the firm's equity. The length of the per iod dur ing which the entrepreneur cannot trade her shares on the secondary market is found to be a signaling mechanism that complements ownership retention. For some firms, an increase i n the holding period allows a lower level of under-diversification, whereas for others, i t requires a higher retention level. For yet others, the entrepreneur cannot communicate her private information w i t h the m i n i m u m retention period permitted by regu-lations and only a longer retention period allows her to be distinguished from entrepreneurs wi th lower-quality firms. The model also shows that there are realistic situations in which entrepreneurs prefer to retain a port ion of their firm's shares for longer than the m i n i m u m re-tention period imposed by regulations, and others i n which the entrepreneur prefers the shortest period possible. The opt imal combination of under-diversif ication and commitment is shown to depend on the firm's information structure and the probabi l i ty d istr ibut ion of its outcomes. The model 's empir ical implicat ions are tested on a set of I P O firms. A l though the results of the tests are not strong enough to reject the nu l l hypotheses wi th any standard degree of confidence, most of the tests show differences i n retention levels and in firm values which are consistent w i t h the predictions of the model . The scarcity of available data typical ly associated Chapter 1. Introduction 3 with new firms and the refinement of the model's implications are the main reasons for this lack of support. C h a p t e r 2 Review of the Literature 2.1 Signaling 2.1.1 Ownership Retention The problem examined here is an extension of that investigated by Le land and Py le (1977) in their seminal article. A risk-averse entrepreneur is the sole owner of a private f irm and wants to share its risk wi th outside investors. Th i s can be triggered, as i n Le land and Py le , by a new investment project the f irm is facing which would significantly increase the firm's risk. Whatever the reason for her decision, the entrepreneur can shed some of the firm-specific risk she is bearing and get a better balanced investment portfolio by making an in i t ia l public offering of her firm's shares. She may, however, have difficulty convincing investors, who know very l i t t le about the firm, to pay the " t rue " value of its shares.^ A l t h o u g h she has superior knowledge about her firm's future performance, she faces a credibi l i ty problem i n the market since a l l entrepreneurs, whatever the quality of their firm, have the incentive to boast about its high value. Le land and P y l e (1977) suggest that she can send a signal to the market about the value of her firm by retaining part of its equity (and thus of its r isk) . T h i s signal is costly for her since it prevents her from holding a completely diversified portfolio and exposes her to firm-specific risk. In order to be an effective communicat ion device, the signal must have a lower marginal cost for entrepreneurs wi th high-quality firms than for those wi th low-qual i ty firms.^ For the same level of r isk, the owner of a low-quality firm stands more chance of loss than that of a ' T h e true value of a firm is here defined as the expected value of the firm's future cash flows. ^Spence (1973) had noted this necessary condition for signal efficiency. better firm and the difference is sufficient to discourage mimiclcing by the former. Le land and Py le model the entrepreneur's risk-aversion by a negative exponential von Neumann-Morgenstern ut i l i ty function over the l iquidat ion value of her firm. Th is final value is a normally distributed random variable wi th mean n and variance CT^. A l though the en-trepreneur does not know what the final value of her firm w i l l be, she knows the mean of its d istr ibut ion and that is the information she is t ry ing to communicate to prospective investors. The variance cr"^ is assumed to be common knowledge. This model yields a separating equi l ibr ium where the owners of firms of each possible value opt imal ly retain a specific port ion of their firm's shares and investors correctly infer firm value from each firm's signal. The level of ownership retention is increasing in firm quality (i.e., the mean fi) making imi ta t i on too costly for low-quality firms, and thus permit t ing efficient communicat ion. Th i s basic model has been extended to examine other phenomena observed around in i t ia l public offerings. Hughes (1986) assumes the entrepreneur has private information about both the mean and the variance of her firm's l iquidat ing d iv idend. Th is creates a demand for a two-dimensional signal because a single signal cannot efficiently communicate information about both mean and variance. It would lead to a part ia l ly pooling equi l ibr ium where some firms wi th different values would send the same signal to investors who could not differentiate between them. In addit ion to ownership retention, the entrepreneur uses direct disclosure of her private information. In order for this to allow efficient communicat ion, there must be a heavy penalty imposed for outcomes fa l l ing too short of the expected value (which courts might interpret as indicat ing untruthful disclosure). T h e entrepreneur may share the risk of this penalty w i t h an investment banker by paying a fixed underwri t ing fee. Hughes finds a separating equi l ibr ium i n which firms use a combination of retained ownership and direct disclosure as signaling devices when considering a first equity issue. Datar , Fe l tham, and Hughes (1991) also use a setting s imilar to Le land and Pyle 's to examine how audited financial reports contained in the prospectus can be used i n conjunction with ownership retention to communicate the entrepreneur's private information about the expected f irm value (its type) to the market. In their model the entrepreneur first chooses the auditor for the financial statements to be included i n the prospectus. The audited report issued conveys incomplete information about firm value. Investors can infer a range of types that could have produced the audited report appearing i n the prospectus. The quality of the auditor determines the extent of this range of possible types. The entrepreneur's main interest in the audit is the e l iminat ion of some of the lowest types from the set investors consider possible for her firm. The audited report is not sufficient however for fully revealing firm type. Ownership retention is then used to el iminate a l l remaining lower types and allow investors to correctly estimate firm value. The authors show that there exists a unique stable separating equi l ibr ium where each type of entrepreneur first separates from some of the other types by the quality of the auditor she hires and the resulting audited report , and then from the remaining types by retaining part of her firm's equity. In this equi l ibr ium, firms wi th high value or high risk choose high-quality auditors.^ In a model w i t h two firm types and two possible outcomes, Conroy and Hughes (1989) consider the case where the level of ownership retention is unobservable. Depending on the proport ion of good firms i n the market , on the probabi l i ty that a good firm gets a high outcome, and on the entrepreneur's ut i l i ty funct ion, one of two equi l ibr ia obtains i f the retention level is unobservable. In the revealing equ i l ibr ium, the entrepreneur w i t h a good firm retains ful l ownership while the only shares offered on the market are those of bad firms. The non-revealing equi l ibr ium is one i n which the good entrepreneur retains some but not a l l of her firm's shares and sells the rest for less than their ful l value, and the bad types sell short at the same price. Conroy and Hughes show that the good entrepreneur is better off when there exist regulations ^Titman and Trueman (1986) also investigate the choice of auditor around initial offerings and reach a conclusion contrary to that of Datar, Feltham, and Hughes; high-risk firms choose low-quality auditors. This conflicting conclusion arises from several key differences in the two models. T i t m a n and Trueman take ownership retention as exogenously determined and assume that the entrepreneur can completely signal her type through her choice of audit quality. The audited report provides additional information about the final value but is not part of the signal per se. requiring disclosure of (and commitment to) retention levels by current shareholders in in i t ia l public offerings. It is not clear i f the bad entrepreneur benefits from these regulations, however. 2.1.2 Underpric ing Underpr ic ing of in i t i a l public offerings has been a puzzle to researchers ever since it was doc-umented by Ibbotson (1975). Baron (1982) tries to explain it as a consequence of information asymmetry between the underwriter of the issue and the entrepreneur who knows l itt le about market conditions.** Rock (1986) models two groups of prospective investors, one better informed than the other about the future performance of new firms. Informed investors subscribe only to underpriced issues, crowding out the less informed because these issues are oversubscribed and must be allocated to a l l subscribers. O n the other hand , only uninformed investors subscribe to over-priced issues so no allocation is necessary. The latter group of investors end up wi th unbalanced portfolios where overpriced issues constitute a larger port ion of al l new issues than would be op t imal . Underpr ic ing of i n i t i a l public offerings i n general is an equi l ibr ium solution to keep uninformed investors i n the market of i n i t i a l offerings. Welch (1989), A l l e n and Faulhaber (1989), and N a n d a (1988) present models of information asymmetry between entrepreneurs and investors where underpric ing constitutes an efficient signaling device. R i sk aversion plays no role i n these models. The cost of signaling is based on the fact that the firm w i l l have to raise more capital at a later date and that more information w i l l then be available to investors. Gr inb la t t and Hwang's (1989) model presents a risk averse entrepreneur wi th two-dimensional private information (mean and variance of future cash flow distr ibution) who uses ownership retention and underpric ing of the issue as signaling devices. Theirs is a three-date model i n which there is a possibil ity that the firm's type may be exogenously revealed at the end of the *MuscareUa and Vetsuypens (1989) find evidence against Baron's result by examining underpricing of initial public offerings of investment banking firms acting as their own underwriters. Underpricing is just as important in these issues as in other issues despite the lack of information asymmetry. first period. The entrepreneur is assumed to sell al l her remaining shares at that point and ex-ternal investors get the whole l iquidat ing div idend at the end of the second period. Two signals are necessary, as is the case i n Hughes (1986), to communicate two-dimensional information efficiently. It is too costly for low-quality firms to underprice and under-diversify at the in i t ia l offering because of the possibil ity that their type w i l l be revealed before the second round of trading. Th i s guarantees credible signaling. 2.1.3 Commitment Most signaling models assume either a one-period model or a model i n which the entrepreneur sells a l l her remaining shares at the end of the first period. Gale and Stigl itz (1989) show, however, that i f there is a second round of t rading between the entrepreneur and investors, Le-land and Pyle 's signaling mechanism can break down because, i n the second round, low-quality entrepreneurs can shed the extra risk they assume i n the first. Low-qual i ty equity is offered at high-quality price w i t h the high-qual ity level of ownership retention but the entrepreneur then dumps retained shares on the market (maybe even the next day) , thus reducing the cost of under-diversif ication. Conroy and Hughes (1989) also show that when the level of ownership actually retained by the entrepreneur is unobservable, the only alternatives for a high-quality firm are ful l retention or underpricing. G r i m b l a t t and Hwang (1989) avoid this result by assuming that there is a positive probabil i ty that firm type w i l l be revealed before the second round of trading. Welch (1989) makes a s imi lar assumption while A l l e n and Faulhaber (1989) assume that the firm pays a dividend that influences investors' beliefs about firm type before the second round of trading. The model developed here presents a risk averse entrepreneur using ownership retention to signal her firm's value, but i t takes into account security regulations aimed at restraining the type of behaviour predicted by Gale and St ig l i tz . The Securities A c t of 1933 contains detailed regulations regarding a l l public share offerings. It requires, among otiier t i l ings, tl iat issuing firms file a prospectus containing detailed infor-mation about their history, their past performance, and their future prospects. This prospectus must be made available to a l l prospective investors a few months before the actual share issue. The A c t also includes a provision called Rule 144 which requires a m i n i m u m holding period of two years on a l l shares acquired through private placement before these shares can be sold on the secondary market. Th is Rule applies to al l companies whose shares are available on the secondary market but it is a constraint mainly for shareholders involved i n an in i t ia l public offering. They have acquired a l l their shares i n private placements and many have done it wi th in the two years preceding the offering. For these firms the Ru le in effect allows current shareholders to sell their shares as part of the offering but not i n the secondary market unless they have held them for at least two years. In addit ion to Rule 144, some State regulations, called Blue Sky laws, impose holding peri -ods as long as five years on owners of certain firms deemed part icular ly risky. Such laws were enacted to prevent unscrupulous entrepreneurs from offering "pieces of blue sky" to unsuspect-ing investors. Here is how one prospectus presents the effects of such laws on the issue to be made. . . . the Directors, officers and managerial employees of Jackpot and other stock-holders who purchased shares of Jackpot C o m m o n Stock prior to this offering have agreed to place their Jackpot C o m m o n Stock [... ] i n escrow at the Val ley Bank of Nevada after completion of this oflfering i n order to satisfy the " B l u e S k y " laws of various jurisdict ions. The escrow has no terminat ion date but the Escrow Securities may be released from escrow based upon an audit made by an independent public accountant, that Jackpot has had net income for two consecutive years [...] of 6% a year on the value of a l l C o m m o n Stock that w i l l be outstanding after the offering is completed [... ] and that the [... ] publ ic accountant's report w i l l not contain any qualification w i t h respect to Jackpot 's abi l i ty to continue as a going concern.^ ^From the June 1981 Prospectus of Jackpot Enterprises Inc. Even after the regulatory holding period lapses, there is a restriction on the number of shares the shareholder can trade i n each quarter. Rule 144 further prohibits al l trades for al l current shareholders i n the ninety days following the issue. These regulations do not guarantee that current shareholders w i l l retain their shares unt i l the end of the holding per iod , however. The Ru le allows current shareholders to sell their remaining shares as part of future public offerings by the f i rm. The firm must then go through the whole registration process and issue another prospectus containing audited f inancial statements as well as hire an underwriter for the new issue. Th is process is very costly for the firm but Welch (1989) finds that one th i rd of firms making an i n i t i a l public offering between 1977 and 1982 had made a second offering by 1986. Moreover, the proceeds from these seasoned offerings were on average three times those of the first offerings. F i r m s whose shareholders are not subject to a regulatory holding period beyond the statu-tory ninety-day m i n i m u m , because they have acquired their shares more than two years before the issue, sometimes include a commitment i n their prospectus whereby the pr inc ipal share-holders voluntari ly impose a holding period on themselves. B u l b - M i s e r Corporat ion of A m e r i c a describe such a commitment i n its December 1981 prospectus. . . . the three stockholders of the Company have agreed not to sell their shares for at least three years from the date of this Prospectus, without the Underwriter 's consent, which restrict ion would terminate in the event the Company realizes pre-tax earnings from operations of at least $500,000 i n either of the first two fiscal years ending after the date of this Prospectus. Such pre-tax amount was a negotiated amount and should not be construed as an estimate of any future earnings. Such a promise i n itself may be considered as empty by investors since the entrepreneur may have the intention of coming to the market only once to try and make a quick profit. In order to make the commitment more credible, the underwriter of the issue is made answerable for the keeping of the promise. Underwriters are i n the market on a long term basis. They have a reputation to uphold so i t is i n their interest to restrict trades by insiders that would make investors wary of the future offerings they wi l l underwrite. The i r guarantee thus makes volun-tary commitment credible just as the legal system enforcing S E C regulations makes regulatory commitment credible. In the rare cases where the entrepreneur wants to shorten the voluntary holding period, the underwriter 's decision to allow the sale is based on the performance of the stock on the secondary market. Rule 144 also requires that quarterly financial statements be filed wi th the S E C ninety days after completion of the issue. The law thus requires that an earnings announcement be made before the second round of t rad ing between the entrepreneur and investors. Very few authors acknowledge the existence of such regulations. Gale and Stigl itz (1989) consider them but conclude that the commitments described above are not efficient in the context of their model . Fe l tham, Hughes, and Simunic (1991) assume a holding period of two years for a l l f irms. Conroy and Hughes (1989) recognize the benefits of these regulations when comparing their results w i th and without disclosure and commitment . This study seeks to integrate commitments as part of a signaling strategy the entrepreneur chooses i n an effort to communicate her private information to prospective investors and to issue her firm's shares at their true value. It also integrates an information release before the second round of trading between entrepreneur and investors. 2.1.4 E q u i l i b r i u m One of the difficult issues i n signaling models is the type of equi l ibr ium that emerges. A separating equi l ibr ium i n which each type of firm sends a different signal to the market occurs when investors, upon observing the signal sent by a firm, can unambiguously infer its type and make appropriate decisions. Not a l l s ignaling games lead to separation, however. In certain circumstances, a separating equi l ibr ium does not exist and i n others the model leads to or includes a pool ing equi l ibr ium, where a group of types (or aU of them) send the same signal. Investors receiving a signal know which group it comes from but not the type of the firm that sent i t . They are unwi l l ing to pay more than the average value of firms in the group for the shares offered to them. M a n y signaling models have pooling equil ibria.^ The difficulty wi th pool ing is that some firms (the best types in a pool) have the incentive to find a better strategy to convey their private information. Theirs are the underpriced shares, so they are l ikely to defect from the equi l ibr ium strategy of the pool and offer contracts that investors wi l l accept and that w i l l make them at least marginal ly better off. For this reason, this study restricts its analysis to separating equi l ibr ia . The investment game considered here is a sequential game in which the informed player (the entrepreneur) moves first by offering some of her firm's shares for a certain price. Investors, who are uninformed w i t h respect to this firm's value, then get to move by either accepting or rejecting the entrepreneur's offer. The equif ibrium concept most appropriate for this type of game is a (Baysian) Nash equi l ibr ium where none of the players has incentive to change his or her strategy, given the other players' strategies. Games i n which the informed player moves first have been shown to always lead to many pure-strategy Nash equilibria. ' ' ' Some of these are implausible , however, based as they are on beliefs by players that are not credible under some definitions. Hence, the equi l ibr ium concept is often refined to eliminate implausible solutions and retain those that make most intui t ive sense. M a n y such refinements have been suggested i n the l i terature. A m o n g the first was Kreps and Wi lson 's (1982) sequential equif ibrium for games where players do not move simultaneously. A Nash equif ibrium to a game is a sequential equif ibrium i f there exists a set of befiefs such that each player would keep his equi l ibr ium strategy even i f he is actually faced wi th off-equi l ibr ium moves by other players. The requirement is that each player bases his or her strategy on some befiefs about off-equifibrium moves by other players. Hence, for the equi l ibr ium to be sequentially rat ional , the investor who is offered a contract not anticipated in equi l ibr ium strategies should have befiefs about who might have offered this contract such that he would ^Welch (1989) and Allen and Faulhaber (1989) get pooling equilibria in certadn situations. ' ' in contrast, insurance games which have been investigated by Rothschild and Stiglitz (1976), Wilson (1977), and Riley (1979), among others, do not always lead to a separating Nash equilibrium. The existence of such an equilibrium depends on the proportion of "bad risk" policy-holders in the market. not change his strategy. Some sequential equi l ibr ia are supported by implausible beliefs. Take for example a pooling equi l ibr ium i n an investment game i n which a l l types offer the same contract, and each off-equi l ibr ium contract is rejected on the basis that investors believe that it is offered by the "worst" type. Th is belief is clearly implausible for contracts that are only preferred to the pool ing contract by types for which the investors would not lose money. Hence, while the pool ing equi l ibr ium is a sequential equ i l ibr ium, it is not plausible. A further refinement of the equi l ibr ium concept was proposed by C h o and Kreps (1987) w i t h what they call the Intuitive Cr i t e r i on . It is an application to signaling models of the concept of stabil ity developed by K o h l b e r g and Mertens (1986) for generic sequential games. The Cr i ter ion requires that a player faced w i t h an off-equilibrium move retains his equi l ibr ium strategy only i f it is rat ional to do so, given all types that would have an incentive to defect from their equi l ibr ium strategy to the observed move. In the investment game, the equi l ibr ium strategy for investors could be to accept a l l equi l ibr ium contracts plus those for which the price is less than the average value of a l l firms whose shareholders would be made better off by a part icular off-equilibrium contract. The entrepreneur's strategy would be to retain a portion of her firm's shares that would be different for each possible type and sell the rest at its true value. Th i s equi l ibr ium would satisfy the Intuitive Cr i ter ion because the investor facing an off-equi l ibr ium offer would consider a l l types that had an incentive to make such an offer and would accept i t i f he expected to make money on the average f irm of that group. It would not be stable i n the Koh lberg and Mertens sense i f lower types had more incentive to offer that part icular contract, however. Investors would then lose money systematically, on average. The Intuitive Cr i ter ion eliminates many implausible equi l ibr ia in signaling games and constitutes a necessary condition for stabi l i ty as defined by Koh lberg and Mertens (1986). However, there also may exist some implausible equi l ibr ia that satisfy the intuit ive cr iterion. Th is is because it does not consider which types are more l ikely to gain from defection. Banks and Sobel (1987) and C h o and Kreps (1987) develop necessary and sufficient con-ditions for Kohlberg and Mertens ' equi l ibr ium stabil ity in signaling games. These conditions have been applied by Datar , Fe l tham, and Hughes (1991) to an investment game similar to the one described here. They require that the player offered an off-equilibrium contract consider what types are most l ikely to have made such an offer before deciding whether to accept it or not. A n equi l ibr ium is stable if investors reject off-equilibrium contracts only when they expect to lose money by accepting i t from the type that has the most incentive (and is the most l ikely) to offer i t . 2.2 E m p i r i c a l Studies The second part of this dissertation proposes to test the model 's empirical implications on data from a set of firms making an i n i t i a l publ ic offering. Some of these implications are similar to what usually arises i n signaling models, but they are enriched by the inclusion of commitments in the signaling strategies entrepreneurs can select. The level of ownership retention and the length of the retention period are considered as two elements of a signaling strategy chosen by the entrepreneur. Different types of firms are shown to present different strategies, based on their risk and information characteristics. The tradit ional relationship between level of retention and firm value, for example, can be investigated for different groups of firms that have similar risk and information characteristics. Because i t includes information release, the model also yields results l ink ing market reactions to this release and signaling strategies. Th i s l ink is investigated empirical ly i n the context of the first earnings announcements after the firm's first share issue. 2.2.1 E m p i r i c a l Investigations of Signaling Models Leland and Pyle ' s results were first tested empir ical ly by Downes and Heinkel (1982) who found a significant positive relation between the level of under-diversification and the value of the firm. R i t t e r (1984) contests this result though, arguing there is misspecification in the previous statist ical model . W i t h a different model , he compares three hypotheses l ink ing ownership retention and firm value and finds support only for his agency hypothesis by which a lower level of retention indicates a lower motivation for the entrepreneur to exert effort in the management of her firm, leading to a lower value of future cash flows as perceived by investors. K r i n s k y and Rotenberg (1989) test a model similar to Le land and Pyle ' s w i th the quality of underwriter for the issue is an addit ional signal. Hughes (1989) suspects that a problem common to a l l three studies is the handling of heteroscedasticity. Signal ing models usually assume that a l l firms have the same cash flow variance. Heteroscedasticity i n the data can bias the standard error of estimates, distort ing standard significance tests. He decomposes firm-specific risk into two components, one that is constant across firms and one that varies w i t h firm size. W i t h this he finds significant support for Le land and Pyle ' s result w i th two different I P O data sets and various model specifications. C larkson et al. (1991) test Le land and Pyle 's result using Canadian data . Reviewing previous testing performed on I P O data , they suggest what seems to them the best measures of the basic variables used i n such tests and again find support for ownership retention as a signal. Fe l tham, Hughes and Simunic (1991) present empir ical evidence on Datar , Fe l tham, and Hughes ' (1991) signaling model inc luding audit quality and audited reports as communication devices, i n addit ion to ownership retention. A u d i t e d reports are measured as the book value of equity after the issue and audit quality is represented by a dichotomous variable: H igh for the (then) " B i g E i g h t " audit firms and Low for the smallest firms.* The tests performed are s imilar to those of previous studies but the sample is divided i n two subsamples based on auditor qual ity and matched on firm size. The coefficient estimates are then compared across the subsamples. Since firm-specific risk is related to firm size, heteroscedasticity is adjusted for by scaling the regression equation by book value of equity, a proxy for size. The authors find a significant relationship between ownership retention and firm value, as does Hughes (1989), but the coefficients are not significantly different between firms choosing high- vs. low-quality * Companies audited by medium-sized auditors are dropped from the sample. auditors, when adjusting for differences i n size and risk. Fel tham, Hughes and Simunic (1991) also try to discriminate between Datar , Fe l tham, and Hughes' (1991) and T i t m a n and Trueman's (1986) results about the relationship between f irm-specific risk and auditor quality. W h i l e the first study finds a positive relation, the second finds the opposite. Fe l tham, Hughes and Simunic (1991) compare several measure of risk, both ex ante and ex post, between their subsamples. T h e results are not conclusive, but this may be due to the fact that audit cost, which varies wi th audit quality and audit risk, is not incorporated in the model and acts as a confounding factor. 2.2.2 M a r k e t Reaction to Earnings Announcements The model presented i n this study yields an empir ical impl icat ion that l inks signaling strategies wi th the time-series behaviour of the firm's earnings. The fundamental problem in testing this impl i cat ion wi th I P O data is the estimation of this behaviour. The sample firms have typical ly been operating for a short t ime , i f at a l l , before the issue and, even if they have been i n existence for some t ime, their prospectus contains only annual earnings for the past five years. It may be useful to survey the accounting l iterature in order to find proxies that could be used for the time-series behaviour of earnings of firms without history. One source of information is the set of articles that investigates the effect of different f irm characteristics on the behaviour of their earnings. There has also been recently many studies on the relationship between earnings behaviour and the market reaction to earnings announcements. These two areas of research are surveyed i n the following paragraphs. Time-Series Beliaviour of Earnings Lev (1983) examines some determinants of the time-series properties of earnings. In part icular , he investigates how the product of the f irm (durable vs. non-durable) , the competitiveness of the industry i n which it evolves, the size of the firm, and the capital intensity of its production process influence the time-series behaviour of its earnings. He conjectures that , the demand for non-durable goods being more stable, firms producing these goods should have more persistence i n their earnings. Monopol ist ic firms should also have more persistence. Large firms, having i n general a more stable growth and being more diversified, should have stable earnings as well , while capital intensive firms should have more volatile earnings since they cannot react very quickly to changing conditions i n the market for their product . B y regressing autocorrelation coefficients of first differences of earnings, as well as three measures of the variabil ity of earnings on these four determinants, he finds that product type, competitiveness, and firm size are significant factors i n the time-series behaviour of earnings. A lbrecht , Lookab i l l , and M c K e o w n (1977) examine the commonalities i n time-series be-haviour of earnings between firms i n the same industry. After est imating an A R I M A model for each firm i n the sample, they compare the results of this estimation w i t h i n each of three indus-tries: food, chemicals, and steel. T h e y find that firms i n the steel industry exhibit a first-order autoregressive behaviour, chemicals follow a random walk, and they detect no commonalities between firms of the food industry. W h e n they deflate earnings by shareholders' equity of the previous per iod , however, aU firms' earnings follow a random walk. Easton and Zmijewski (1989) examine the relationship between the time-series behaviour of earnings and the market 's reaction to earnings announcements. T h e y first estimate the perceived persistence of earnings for each sample firm by regressing forecast revisions following earnings announcements on unexpected earnings. If analysts make a larger revision (per dollar of unexpected earnings) of their forecasts of future periods' earnings, it indicates that the firm's earnings have a larger permanent component. In this est imation, they use a random coefficient model , to take into account variations across firms. They also use a random coefficient model to estimate the correlation between earnings response coefficients and perceived earnings persistence. They find a positive correlation which suggests, as their model predicts, that the market reacts more strongly to earnings containing a higher degree of persistence. Earnings Response Coefficients Ever since B a l l and B r o w n (1968) first documented the stock price reaction to earnings an-nouncements, a large body of accounting research has been devoted to the investigation of this reaction and of its properties. Researchers have tr ied to develop better measures of the information released at the t ime of the announcement that was the exact cause of this reaction. They have also explored stat ist ical methods that would best isolate the reaction to the earnings per se from reaction to other events occurring at the same time. W h e n a firm makes an earnings announcement, the market reacts to the unexpected portion of the earnings number, since a l l information previously known is already incorporated into the price. Hence, one must first measure this surprise component i n order to measure the reaction it generates. Foster (1977) suggests a time-series model to estimate the market's earnings expectation before the announcement. Th i s model assumes that earnings follow a first-order autoregressive process over t ime. B r o w n , Gri f f in , Hagerman, and Zmijewski (1987a,b) find that analysts ' forecasts of future earnings are better estimators of earnings expectations than univariate time-series models. Easton and Zmijewski (1989) further note that the later the forecast is made before the announcement, the better it measures the market 's expectation just before the announcement. T w o types of studies have been made about the price reaction to earnings announcements. Event studies examine the reaction to the actual announcement and typical ly measure this reaction over a short t ime window centered on the day the announcement is made. Associa-t ion studies examine the relation between the reaction and the information contained in the earnings number. They measure the reaction over a longer period after the announcement and seek to establish the consistency of earnings numbers wi th underlying events and information incorporated i n stock prices. K o r m e n d i and L ipe (1987) seek to ameliorate measurement problems by estimating s imul-taneously the unexpected component of earnings, by a second-order autoregressive time-series model , and the market 's reaction to that component. They then regress this earnings response coefficient on a measure of earnings persistence and find a positive relation, as do Easton and Zmijewski (1989). Col l ins and K o t h a r i (1989) decompose the earnings-return relationship into its cross-sectional and temporal determinants. They find that cross-sectional determinants are positively related to earnings persistence and growth opportunity and negatively related to systematic risk. These vary across firms and must be taken into account i n the est imation of earnings response coef-ficients. Col l ins and K o t h a r i also f ind that the temporal determinants of these coefficients are negatively related to the risk-free rate, a fact that is ignored i n most studies where the response coefficients are assumed to be stable over t ime. ImhofF and Lobo (1992) examine the relationship between ex ante earnings uncertainty and earnings response coefficients. They posit that there are two types of earnings uncertainty which have two contradictory effects on E R C s . If earnings are uncertain because there is uncertainty about the value of the f i rm, the earnings announcement resolves some of i t and the price reaction is larger, the more uncertainty there is . If investors are uncertain about the earnings number because of possible earnings management or the lack of l ink between earnings and future cash flows, however, earnings contain l i t t l e information and the price reaction w i l l be smaller for firms wi th more of this type of uncertainty, which is noise. Imhoff and Lobo use the variance i n analysts ' earnings forecasts immediately before earnings announcements as a proxy for the amount of noise i n the earnings number. They find significant differences i n average E R C s between three subsamples based on magnitude of forecast variance. C h a p t e r 3 T h e M o d e l A n entrepreneur seeks to raise capita l for an investment project w i t h a positive net present value. Being risk-averse, she seeks to share the risk of the project 's outcome with investors. Very l i t t le public information is available about the quality of the investment project, and the entrepreneur cannot directly communicate her private information to investors in a credible manner. However, she can send a signal to the market about the value of her project by retaining part of the equity, thus bearing more risk than would be op t ima l i n a well-balanced portfolio. The impl ic i t cost of this under-diversification w i l l keep entrepreneurs wi th projects of a lower quality from imi ta t ing her and a separating equi l ibr ium w i l l result. This is a common result i n one-period models.^ In the model presented here, the firm does not cease to exist after one period. The investment is made at the beginning of the first period and generates cash flows at the end of each of two periods. The first section of this chapter presents a general description of the model and of its underlying assumptions. Section 3.2 examines the situation i n which security regulations require a l l entrepreneurs making an i n i t i a l offering to keep the same retention level for two periods, while i n Section 3.3 the length of mandatory retention is one period. Section 3.4 compares the two preceding mandatory retention regimes and then explores signaling strategies when entrepreneurs have the choice of both retention level and length of retention period. Section 3.5 introduces the possibil ity that the firm's ex ante value wiU be exogenously revealed at the end of the first period and examines how this affects the results of the previous section. Section 3.6 presents five special cases that l ink the model more closely to the empir ical domain. The last 'See for example Leland and Pyle (1977), Hughes (1986), Grinblatt and Hwang (1989), and Datar, Feltham, and Hughes (1989). two sections present tlie empir ical implicat ions of the model and a conclusion on the theoretical contribution of this thesis. 3.1 Description of the M o d e l A t t ime to, the entrepreneur offers a certain number of shares at a certain price. She has to release a prospectus which contains, among other information, the contract she is offering prospective investors, z = ( P , 0:1,02), where P is the offering price and at is the proportion of the firm's equity she proposes to retain in period t.^ Investors can either accept or reject the contract. T h e beliefs they form about the value of the project upon observing contract 2 determine the probabi l i ty d{z) that they w i l l reject the offer. T h e amount K is invested i n the project whether the offer is accepted or not. If the issue is not successful, the project is financed by debt. A t ti information is released about the firm's performance i n the first period. The information made available to investors at that time can be interpreted as the earnings announcement and is represented by y. In order to simplify the notation it is assumed that any first-period cash flow is reinvested i n a riskless asset and the project 's terminal value is determined unambiguously at the end of the second period. If the ut i l i ty function is assumed to be mult ip l i cat ive over t ime, the qualitative results would be precisely the same i f the cash flow was distr ibuted as a dividend at ti rather than reinvested in a riskless asset. After a l l market part ic ipants observe y, there is another round of trading in which the entrepreneur may sell some of her remaining shares on the secondary market without having to go through the registration process again. The price of these shares depends on investors' updated beliefs, once they have observed y and the number of shares the entrepreneur wants to sell at 1^.^  A t t2, the terminal value x is observable by a l l and is added to current shareholders' wealth. X is the value of the f i rm at the end of the longest holding per iod , so it allows comparison list of variables is provided in Appendix A . ' A t «1 there is no formal announcement of « 2 . However, because insiders' trades are closely monitored, an entrepreneur cannot sell large blocks of her stock without investors knowing about it. Hence we assume that the percentage of ownership retained in the second period is observable at ti. between the two retention periods. The second round of t rading at allows the entrepreneur to take a position in her f irm's stock in the first period and then sell her shares on the market before the end of the project, reducing the total risk she has to bear. A n y funds in excess of K obtained from selling stock at either to or ti are invested in a riskless asset which provides a certain return at t2. 3.1.1 Timel ine The problem confronting the entrepreneur and investors can be viewed as a sequential game between two players. The game is in i t iated by the entrepreneur who offers a contract. Investors are passive players who accept or reject the offer made to them. The following timeline describes the unfolding of the investment game. to ti t2 Entrepreneur Earnings Terminal value offers contract. announcement. determined. Investors Entrepreneur can accept or reject. sell shares on secon-dary market . Figure 3.1: T imel ine 3.1.2 Assumptions It is assumed t l iat tiiere is no marlcet-wide rislt, only firm-specific risic.'* W i t h o u t loss of general-ity, the risk-free interest rate is set at zero.^ The entrepreneur is risk-averse, has a von Neumann-Morgenstern ut i l i ty funct ion, and maximizes her expected ut i l i ty over her wealth at the end of the project , at <2- Her ut i l i ty function has the following form: UiW2) =-e-''^' (3.1) where 6 is a measure of her risk-aversion and 14^ 2» her wealth at the end of the second period, has a normal d istr ibut ion w i t h mean E ( W 2 ) and variance Var(VF2). These two assumptions i m p l y that the entrepreneur maximizes her expected ut i l i ty over wealth by maximiz ing E{W2) - \ b Var(H^2).^ (3.2) Investors, because they can hold diversified portfolios of securities, are assumed to be risk-neutral w i t h respect to firm-specific risk. T h e value of the f i rm, fj,, is defined as the present value of the expected terminal dividend from the investment project. T h e product ion process generates two random variables: i/> at i i , and X at ^2- V' can be thought of as the f irst-period earnings number as it is a measure of the project 's outcome for the period. It contains information about the value of the firm and about l iqu idat ing dividend x. Th i s information is revealed publicly. To simplify the presentation of the analysis, the information reported at ti is represented by a random variable y such that x and y are bivariate normal , each wi th mean n- The transformation of ^ into y must be l inear to preserve the normality of the distr ibution of ^ and * Introducing market-wide risk would not change the basic results. If economy-wide risk exists, the entrepre-neur holds a two-part market portfolio. The first part represents her appropriate share of market-wide risk and the second compensates for any firm-specific risk she bears as a result of her ownership retention and depends on the correlation between the firm's and the market's outcomes as well as on her level of under-diversification. *In fact, the variables are scaled in such a way that the risk-free rate is zero. *Leland and Pyle (1977), Hughes (1986), and Datar, Feltham, and Hughes (1991) also use this combination of negative exponential utility function and normal distribution of outcomes while Grinblatt and Hwang (1989) assume (3.2) directly as the entrepreneur's utility function. is equivalent to a rescaling of ip so that i t has mean fiJ Investors know the variance-covariance m a t r i x of the distr ibut ion of x and y but only the entrepreneur knows fi. The expected terminal value /X is a measure of the quality of the envisaged investment project, and is used to define the type of the f i rm. There is a continuum of possible types: / i G [P',Jj], where fi defines a project w i th the lowest net present value possible and JL the project w i t h the highest. A l l projects are assumed to have a positive net present value, i.e., K < ii. y is an information signal about the firm's f inal value x. Its usefulness depends on A, a measure of y^s informativeness about fi, and on p, a measure of the correlation between x and y. The variance-covariance matr ix has the following form: Gov (x, y\p,) = where 0 < p < 1 - - (3.3) 0 < A. ^2 pXa^ pXff^ X'^cr^ Parameters A, p, and cr^ are assumed to be common knowledge. The investors infer the mean p(z) from the contract they are offered at to and are assumed to have no uncertainty about p, after that date. A t ti, after receiving report y, they revise their prior beliefs about a;, (f>{x\p{z)) = J^{fj,{z),(T^), to posterior d istr ibut ion ^{x\y,p{z)) = ^f{^i{z,y),a^l-p')). (3.4) where ti{z,y) = piz) + ^{y-p{z)) (3.5) A is a measure of the informativeness of y w i th respect to the ex ante value of the f i rm, p. W h e n X = 0, y has no variance and perfectly reveals p. W h e n X = 1, y has the same variance as X and , hence, y is just as informative about ^ as x would be. T h e informativeness of y about p is thus inversely related to the value of A. p is the correlation between x and y. If p is zero, the covariance between x and y is zero and the revelation of the first-period earnings only gives information about the ex ante value of the '^This rescaling also takes into account the risk-free rate of interest so that y and x are denominated in similar currency. The relation between ip and y is analyzed more fully in Section 3.6. firm. If separation occurs at to, investors correctly infer p, at that time and revelation of y at ti is useless to them.® Indeed, the latter are only interested i n predict ing x, the final value of the firm, and the release of y w i l l not influence the stock price. U p = I, y completely reveals x at the end of the first period and no uncertainty remains. If p = A, y is a sufficient statistic for {x,y) w i t h respect to p,. T h a t is , y contains a l l the information known at ti and reveals p, as well as x would and a; is a garbled version of y, i n the sense of Blackwel l (1953). In fact, (3.5) becomes E{x\y,p{z)) = y and variables x and y follow a M a r k o v process over time. 3.2 T w o - P e r i o d M a n d a t o r y Retention In the first stage of the analysis, i t is assumed that the mandatory retention period extends unt i l t2 for a l l firms. T h i s can be seen as Rule 144 imposing the same holding period to a l l firms. Th i s implies that = Q2 = a. The entrepreneur seeks to maximize her expected ut i l i ty over her wealth at t2 W2 = i l - a ) P - K + ax (3.6) while making sure that investors w i l l accept her offer. They w i l l accept i t if, in equi l ibr ium, they do not expect to lose money. The issue price must be lower or equal to the value they infer from contract z, p(z). T h e entrepreneur can thus set P = p{z). Investors are also assumed to have rational expectations so that , i n equi l ibr ium, the d is tr ibut ion mean they infer from the offered contract is equal to the firm's actual d is tr ibut ion mean. ^ ( K M ) ) = M (3.7) where z{p) is the contract ( P , a , a ) that is opt imal for an entrepreneur owning a firm of type p. In other words, they have rat ional expectations i n making inferences from signal z and do not want to lose money systematical ly on this type of contract. In the prospectus released before the issue, the entrepreneur states that she wi l l not sell her shares before the end of the second period. Th i s commitment is credible for investors i f there is *It would not be useless if entrepreneur and investors could write an optimal contract with payoffs based on both X and y. an enforcement mechanism which imposes very high penalties on entrepreneurs who go against regulations. After selling securities to the publ ic , an entrepreneur must have no way to go back to the market and sell more shares, no matter how profitable the project is in the first period and , more important ly , no matter how wi l l ing investors are to purchase these new shares. The mandatory retention period considered here is enforced by the S E C through the legal system. The maximizat ion problem resulting from the inclusion of (3.6) and (3.7) into (3.2) is very s imi lar to Le land and Pyle ' s , since the entrepreneur cannot take advantage of the release of information at the end of the first period: m&x{l - a) p{z) - K + ap - I ba'^a^. (3.8) Proposit ion 1 When the entrepreneur has to commit to retaining some of her firm's shares for two periods, there exists a unique stable separating equilibrium. The optimal level of ownership retention a(p) for a firm of type p is given by a{p) + \nil-a{p)) = ^ (3.9) and it is decreasing in firm-specific risk . The level of expected utility attainable by the entrepreneur if she offers the optimal contract z(p) = (p, a{p)) is Uizip), p) = p - K - \ ba^a\p).^ (3.10) The entrepreneur can always use ownership retention as a signaling device in this setting, whatever the value, r isk, or information structure of her firm, or her risk aversion. There always exists a level of a < 1 that can convince investors of the value of her firm and keep entrepreneurs wi th lower value firms from offering the same contract. In this equi l ibr ium, a firm wi th the lowest value is sold outright {a{p) = 0) and the opt imal level of under-diversification is strict ly increasing i n firm value {a'{p) > 0). The cost of s ignaling, which is the risk the entrepreneur has to bear, is increasing i n firm-specific risk. If the risk is higher, the revelation level necessary for separation is lower, ceteris paribus. *A11 proofs are presented in Appendix B . 3.3 O n e - P e r i o d M a n d a t o r y Retention In Section 3.2, it was assumed that the mandatory retention period extended to t2 for aU firms. Th i s section presents a world where the mandatory retention length is one period. Each entrepreneur chooses the level of ownership retention that is opt imal for her but she cannot sell the retained shares before the end of the first period. A t that t ime, she may choose her level of retention for the second period. Gale and Stigl itz [1989] show that when there is no useful information released before the second round of trading, signaling wi th ownership retention does not allow efficient communi-cation. Entrepreneurs could shed the extra risk they have taken before the outcome is known and the equi l ibr ium unravels. The s i tuat ion here is different because, at to, investors know that information w i l l be released at ti about the past and future performance of the f i rm, before the entrepreneur is allowed to sell her shares. A t to the entrepreneur has to decide on the issue price P and her level of retention for the first per iod , a i , and then, at ti, her level for the second period. The contract here has the form z = ( P , 0 1 , 0 2 ) . The entrepreneur's decision problem can be writ ten max max E{W2{z)) - h feVarfVFaC^ (3.11) where W2{z) = (1 - 0 1 ) F ( o i ) -K + iai- 0 2 ) Viiz,y) + o j f = Entrepreneur's wealth at ^2-F ( a i ) = / / ( o i ) = Value inferred by investors from o i at • Vi( - ) = ^ ( o i , Q 2 , y ) = Value inferred by investors from o i , 0 2 , and j / at <i. M a x i m i z a t i o n (3.11) is solved by dynamic programming. The first stage is to determine the opt imal level of 02 for each possible value P, o i and y may have taken i n Per iod 1, assuming that the entrepreneur has been successful at to i n signaling her f irm type. Th i s means that there was separation at to, and hence = P (3.12) Vi{z,y) = ^ + (y-^)R. (3.13) The problem facing the entrepreneur at is thus max{l-ai)p-K + {ai-a2)ip + {y-p)i ) + « 2 (/i + ( y - A ^ ) ^ ) - i ba^l-p')al (3.14) The second stage is to determine the op t ima l separating a i and the issue price that can be chosen at the beginning of the first per iod , given the opt imal level of 0 2 for each possible level of ai, P, and y. In the solution of (3.14), the opt imal value of 0:2 is zero for al l values of ai, P ( a i ) , and y. The contract to be offered at to hence has the form z = ( F , a i , 0 ) . Inclusion of this solution into (3.11) yields the decision problem to be solved at to: max (1 - ax)p{z) - K + a i [p{z) + ( M - p{z)) ^]-\p' <T^a\. (3.15) Proposit ion 2 When the entrepreneur can retain some of her firm's shares for one period only, there exists a unique separating equilibrium which meets the Cho-Kreps intuitive criterion for stability if, and only if, either p> X or 0 < ^ < - A 2 ( i + l u ( l - f ) ) . (3.16) When a solution exists, the optimal level of ownership retention in the first period is given by i a^{p)+ln{l-i a^ip)) = - ^ (3.17) and it is decreasing in firm-specific risk. The entrepreneur sells all her remaining shares at the end of the first period. The maximum expected utility for an entrepreneur with a firm of type p is Uizip), p) = p - K - l bcr'p'alip). (3.18) The equilibrium is stable for p> X. Whether the entrepreneur's problem given by (3.15) has a solution depends on the relative sizes of p and A. If p > A, a solution exists for a l l types of firms. If it is smaller, however, there are many situations i n which the entrepreneur cannot reveal the value of her firm even by retaining 100% of its shares for one period only. The r ight-hand side of (3.16) is an increasing function of p. W h e n y contains l itt le infor-mation about X, that is when the correlation between y and x is low, the condition is very restrictive and a solution is unlikely to exist, unless p - pis very small and /o r ba^ is large. In effect, w i t h One-Period mandatory retention, a separating equi l ibr ium exists when there is not much to signal , the cost to the entrepreneur of bearing risk is h igh , or the market value of the f irm at ti is significantly influenced by the information released at that t ime. Otherwise, Gale and St ig l i t z ' (1989) result obtains and the equi l ibr ium unravels. S imi lar ly , the stabil ity of the equi l ibr ium depends on the firm's information structure. If p > X the separating equi l ibr ium is stable whatever the value or risk of the f i rm. If p < A, stabi l i ty depends on the specific values of the two parameters. 3.4 O p t i m a l Strategies 3.4.1 Comparison of M a n d a t o r y H o l d i n g Periods In this section, a comparison is made between two systems in which the mandatory holding period is either one or two periods, i f a firm goes publ ic . In each system, the legislative author-ities set the m i n i m u m holding period and entrepreneurs have no credible way of committ ing for longer than that m i n i m u m . Since investors always get an expected profit of zero, whether or not they accept the contracts offered, a change of regulation regime leads to a Pareto improvement i f a l l entrepreneurs benefit at least weakly from the change and at least one entrepreneur sees her expected ut i l i ty increase. For s implic i ty of presentation, i t is convenient to change the definition of contract z. W h e n One-Per iod retention allows separation, the entrepreneur always sells a l l the retained shares at i l . The level of retention a2 is thus either zero or equal to q i . A contract can be defined as z = (P, a, r ) , the issue price, the level of retention, and the length of the holding period which can take values 1 or 2. The equi l ibr ium contract w i th a retention period of length r can be defined as Z{P,T) = {p,a{p,T),T), where a ( / z , r ) is the opt imal retention level for type p w i th a holding period of length r . It is also useful to define f irm type p* as the highest type for which One-Period retention is available. It is the m i n i m u m between the highest possible type Ji and the highest type satisfying (3.16). Th is definition facilitates the separation of firms into two groups, those that can go publ ic at to and those that cannot. The first group includes a l l firms, i f p > A, and the set of firms [i£,p*] ii p < X. The firms i n the second group are assumed not to go public at all.^° Proposit ion 3 If p < X then all types p < p* can go public under both retention regimes and entrepreneurs retain a lower level of ownership under Two-Period than under One-Period mandatory retention. If p > X then all types can go public under both regimes and there exists a type p' such that all entrepreneurs with p < p' retain a larger portion of ownership under the One-Period retention regime and those with p > p' retain more under the Two-Period retention regime. W h e n p > X, the information made public at ti is very informative about both the ex ante and the terminal values of the firm. T h e stock price at ti is expected to incorporate al l that information, so retention i n the second period is not so crucial for information communication. Hence, for the high-value firms, the retention level required i n the two-period retention regime is not lower than i n the one-period regime. W h e n p < X, y is less informative and a higher re-tention level is necessary to convince investors of the firm's value, under One-Period mandatory ' ° A s an alternative, one could assume that all firms with types ^^ > ft' go public at ti rather than to. That is, they retain a i = 1 and then offer contract z = {P,l,a2,y) at <i, report y being included in their prospectus. When a firm goes public at ti, it can take advantage of the fact that the worst type making an IPO at that date is n'. It can also benefit from or be hurt by the release of y. The expected value of x at t\ for type fi is Kv) = /* + (y /*) A and its variance is <T*(1 — p^). Hence, 02(11, y) is such that Since «2 ( /J , y) is a non-linear function of y and y is uncertain at to, it would be very difficult to make ex ante comparisons between utility levels under the two mandatory retention regimes. The assumption that types above n' never go public is thus maintained in the analysis to follow. retention. Proposit ion 4 / / p > A, One-Period mandated retention is Pareto preferred to Two-Period mandated retention. If p < A, One-Period mandated retention is preferred by all types p < p* if and only if A < 1. All types p > p* prefer Two-Period mandated retention. For a l l types that can go public under One-Per iod mandatory retention i.e., for al l p < p*, the entrepreneur is better off w i th the shorter retention period, even i f the level of retention is lower for the longer retention per iod , except when A > 1. In this case, the information released at ti provides a less precise signal about p than would x. If y is more informative than x about p, One-Per iod mandatory retention is preferred. If not, the entrepreneur would have to bear the risk l inked to both the high level of retention necessary w i t h r = 1 and the uncertainty of stock price at i i , because of the low precision of y. Th is is more risk than she would have to bear w i t h Two-Per i od retention. Entrepreneurs w i t h firm value higher than p* have to retain ful l ownership in the One-Per iod retention regime. They have to bear the entire risk of their firms for two periods. Th is is more than they would bear in the Two-Per i od retention regime, since a l l firms can retain a < 1 i n that regime. They prefer the latter. Hence, i f A < 1, a l l types for which signaling is possible under both regulatory regimes prefer One-Per iod mandatory retention, even i f some of them (the lower types) have to bear more risk i n the first period. If A > 1, y is not very informative about p and a(p, 1) makes entrepreneurs bear so much risk in the first period that they are better off retaining a{p,2) for two periods. Entrepreneurs who cannot go publ ic under One-Per iod mandatory retention prefer the other regime where they can shed at least some of their firm-specific risk. 3.4.2 Choice of Strategy In this section, One-Per iod and Two-Per i od retention periods are considered as two alternative signaling strategies. Regulations require a m i n i m u m holding period but entrepreneurs can choose to commit to a longer one. Some entrepreneurs can only communicate their private information by retîiining ful l ownership for two periods or commit t ing to a level of retention a < 1 for two periods. T h e others choose the retention level and the holding period that provides them wi th the highest level of expected ut i l i ty . Proposit ion 4 shows that i f A < 1, entrepreneurs are better off w i th the shorter holding period, even if it requires a higher level of retention, while they prefer Two -Per i od Commitment \{ X > 1 OT p > p*. For a given information structure, one would expect lower-value firms, for which the m i n i m u m commitment is possible, to choose to offer contract z = (p,a{p, F i r m s w i t h values above p* would choose offering z = {p,a{p,2),2) over never going publ ic . Proposit ion 5 If X > I all firms choose Two-Period Commitment and their level of retention is the same as under Two-Period mandatory retention. If X < 1, all types p 6 \j£,p*) choose One-Period Commitment, while all p E [fi*,]^] choose Two-Period Commitment. The level of retention for the first group is the same as under One-Period mandatory retention. The level of retention for the high-value group is lower than under Two-Period mandatory retention. The difference between strategy choice and mandatory change is that entrepreneurs wi th firms of types less than p* choose the m i n i m u m holding per iod , i f A < 1. They are better off w i t h this choice than under Two -Per i od mandatory retention. It is thus less costly for higher-value firms to separate from that group than i n a regime where a l l entrepreneurs had to commit to a retention level for two periods. Construct ion of a retention level for types above p* uses a boundary condit ion that is equivalent to having the "worst type" greater than W i t h this new definition of the boundary condit ion , the level of retention necessary wi th Two-Per iod Commitment is lower than it was when a l l firms had to commit for two periods. Hence, the choice of a holding period i n itself is a signal which conveys information to the market. Investors know that , for A < 1, only firms w i t h value below p* choose r = 1. It must be noted that a l l firms have p < p* when p > X, in which case a l l firms choose r = 1 and the choice conveys no information.^^ 3.5 R a n d o m Revelation of F i r m Value after One Period Mandatory earnings announcements are not the only sources of public information about the firm's value. For example, the signing of a major contract or the discovery of a large quantity of o i l may influence investors' valuation of a firm.^^ Th i s type of information is introduced into the model by assuming there is a probabi l i ty p (0 < p < 1) that the ex ante firm value n w i l l be revealed exogenously at ^ i . Th is assumption is s imilar to the approach taken by Gr inb la t t and Hwang (1989). Unfor-tunately, introducing this probabi l i ty destroys the normal d istr ibut ion structure of the model , which implies that maximiz ing E{W2)-^ 6Var(W^2) (3.19) is not equivalent to max imiz ing the entrepreneur's expected ut i l i ty . To avoid complexity i n this case, it is assumed, following Gr inb la t t and Hwang , that the entrepreneur's objective is to maximize (3.19). The analysis is equivalent to the previous case i f p = 0, however. 3.5.1 T w o - P e r i o d M a n d a t o r y Retention The regulatory environment assumed here prohibits trades by entrepreneurs at ti, unless firm value has been revealed. Th i s is close to the s i tuation Jackpot Enterprises refer to in the excerpt from their prospectus presented on page 9. T h e entrepreneur has to retain part of her firm's shares for two periods but , i f the value of her firm is revealed exogenously at ti, for example by very good results that could hardly be attained by a low-value firm, she can then trade some or a l l of her shares. A s was the case i n Section 3.3, she would then sell a l l her remaining equity i n the f i rm. T h e decision problem she has to solve at to can be stated as m a x ( l - a)fi{z) -K + ap-^ ba'^a2{pp^ + (1 - pf). (3.20) " D a t a r , Feltham, and Hughes (1991) also present a signaling context where the choice of an audit quality conveys information about firm type and can influence the level of risk to be borne by the entrepreneur. " S e e Welch (1989) for other examples of exogenous revelation. This formulation reflects the fact that , at ti, there is a probabil ity p that the entrepreneur wiU sell her shares ÎOT p + {y - p)^ , and a probabi l i ty l - p that she w i l l have to retain them unt i l t2 and then receive their terminal value ax. Proposit ion 6 When the Two-Period mandatory holding period can be shortened in the event of exogenous revelation of firm value, there exists a unique stable separating equilibrium where the optimal level of ownership retention a{p,2,p) is given by aip,2,p) + l n ( l - aip,2,p) = ,^2^J;[,_pyy (3.21) The expected utility of the entrepreneur, if she offers optimal contract z{p,2,p) = {p,a{p,2,p)), is U{z{p,2,p),p) = p - K - \ ba\pp' + {l-pf)a\p,2,p). (3.22) Here, the level of ownership retention depends on the probabi l i ty p that f irm value wi l l be revealed. Note that i f p = 0, (3.21) and (3.22) are the same as the level of retention and the expected ut i l i ty determined i n Propos i t ion 1. A s p increases, so does the possibility that the entrepreneur w i l l sell her shares at ti. Whether the level of retention necessary for separation increases because of the added level of uncertainty introduced by p depends on the information contained i n y. For small values of p and p, i t is more costly to convince investors of p w i th this added uncertainty and the retention level increases wi th p. Proposit ion 7 Under two-period mandatory retention, the possibility of exogenous revelation of firm value at ti leads to a Pareto improvement if entrepreneurs whose firm value has been revealed are allowed to sell their shares after one period. A l t h o u g h they may have to retain a larger port ion of their firm's shares, entrepreneurs have a higher expected ut i l i ty i f there is a possibil ity that their f i rm value w i l l be revealed and that they w i l l then be allowed to shed a l l risk i n the second period. T h i s decrease i n risk in the second period more than compensates for the possible increased risk i n the first period. 3.5.2 O n e - P e r i o d M a n d a t o r y Retention T h e regulatory environment assumed in this section is essentially the same as in Section 3.3. There is , however, a probabi l i ty p that f irm value w i l l be revealed at t\. A t that t ime, the entrepreneur faces the same problem as i n (3.14), whether p was exogenously revealed or not, since separation at to is s t i l l assumed to have communicated f irm value to investors. The opt imal strategy, as before, is for the entrepreneur to sell a l l her retained shares at the end of the first period. The decision problem she faces at the beginning of the first period is different from (3.15), however. She can take advantage of the possible exogenous revelation of her firm's value. She also has to take on the increased risk introduced by the randomness of revelation. Proposit ion 8 When, under One-Period mandatory retention, there is a positive probability of exogenous revelation of firm value at the end of the holding period, there exists a unique separating equilibrium which meets the Cho-Kreps Intuitive Criterion for stability if, and only if, p> X or When a solution exists, the optimal level of ownership retention for an entrepreneur with a firm of value p is given by max{l-a)piz)-K-\-a (l - ^ ) (pp + (1 - p)p(z))a ^ ^ _ i ba'Ul-^)'pil-p)ip-piz))' + a'p' (3.23) (3.24) where a; = l - ( l - p ) ( l - f ) . oja{p,l,p) + ln{l-ua{p,l,p)) = (3.25) and her expected utility is Uiz{p,l,p), p) = p - K - l ba''p'a\p,\,p). (3.26) The existence of a solution depends, once again, on the informativeness of the earnings announcement about both p and x. T h e r ight-hand side of (3.24) is an increasing function of p and, hence, the condition is less restrictive the more informative y is about the terminal value. It also depends, i n this case, on the probabi l i ty of revelation, p. If p > A, the information released by the firm at ti is very informative about both the ex ante and the terminal value of the firm. In part icular , when p = A, j / is a suflîcient statistic for x and y w i t h respect to the ex ante value and x is a "garbled" version of y, i n the sense of Blackwel l (1953). One-Period retention is possible for al l firm values when p > A. Proposit ion 9 / / p < A, random revelation of firm value at the end of the holding period leads to a Pareto improvement under One-Period mandatory retention and the retention level necessary for separation is lower than it would be in the absence of exogenous revelation. If p > A, random revelation increases the level of retention and makes all entrepreneurs worse off. It leads to no change if p = A. If p = X, y reveals a l l the information available about firm value. The exogenous revelation of p changes nothing i n the level of retention necessary for separation at to. A l l entrepreneurs are thus indifferent to the probabi l i ty of random revelation. If p > A, y is very informative about both x and p, so the gain i n information at t\ is not enough to compensate for the higher retention level made necessary by the uncertainty introduced by p. If p < A, y is not very informative about x and p and random revelation increases possible information at ti to such an extent that the level of retention necessary for signaling at to decreases. The entrepreneurs are thus better off since they have to bear a lower level of risk. 3.6 Special Cases The information structure assumed i n the model lends itself to the investigation of special cases that may be interesting empirical ly. Th i s section examines five special cases of the structure. These are extreme cases of the information structure which allow exploration of some of the results derived i n previous sections. They may help understand how these results could apply to real-world situations. The first two cases involve the statist ical relation between y and x. In one, Information y is assumed to be uninformative about x (p = 0) and i n the other it is assumed to be the best estimate of the firm's final value (p = A). The three other cases are concerned wi th the statistical relation of financial reports across t ime. In the first one, the reports are independent, in the second they follow a Markov process, and i n the last they contain transitory and persistent components. 3.6.1 Information Structure In the first two situations, y is information released at ti about what the entrepreneur knew when she made the i n i t i a l offering at to. It may be, for example, the result of a study she had undertaken before making the issue and that is publ ic ly reported at t^. It is not perfect revelation of p but rather a noisy signal about firm type. The amount of noise in the signal is inversely related to A. Th i s signal may, or may not, be correlated w i t h terminal value x. The importance of the correlation is measured by p. ' Independent Information The first extreme case considered is one where there is no correlation between signal y and final value x. T h a t is , y gives noisy information about the entrepreneur's private information at to but contains no new information about the performance i n the first period which could influence the value x takes at ^2- Correlat ion p is assumed to be zero and A is str ict ly positive. Due to signaling activit ies , the entrepreneur's private information p is inferred by investors at to. A t that t ime , i t is the best estimate available of the firm's final value. At ti,y is released but i t gives no new information about x , that is 4>{x\y,piz)) = 4>ix\piz)) = M{p{z)y). (3.27) Corol lary 1 When the information released at ti is uninformative about the firm's final value, One-Period retention is not available as a signaling strategy. N o level of retention less than ful l ownership can convince investors of the value of the f irm. The cost of bearing risk for the entrepreneur is not high enough, even with ful l retention, to make separation possible. Th i s is essentially Gale and Stigl itz 's (1989) result. Information Follows a M a r k o v Process Here, the assumption is that p = A, so that information variable y is a sufficient statistic for x and y w i t h respect to ex ante f irm value p. It contains a l l information then available about the expected value of x because the noise affecting the realization of y also affects final value x. In fact, under this assumption, E{x\y,p{z)) = y. Hence, y becomes the stock price at ti. Corol lary 2 When the information available at ti is a sufficient statistic for x and y with respect to ex ante firm value, there always exists a unique stable separating equilibrium where the entrepreneur chooses to retain a portion of her firm's shares for one period only, even though it requires a higher retention level. This is the extreme opposite of the previous result. In this setting, i f A < 1, a l l firms choose One-Per iod Commitment while i n the previous case, a l l chose Two-Per iod Commitment because it was the only signaling strategy available. These contrasting results hint to the fact that the various signaling strategies observed i n I P O markets may be the result of differences in information generating processes between firms. 3.6.2 Outcome Structure The next three cases explore the statist ical properties of the economic variables underlying the information structure of the model . The investment project for which the issue is made produces cash flows i n each of the periods it spans. In the exploration of these cases, ip denotes the cash flow reported at ti and its mean is assumed to be a linear function of p. The information variable y is a l inear transformation of V'- In part icular , y is a one-dimensional representation of ip, that is scaled so that y has a mean of p. Th i s representation simplified the preceding analysis, but now the focus is on the relation between x, V», and p. The joint d istr ibut ion of x and is assumed to be of the form \ • / X ~ N l^ \ . / (^) . pcra^ pcTCT^p where /( /x) is a linear function of p. For example, i f and f{p) = ap^c y = dtp + e then the expected value of y is E{y\p) = {ad)p + icd + ey^ Scaling y so i t has mean p requires and which implies H = i a •0 c ^ a a (3.28) (3.29) (3.30) (3.31) (3.32) (3.33) T h e joint d istr ibut ion of a; and y obtained by this transformation has the covariance matr ix given by (3.3) i f A = (3.34) '•'The transformation to obtain y must be linear to preserve the normal distribution. It must also be indepen-dent of Ii since the latter variable is not known by investors and it would be impossible to know the covariance matrix, as it is assumed in the model. Hence, A decreases wi th a, the rate at which the mean of ip increases wi th p, and increases with cT^/cr, the relative standard deviations of i/^ and x. The next section provides three examples i l lustrat ing three basic cases: (1) p < 1 < A, (2) /) = A < 1, and (3) A < /? < 1. Independent Outcomes Let ^1 and ip2 denote the productive outcomes generated by the investment in the first and second periods, respectively. They can be thought of as the operating cash flows (or the earnings numbers) reported i n financial statements at the end of each period. The first period cash flow, ipi, is assumed to be invested i n a riskless asset unt i l <2 and it is scaled to adjust for the riskless rate of interest. The final value at t2 is thus given by x = V^i + V'2. (3.35) The cash flows are characterized i n the following way: V'l = è ^ + ^ i (3.36) ^2 = è/^ + e2 (3.37) where €t~A^(0 ,<7^) and cov (6i ,€2) = 0. (3.38) In fact, cash flows 4>i and ^2 are independent draws from a same distr ibut ion wi th mean ^p and variance aj. In this setting, the first period cash flow is equivalent to variable ip as defined on page 39 and y, the information released at ti, is equal to 2^ » so it has mean p. Hence, - Af{\p,(7J), (3.39) x - Af{p,(7^), (3.40) y ~ Af{p,2a% (3.41) cov{x,y) = a^ = 2a^ (3.42) Combin ing (3.3), (3.40), (3.41), and (3.42) determines values for p and A for independent cash flows, 1 " = 71 and X = V2. This is an example of a s ituation where A > 1. T h e results for Two -Per i od Commitment are not affected by this (or any other) specification of the information structure, since this signaling strategy takes no advantage of the information released at the end of the first period. The situation is different, however, w i t h the shorter holding period. Corol lary 3 When the outcomes generated by the investment project are independent across periods, there exists a unique stable separating equilibrium with Two-Period Commitment which dominates One-Period Commitment. One-Period Commitment exists if, and only if, 0 < f^^^ < 0.386. (3.43) Condi t ion (3.43) above is very constraining and One-Per iod Commitment requires very high retention levels for low-value f irms, while i t is not available for better firms. Hence, even if i t is available, the entrepreneur prefers Two-Per iod C o m m i t m e n t . Shorter commitment should therefore never be observed when the productive process generates outcomes which are statistical ly independent across periods. Outcomes Follow a M a r k o v Process The second case involves a s i tuation where the realization of the f irst-period cash flow becomes the mean for the productive outcome of the second period. Let i'l = Ip + €I (3.44) and 1p2 = ^1 + f2 (3.45) = I + ei + 62 (3.46) where £i and £2 are defined as in (3.38). A g a i n , rp = rpi and y = 2ip, which imply X (3.47) (3.48) y (3.49) and cov(a;, y) (3.50) where (3.51) T h i s , combined w i t h equation (3.3), implies that when the first-period cash flow determines the expected value of the second-period outcome. Corol lary 4 When the cash flows from the investment project follow a Markov process, there always exists a unique stable separating equilibrium where the entrepreneur chooses to retain ownership in her firm for one period only. This is an i l lustrat ion of the result found i n Proposi t ion 4 for p > A. One-Period C o m -mitment is always available as a strategy for the entrepreneur whose firm generates this type of cash flows, and it is preferred to Two -Per i od Commitment . One would then expect to see shorter commitment periods for a l l firms w i t h these characteristics. Persistence Component of Outcome This last case is an example where the first-period outcome contains a random component that w i l l infiuence the real ization of the second-period outcome. Th i s is analogous to persistence components i n earnings. A l t h o u g h the expected value of x is not affected, the random shock that affects outcome i n the first period also affects results in the next period. Let ^1 = è ^ + i e i (3.52) V'2 = ^P+^ei+e2 (3.53) where and A s i n the previous cases. and Hence, and ei ~ Af{0,y), (3.54) €2 ~ Af{0,\a% (3.55) C o v ( e i , f 2 ) = 0. (3.56) ^P = rpi, (3.57) y = 2i> (3.58) = M + ^ e i , (3.59) X = V i + -^2 (3.60) = p + €i + €2. (3.61) ~ Ar(lp,±y), (3.62) X ~ M{p,(T% (3.63) y ~ ^f{p,i-^cT% (3.64) cov(x,j / ) = 1^ 2. (3.65) This implies that A = 1/4 (3.66) p = 1/2. (3.67) So this is a s ituation i n which p > X. From Propos i t ion 2, we know that separation wi th One-Per iod Commitment is possible for a l l firms and, from Proposit ion 4, that this strategy is preferred by a l l , even i f the retention level is higher than it would be wi th Two-Per iod Commitment , since A < 1. The retention level for One-Per iod Commitment is lower than 50% for a l l f irms, since ^ = ^, and it is higher than what would be necessary for Two-Per iod Commitment for a l l firms wi th a{p, 1) < 49%.^'* 3.7 E m p i r i c a l Implications The model developed i n this chapter makes i t possible to distinguish between two groups of f irms, based on their risk and information characteristics: those who choose the min imum retention period allowed by regulations and those who commit to a longer retention period. Proposi t ion 3 shows that , depending on f irm value, the retention level may be higher or lower wi th the m i n i m u m retention per iod . It is higher for low-valued firms and lower for high-valued firms for which short retention is available. Proposit ions 4 and 5 show that there may exist situations where the m i n i m u m retention period is preferred and other equally realistic situations i n which firms prefer longer holding periods. U p > X, a l l firms prefer and would choose short retention. If A > 1, a l l entrepreneurs are better off w i th longer retention. In other cases, low-quality firms prefer short and high-qual i ty firms prefer long retention. Corollaries 3 and 4 also suggest a relationship between the time-series behaviour of reported earnings (or operating cash flows) and signaling strategies. If the reports are independent draws from the same d is tr ibut ion , a l l firms prefer longer holding periods. If the firm's early reports are sufficient statistics w i th respect to its ex ante value, the shorter retention period allows ^*This result uses function A ( a ) as defined in (B.74). separation and a l l such firms choose this strategy. Moreover, the example of a firm whose reported earnings contains a persistence component also points to shorter retention. It is then possible to make predictions about the signaling strategy of a firm from the time-series behaviour of its reported performance. 3.8 Conclusion The model described i n the previous sections includes both ownership retention level and length of retention period as signaling devices for the entrepreneur making an in i t ia l public offering. It is different from previous signaling models i n the l iterature in that i t incorporates securities regulations which play an important part i n the decision to go publ ic . The results of the analysis establish a relationship between a firm's risk and information characteristics and its choice of both retention level and retention period. If one interprets p as the anticipated long term value of the f i rm and x as its value at the end of the longest possible retention per iod , the report released at the end of the m i n i m u m retention period may be viewed as more informative about the firm's long term value, the lower A is. S imi lar ly , p may be viewed as a measure of the informativeness about unantic ipated changes i n value i n the first two periods. A n impl ic i t assumption i n some signaling studies is that entrepreneurs prefer to keep the retention period as short as possible.^^ However, for some entrepreneurs the m i n i m u m retention period does not allow separation while others may prefer a longer holding per iod , even i f they could sell their f irm's shares at their true value w i t h the m i n i m u m retention per iod . The results of the analysis show that , i n general, higher-quality firms are more l ikely to have to resort to a long holding period {ceteris paribus), since it takes a higher level of retention to convince investors of their firm vaJue than i t would for a lower-quality firm and the retention level for short retention has more chance of being above one. Longer retention periods may also be necessary when the information content of the financial '^Grinblatt and Hwang (1989), Welch (1989), and many others make such an assumption. reports released by a firm is low and very l i t t le uncertainty is resolved at the end of the m i n i m u m retention period. The retention level may be so high that it is less costly for the entrepreneur to commit to a longer holding period. Th i s is the case of firms who go public very shortly after their formation, before operations really begin. W h i l e they are i n the development stage, their financial reports contain very l i t t le information about their future performance or their long term prospects. Th is may also be the case of firms whose periodic results are influenced more by transitory shocks than by long term factors, as the example of Section 3.6.2 suggests. The introduct ion of random value revelation in Section 3.5 allows insight into the influence information sources other than financial reports may have on the process surrounding in i t ia l offerings. The results provide theoretical grounds for phenomena like the Blue Sky Laws and condit ional commitments such as the one appearing i n Bu lb -Miser ' s prospectus and presented on page 10. It is important to note, however, that i n this analysis only l inear contracts are considered. Contract z is assumed to provide each of the players wi th a payoff that is linear i n the terminal firm value. Th i s may not be the opt imal contract since i t is possible that the contract that maximizes the two players' expected ut i l i ty is non-linear. A n opt imal contract would be based on the realization of y as well as on a; because it would take advantage of a l l information observable by both parties. T h e inst i tut ional arrangements observed i n the market seem to l imi t the choice to linear contracts, however. Chapter 4 E m p i r i c a l Analysis 4.1 Sample Description T h e sample used i n testing the various empir ical implications of the model is based on Simunic and Stein's (1987) I P O data set. It contains a l l firms that made an i n i t i a l public offering in the Un i t ed States in 1981, except for 43 that were deleted for a variety of reasons.^ Of Simunic and Stein's or iginal 469 companies, 5 were dropped because the shares issued were restricted to a very small group of potential investors.^ The list of the 464 firms constituting the sample used i n this study appears i n A p p e n d i x C and Table 4.1 shows the d istr ibut ion i n the calendar year of their issue dates. There is a concentration of offerings from A p r i l to June . It should be pointed out that 1981 was a "hot market" t ime for IPOs .^ The information about ownership retention periods was collected from the prospectus of each of the 464 firms, usually i n the section relating to Rule 144 Restrictions on outstanding shares. W h i l e most firms are fairly precise about the restrictions apply ing to their shares, some make ambiguous statements and spread the information over several sections of the prospectus. Accordingly , some judgement was required to classify the retention periods and determine their length. The earnings announcement dates were taken from the Wall Street Journal Index for 1981, 1982, and 1983. The dates collected were the date of the first earnings announcement after the issue, whether i t was for quarterly or annual earnings, as well as the date of the first annual earnings announcement. T h e Index includes first earnings announcement dates for 215 of the 'Some firms had had shares traded publicly before, some were not-for-profit organizations, and some offerings were really exchange oflferings. ^For example, to the residents of Colorado, or to Savings and Loan firms. 'See Ritter (1984b). Table 4.1: Dis t r ibut ion of issue dates for 1981 I P O firms. Number of % of original M o n t h firms sample January- 18 3.88 February 28 6.03 M a r c h 27 5.82 A p r i l 57 12.28 M a y 57 12.28 June 55 11.85 J u l y 39 8.41 August 31 6.68 September 30 6.48 October 39 8.41 November 48 10.34 December 35 7.54 Tota l 464 100.00 464 firms, and first yearend announcement dates for 212 of them. Tables 4.2 and 4.3 present the distr ibution of first earnings and first annual earnings announcements, respectively, over calendar t ime. A s might be expected, there is a majority of 31 December yearends resulting i n a concentration of announcements in February and M a r c h 1982. D a i l y returns were collected for a period of 122 days centered on each of these announcement dates, i n Standard and Poor's Daily Stock Prices OTCand on the C R S P daily returns tape. This leaves 160 firms w i t h complete returns data for first earnings announcements and 197 for first annual earnings announcements. T h e firms indicated as having insufficient data i n Tables 4.2 and 4.3 are those for which an announcement date was determined, but for which the returns data was incomplete. A s could be expected, the number of those firms is much higher for first announcements, which often take place less than 60 trading days after the issue. However, returns data is missing for some yearend announcements because of delisting or mergers which occur frequently wi th newly publ ic companies. The two announcement dates coincide for 114 of the firms with complete returns data . T h a t is , the first earnings announcement after the issue is for annual earnings. These firms are common to the samples described in Tables 4.2 and 4.3. Table 4.4 gives descriptive statistics about the whole sample of 464 firms. For each of the variables examined, the sample is split into three groups based on the length and the type of retention period to which the entrepreneur commits i n the prospectus. Short retention period refers to the m i n i m u m retention period allowed by S E C regulations, which is 90 days. A firm is classified as having a long retention period i f the prospectus indicates a proposed retention period exceeding 90 days. T h i s long retention may be required by Ru le 144, in which case the firm is classified as having long mandatory retention, or i t may be a commitment the entrepreneur makes voluntari ly which exceeds i n length any mandatory retention period for the firm. The most str ik ing feature of Table 4.4 is the difference i n size and age between firms with short and long retention periods. In part icular , i t appears that large firms (as defined by the Table 4.2: Dis t r ibut ion of dates of first earnings announcements following issue Number of % of original % of final M o n t h firms sample sample 1981 M a y 2 0.43 1.25 June 2 0.43 1.25 J u l y 3 0.65 1.88 August 12 2.59 7.50 September 9 1.94 5.62 October 5 1.08 3.13 November 10 2.16 6.25 December 11 2.37 6.88 1982 January 12 2.59 7.50 February 22 4.74 13.75 M a r c h 24 5.17 15.00 A p r i l 14 3.02 8.75 M a y 8 1.72 5.00 June 6 1.29 3.75 J u l y 2 0.43 1.25 August 2 0.43 1.25 September 6 1.29 3.75 October 1 0.22 0.62 November 7 1.51 4.38 December 1 0.22 0.62 1983 January 0 0.00 0.00 February 0 0.00 0.00 M a r c h 1 0.22 0.62 F i n a l sample 160 34.48 100.00 F i r m s w i t h insufficient returns da ta 55 11.85 F i r m s without announcement date 249 53.65 Or ig ina l sample 464 100.00 100.00 Table 4.3: Dis t r ibut ion of first annual earnings announcements following issue Number % of original % of final M o n t h firms sample sample 1981 August 5 1.07 2.54 September 7 1.51 3.55 October 3 0.65 1.52 November 9 1.94 4.57 December 10 2.16 5.08 1982 January 7 1.51 3.55 February 28 6.02 14.21 M a r c h 36 7.76 18.26 A p r i l 21 4.53 10.66 M a y 13 2.80 6.60 June 12 2.59 6.09 J u l y 8 1.72 4.06 August 10 2.16 4.57 September 10 2.16 5.58 October 4 0.86 2.03 November 5 1.07 2.54 December 2 0.43 1.02 1983 January 1 0.22 0.51 February 1 0.22 0.51 M a r c h 2 0.43 1.02 A p r i l 0 0.00 0.00 M a y 1 0.22 0.51 June 1 0.22 0.51 J u l y 0 0.00 0.00 August 0 0.00 0.00 September 0 0.00 0.00 October 1 0.22 0.51 F i n a l sample 197 42.45 100.00 F i r m s w i t h insufficient returns data 15 3.23 F i r m s without announcement date 252 54.30 Or ig ina l sample 464 100.00 100.00 Table 4.4: Descriptive statistics of pr inc ipal variables for ful l sample of 1981 I P O firms Retention period M e a n (standard deviation) Differences' ' (^values) Short ( N = 126) Long Voluntary ( N = 198) Long Mandatory ( N = 140) Voluntary Mandatory Assets i n place*" 13.80 6.90 3.19 6.90 10.61 (25.913) (25.968) (14.646) (2.334)'= (4.047)= Net proceeds from 10.49 5.27 4.39 5.22 6.10 issue"^ (13.306) (7.101) (5.248) (4.052)<= (4.819)= F i r m value* 42.80 20.18 14.49 22.62 28.31 (61.665) (38.167) (23.812) (3.691)= (4.840)= F i r m age (in years) 10.50 6.41 1.64 4.09 8.86 (11.698) (8.663) (3.320) (3.375)^ = (8.213)= Retention level'^ 52.24 48.74 47.58 3.50 4.66 (in percentage) (18.476) (17.307) (18.274) (1.731)'= (2.069)= Length of retention 3.00 15.33 15.76 0.43 period (in months) (0.000) (10.006) (6.217) (0.485) "Differences between short and long voluntary retention, on the one hand, and between short and long mandatory retention, on the other. ""Book value of assets before the issue, in millions of U.S. dollars. •^Significant at the 5% level, one-sided t-test. "'In millions of U.S. dollars. 'Issue price x number of shares outstanding after the issue, in millions of U.S. dollars. ^Percentage of shares outstanding after the issue owned by principal shareholders. three alternative measures of size included in the table) prefer short retention to long retention. Entrepreneurs whose firms have been i n operation for a long time also seem to choose short retention. Th is may imply that older firms tend to have financial statements that are more informative about future f irm value than firms start ing operations. A l t h o u g h ownership retention level is close to 50% for al l three subsamples, suggesting many entrepreneurs may have sought to retain control of their f i rm, as well as signal their type, note that the level is higher for firms wi th short retention period. Th is result may be due to the size difference between the subsamples, however, and is investigated in more detail i n section 4.3. A l t h o u g h the ages of firms choosing long retention voluntari ly and those for which it is mandatory are quite different, as would be expected given the current regulations, the average retention length is quite s imilar between the two groups of firms. 4.2 Valuat ion M o d e l M a n y tests of signaling valuation models s imilar to the one developed i n Chapter 3 have been performed and reported i n the literature.'* Most of them have found significant support for Le land and Pyle 's model or variations of i t . Proposit ions 1 and 2 suggest a refinement in the relationship between ownership retention level and f irm type: the relationship should hold for groups of firms w i t h s imilar retention period lengths. For long retention periods, the relationship between f irm type and retention level is given by (3.9): p = / £ - 6(7^(0 - f l n ( l - a)) where p is the firm's type, p is the f irm value investor would infer i f the entrepreneur was not engaging i n signaling behaviour, 6cr^ is a measure of the entrepreneur's risk exposure, and a is the ownership retention level. For firms w i t h short retention periods, the relationship is given *Downes and Heinkel (1982), Ritter (1984), Qarkson et al. (1991), and Feltham, Hughes and Simunic (1991), to name a few. by (3.16): p = p-ba^X\j^a+ \nil-fa)) where f is a measure of the informativeness of earnings about future firm value. In order to test these valuation functions, i t is necessary to find a surrogate for p. Fe l tham, Hughes and Simunic (1991) use the book value of the firm's equity after the issue as this surrogate and the same measure is used here. The relation (4.2) could then be tested with regression equation Vj=0'o + f3J<j+(32àj + Uj,' (4.1) where â = - ( a + l n ( l - a ) ) and Kj is the book value of f irm j ' s equity.^A problem with this procedure is that the model assumes that ^2 = ba'^ is the same for a l l firms, whereas it need not be i n reality. O f the many approaches used to alleviate this potential source of heteroscedasticity, Fe l tham, Hughes and Simunic 's (1991) method is employed here. They assume that firm-specific risk is l inked wi th f irm size, i m p l y i n g that control l ing for size should then control for differences i n risk.''^ They exercise this control i n two ways: first, the regression variables are scaled by Kj (a proxy for firm size). If one assumes that the intercept fi^ is a linear function of size, scaling of (4.1) yields iVilKj) = (/3o + /3i) + f32{àj/K,) + (uj/Kj), (4.2) where PQ = P'Q/KJ. Second, when comparing subsamples for the impact of audit quality, they match firms by size as measured by Vj, total prior assets, or total proceeds.* In this section, the valuation model is tested using the scaled regression function (4.2) while matching and scaled values are used i n comparisons between firms wi th different retention * Propositions 1 and 2 do not suggest an intercept, but a more general model that considers economy-wide risk would have an intercept term. See Feltham, Hughes and Simunic (1991) for a discussion of this issue. ' a is measured here as the percentage of outstanding shares after the issue owned by "insider" shareholders (those identified in the prospectus as holding more than 5% of the shares before the primary issue). This measure is different from that of Feltham, Hughes and Simunic (1991) who use the percentage retained by directors and officers of the company. It also differs from Downes and Heinkel's (1982) measure of a , the percentage retained by all pre-IPO shareholders. ^Stemming from sources other than differences in audit quality. * While firms are matched on size in some of the tests, no attempt is made in this study to control for audit quality. periods. T i i e ful l sample of 464 firms is divided into three groups: firms with short, long voluntary, and long mandatory retention periods. Regression (4.2) is estimated for each group and the results are presented i n Panel A of Table 4.5.^ Coefficient is positive and significant for both long retention subsamples, but not signif-icant for the short retention group. It must be noted that , for short retention, the relationship between a and value is given by (4.2) and the signal variable A ^ ( f a + l n ( l - fa)) may not be very well captured by â. Unfortunately, p and A are not observable so it is not possible to get a better measure of the retention level signal . In the regression reported in Panel A , f irm value is computed by mul t ip ly ing the number of shares outstanding after the issue by the issue price. Th is does not take into account the phenomenon of underpric ing documented and investigated by many researchers but , as under-pric ing is not included i n the model , it is not clear what impact it would have on the results derived i n Chapter 3. The regressions are also estimated using closing stock price on the t h i r d day of trading i n measuring f i rm value. T h e number of firms for which this data is not available reduces substantial ly the sample size, however. T h e results of this estimation are in Panel B of Table 4.5. F i r m s for which trading price is available are those for which a secondary market developed following the issue. They are not a random draw from the ful l sample. The relative sizes of the three subsamples are indicative of this . Whereas the short retention group is the smallest i n Pane l A , i t is the largest i n Pane l B and it is twice as large as the long mandatory retention group. T h i s difference i n d is tr ibut ion may account for the large difference i n results between the two sets of regressions.^" 4.3 Association between Ownership Retention Level and Length The first empir ical impl i cat ion of the model described i n Chapter 3 is given by Proposi t ion 3 (See Table 4.6): for low-value firms {p < p' or p < p*), the level of retention necessary for ' O n e firm was removed from the short retention group because of error in the data. '"Regressions using the issue price to measure firm value and including only the firms for which the trading price is available yield estimates for 1^2 of 12.44, 4.10, and 4.67 for the short, long voluntary, and long mandatory retention subsamples, respectively. Table 4.5: Scaled regression of f i rm value on ownership retention signal (Vj/Kj) = (/?o + + P2iàj/Kj) + iu,/Kj) where Vj is the market value of equity, Kj is the book value of equity, and â is the retention signal. Estimates (t-values) Retention period Short Long Long Voluntary Mandatory Panel A: F i r m s valued at issue price Sample size 126 197 140 Intercept 3.331 2.937 2.611 (21.961)" (20.027)° (16.813)' Signal 0.884 2.261 3.061 (0.679) (3.403)" (3.805)" Panel B: F i r m s valued at closing price of th i rd day of t rading Sample size 78 69 31 Intercept 3.491 3.185 2.567 (13.487)" (13.025)" (6.704)" Signal 14.252 0.798 11.708 (3.135)" (0.301) (1.996)" "Significant at the 5% level or better. separation is lower for the long retention period than for the short one. Table 4.6: Summary of Propos i t ion 3 results F i r m value Low High p>X a{p,l)> a{p,2) a(p,l) < a{p,2) p<\ a{p,l) > a{p,2) a{p,2) For high-value f irms, either the retention level is higher for longer retention or short retention does not lead to separation. It must be noted that the value which separates low- from high-valued firms is not the same for /) > A and for p < X. In the first case, a l l firms can separate w i t h short retention but the retention level is lower w i t h long retention for firms wi th p < p', whereas i n the second, low-valued firms are those wi th p < p* for which separation is possible wi th short retention. W h i l e the theory indicates the existence of values of ^ that separates low-from high-value f irms, there is no pract ical way to identify those values for each f i rm, since they depend on some unobserved parameters. How to separate the sample on the basis of value is an empir ical question for which the answer has to be arbitrary. It is influenced by concerns for the power of the tests to be performed, and by the need to include only firms for which the relation holds. It is important to note that Propos i t ion 3 speaks only to mandatory commitment. The ordering of retention level holds only for firms that would choose a short retention period i f it were possible, i.e. those for which A < 1. Hence, the test must be based on comparisons between firms whose shareholders were permitted to retain some of their shares for a short period, and who chose to do so, and firms whose entrepreneurs were forced to a long retention p e r i o d . T h i s implies that the group who chose long retention voluntari ly must be excluded * ' T h e maintained hypothesis here is that fiims whose retention period is imposed by regulation would have from the comparisons. In comparing the retention level between short and long retention periods, one must be aware that factors other than retention period affect a. Propositions 1 and 2 (and the results of the tests in the previous section) suggest that a is also influenced by {p - p)/ba'^, p, and A. Since these variables are not directly observable, any attempt to control for them w i l l be imperfect at best. If it is assumed, as i n the previous section, that firm-specific risk varies with f irm size, matching the firms to be compared on firm value may help isolate the relationship between a and r, the length of the holding period. O f the 464 I P O firms, those w i t h long voluntary retention are dropped from the sample. The remaining 266 firms are divided into two subsamples according to the length of their retention period. The firms of these two subsamples are then matched by pairs on their market value. The result ing sample contains 71 pairs. The l imited sample size and the lack of normali ty in the data do not support the dis-t r ibut iona l assumptions underly ing parametric testing. Accordingly, a non-parametric M a n n -W h i t n e y U-test is used to investigate whether the retention level is lower for firms with long mandatory retention than for those wi th the m i n i m u m retention period. The first co lumn of Table 4.7 shows the results of this test. T h e long retention subsample does have a lower average retention level than the short retention group, but the difference is not significant. T h e result of a f-test is also shown, since this type of test is generally robust to deviations from distr ibut ional assumptions. Since the prediction of Proposi t ion 3 is for lower-valued firms, one should seek to el iminate high-valued firms from the test. T h e existence of p* and p' is based on the assumption that p and b<T^ are the same for a l l firms, which they are not i n reality. In this case, it is the value as expressed by {p- y^lba"^ that determines the l imi t between low- and high-value firms. The rat io of market to book value of equity (Vj/Kj) is hence used as a measure of value, as in chosen the minimum retention period, had the entrepreneurs had the choice. Since entrepreneurs can choose the time when they make an initial offering, some of them may have chosen to go public in 1981, knowing Rule 144 would impose a long retention period. " M a r k e t value is calculated by multiplying the number of shares outstanding after the issue by the issue price. Table 4.7: Tests of retention level for short vs. long mandatory retention period on subsamples matched on f irm value. Matched sample Retention period A l l firms Low value" High information' ' Short L o n g Short Long Short Long Sample size 71 pairs 31 pairs 7 pairs Retention leveF: M e a n 50.78 47.99 41.60 42.00 50.00 37.00 M e d i a n 50.00 46.52 43.17 41.58 43.27 40.86 2^statistic'' 0.881 0.070 0.000 (significance level) (19%) (47%) (50%) t-statistic^ 0.854 0.348 0.244 (significance level) (20%) (37%) (41%) "Subsample containing firms whose scaled value is below the sample's median. ''Subsample containing firms whose announcement price reaction is above the sample's median. ' In percentage. ' 'From one-tailed Mann-Whitney U - test. *From one-tailed t-test. Section 4.2, and only the lower half of the sample (those firms with values below the median) is retained in a second test. Th is decrease i n the sample size may have adverse effects on the power of the tests, but i t may also refine the test by inc luding in the sample only the firms for which the relationship should hold. The results in the second column of Table 4.7 are similar to those of the first test. Th i s may be due to lack of power of the test because of small sample size or because some "high-value" firms are included in the sample, thereby confounding the results. Table 4.6 points to a difference i n prediction based on the relative magnitudes of p and A. In order to refine the test, one can try to identify a proxy for the measure of f. Since this ratio is an indicator of the informativeness of information released about the long term value of the f irm and about the events that may change this value in the short term, it could be proxied by the price reaction to the firm's first earnings announcement following the issue. This reaction measures the market 's assessment of the informativeness of earnings. F i rms with high price reaction are considered by investors as having earnings which are useful in predicting their future cash flows. A s w i l l be emphasized i n the next section, the firms for which enough data is available to compute this variable are those that survived and have more chance of being i n the High Value cell of Table 4.6.^'' The th i rd column of Table 4.7 reveals a higher average retention level for short retention, but again the difference is not significant. It also highlights the fact that the returns data necessary to compute price reactions is available for very few long mandatory retention f irms, reflecting the fact that it is available mostly for the larger firms. ' ' T h e price reaction to earnings announcement is computed as the absolute value of coefficient 72^ in regression Rjt = 70j + lljRMt + 72j*jt + i]t, where Rjt is the stock return for firm j on day t, RMI is the market return on day t, and Sj, = 1 for the two days in the announcement window and 0 otherwise. A better measure of investors' assessment of the informativeness of earnings would be the earnings response coefficients ( E R C ) but, as explained in section 4.5, it was not possible to compute them for this sample. ' * T h e average market value of all firms for which reaction coefficients could not be computed is $21.8 million while it is $29.9 million for firms for which the information is available. A parametric test on the means yields a t-statistic of -2.1, which is significant at the 2% level. 4.4 Association between F i r m Value and Length of Retention Period Proposit ion 5 shows that there are conditions under which short retention is preferred and others under which long retention is preferred. Table 4.8 summarizes these conditions. If A and Table 4.8: Summary of conditions for choice of retention period F i r m value Length of retention period Low High p< X<1 Short Long p < 1 < A Long Long p > A Short Short p were observable, the choice between long and short retention could be tested for high versus low value, for those firms wi th p < A < 1. (4.3) Unfortunately, they are not observable and one has to make some assumptions i n order to test this impl i cat ion of the model . If one assumes that the firms for which (4.3) holds are the major i ty i n the I P O market , one would expect that , on average, low-valued firms would choose short retention and high-valued firms, long retention. Th is appears to be contradicted by the descriptive statistics of Table 4.4, however. Propos i t ion 5 makes predictions about the choice of retention period when the entrepreneur has the choice. It is best tested on firms that chose short and long holding periods, excluding the long mandatory retention firms. The maintained assumption here is that a l l firms that have longer holding periods i n compliance w i t h Ru le 144 would have preferred short retention, had they had the choice. Some of the firms wi th long mandatory retention may have chosen to go public at this part icular t ime, knowing about the retention regulations, and could then be considered as having chosen long retention. Others may have been constrained to make an issue in 1981 because of an investment project that could not be postponed. These cannot be considered as having chosen long retention. Since it is not possible to distinguish between the two types of f irms, a l l firms with a retention period imposed by Rule 144 that is longer than their voluntary retention period are first excluded from the sample. Alternat ively , one might consider that the long retention imposed by regulation is , in fact, the m i n i m u m retention period defined i n Chapter 3 as r = 1. The "short retention" firms would then include the long mandatory firms. T h i s approach is taken i n some of the tests in this section. One can also consider that most of the long mandatory retention firms really chose their issue date and, thus, are part of the long voluntary retention subsample. Th i s t h i r d alternative assumption is also included i n the tests to follow. Whatever the assumption made about the group of long mandatory retention firms as a whole, the inclusion of the group in the long or short retention subsample is arbitrary , given that the choice of issue date is left to the firm and that the reasons for this choice by ind iv idua l firms are not observable. The result presented in Propos i t ion 5 is based on the assumption that p and b a'^ are the same for al l f irms. Th is assumption does not hold in the empir ical domain , however. In these circumstances, the prediction is that f i rm value as defined by {p- p)lba'^ is lower for firms who prefer short to long retention period. Since, as mentioned earlier, p and ba'^ are not observable, efforts must be made to isolate the variat ion i n firm size that is l inked to the length of retention from the effects of these variables. T w o procedures are used to that effect. The first consists i n scaling the market value of each firm by the book value of its equity, comparing the averages of Vj/Kj between short and long retention subsamples i n an attempt to measure the extent to which p exceeds fi. The second approach is to match firms to be compared on the book value of total prior assets. If firm-specific risk is related to the size of pr ior assets, this could control for its effect on firm value. It must be emphasized that either of these procedures is only a very rough attempt at control l ing for unobservable variables that affect the relation under study. 4.4.1 Scaled F i r m Values In this first section, the comparison of scaled f irm values is made between short and long reten-tion firm subsamples using each of the three assumptions regarding long mandatory retention mentioned earlier. The firms with long mandatory retention are first dropped completely. There are 323 firms remaining, 126 w i t h short and 198 w i t h long retention periods. The comparisons are made wi th both M a n n - W h i t n e y U-test and i-test, as i n the previous section. The results are presented i n the first two columns of Table 4.9. Table 4.9: Tests of scaled f irm value for short vs. long voluntary retention period Sample Retention period A l l firms Low informat ion" Short Long Short Long Sample size 126 198 32 32 Scaled f irm value'': M e a n 3.388 3.330 3.816 3.361 Med ian 3.272 2.692 3.355 2.986 z-statistic'^ 2.846 1.443 (significance level) (< 1%) (8%) f-statistic ' ' 0.221 1.106 (significance level) (42%) (14%) "Subsample containing firms whose price reactions to earnings announcements are below the sample's median. ' 'Ratio of market to book value of equity after the issue. ' F r o m one-tailed Mann-Whitney U - test. ' 'From one-tailed t-test, The average value is higher for short retention firms, which is contrary to the prediction, and the M a n n - W h i t n e y test detects a highly significant difference, while the parametric test does not. It must be emphasized that in this test, the maintained assumption is that (4.3) characterizes most of the firms i n the sample. T h e results discussed above may be due to the fact that this is not the case. In order to refine the test, the price reaction to the first earnings announcement following the issue is used as a proxy for ^, as i n the previous section. F i rms with a low price reaction can be assumed to be those wi th low ^. There remains the problem of knowing whether A is higher or lower than 1. If there are only a few firms for which it is higher in the market , the test could detect the difference in preference for retention period for low and high value firms. If they are numerous, they w i l l confound the results, since a l l firms wi th A > 1 choose long commitment . The t h i r d and fourth columns of Table 4.9 s t i l l show a higher value for short retention firms, on average, but the difference is non significant for both tests, although it is near significance for the non-parametric test. T h e absence of support for the theory may be due to the presence of many firms w i t h A > 1 i n the sample or to a selection bias. O f the 464 firms contained i n the or iginal sample, only 160 have sufficient data to allow computation of price reactions to the first earnings announcement. These are the firms for which a secondary market developed after the issue and which were considered important enough for the Wall Street Journal to report their earnings announcements. Hence the firms included in the low information subsample are not those w i t h the lowest announcement reactions i n the market . They probably have some of the highest. The same comparisons are made wi th the maintained assumption that the firms in the long mandatory subsample would have chosen the short period had they had the choice and , thus, are at their m i n i m u m retention per iod . Hence, they are included i n the short retention subsample and the comparison is between m i n i m u m retention period and long voluntary retention. T h i s implies that aU 464 firms are included i n the test, which increases the number of degrees of freedom, while potential ly introducing noise into the relationship under study. The results are presented i n Table 4.10. Table 4.10: Tests of scaled firm value for m i n i m u m vs. long retention periods Sample Retention period A l l firms Low information" Short Long Short Long Sample size 266 198 47 33 Scaled firm value**: M e a n 3.146 3.330 3.602 3.392 M e d i a n 2.833 2.692 3.355 3.083 2-statistic'^ 0.918 0.977 (significance level) (18%) (16%) <-statistic'^ -0.742 0.602 (significance level) (28%) (27%) "Subsample containing firms whose price reactions to earnings announcements are below the sample's median. ' 'Ratio of market to book value of equity after the issue. ' F r o m one-tailed Mann-Whitney U - test. ""From one-tailed t-test. Although the average value is lower for firms wi th the m i n i m u m retention period wi th the ful l sample and higher wi th the low information subsample, none of the two tests detects a significant difference. The t h i r d alternative assumption, which is contrary to the previous one, is that firms in the long mandatory chose their issue date knowing that Rule 144 would impose a long retention period on them. They are thus considered as having chosen long retention. This assumption also allows the inclusion of a l l 464 firms i n the test, the results of which are in Table 4.11. They are very s imilar to the results of comparisons excluding long mandatory retention firms Table 4.11: Tests of scaled f irm value for short vs. long retention period Sample Low A l l firms information" Retention period Short Long Short Long Sample size 126 338 34 46 Scaled firm value*: M e a n 3.388 3.163 3.749 3.343 M e d i a n 3.272 2.571 3.355 3.129 z-statistic= 3.565 1.241 (significance level) (< 1%) (11%) t-statistic'^ 1.159 1.174 (significance level) (12%) (12%) "Subsample containing firms whose price reaction to earnings an-nouncements are below the sample's median. *Ratio of market to book value of equity after the issue. •^From one-tailed Mann-Whitney U - test. ' 'From one-tailed t-test. (Table 4.9).The non-parametric test detects a significantly higher value for short retention firms when al l are included while the parametric test finds no significant difference. 4.4.2 M a t c h e d Samples The second approach to control for variations in firm value not related to diff'erences in retention periods is to compare subsamples of firms matched on total assets i n place. The objective of this approach is to obtain two subsamples w i t h s imilar distributions of risk measures (ba^). Hence, a comparison of scaled firm values for the two sets of firms may be a reasonable proxy for the comparison of (p — p)/ba'^. Only two of the three alternative assumptions regarding choice of retention period are used in this section. Table 4.12 presents the results of the parametric and non-parametric comparisons of scaled firm values between short and long voluntary retention, i n Panel A , and between short and long retention, i n Panel B . M a t c h i n g was done i n two stages. The long voluntary retention firms were matched pairwise wi th short retention firms. T h e same procedure was followed wi th long mandatory and short retention firms. Some of the short retention firms were thus matched wi th one long mandatory and one long voluntary retention firms. T h e two matched subsamples (mandatory and volun-tary) were then combined, e l iminat ing the redundancies in the short retention firms. Th i s leads to a fu l l sample containing 99 short retention and 151 long retention firms, and a low informa-tion sample wi th 21 and 28 firms. A l t h o u g h the resulting subsamples are not matched by pairs and are unbalanced, this methodology allows to retain a greater number of observations than the usual pairwise matching techniques. W h e n only the long voluntary commitments are included (Pane l A ) , the differences i n average scaled values is i n the direction predicted by Propos i t ion 5 but the results of the M a n n - W h i t n e y and <-tests contradict each other. W h i l e the parametric test shows an almost significant difference i n the predicted direction wi th the ful l sample, the non-parametric test detects a non-significant difference i n the opposite direction. For the low information subsample, the average firm value is higher for short retention but the difference is not significant. W h e n Table 4.12: Tests of scaled f irm value for short vs. long retention pe-r iod on subsamples matched on total prior assets Matched sample Low A l l firms information" Retention period Short Long Short Long Panel A: Short vs. long voluntary retention periods Sample size 90 90 18 18 Scaled firm value:'' M e a n 3.227 3.926 3.617 3.588 Med ian 3.055 2.837 3.189 3.182 z-statistic^ 0.622 0.427 (significance level) (27%) (34%) ^-statistic' ' -1.417 0.053 (significance level) (8%) (48%) Panel B: Short vs. long retention periods Sample size 99 151 21 28 Scaled f i rm value:^^ M e a n 3.277 3.506 3.424 3.408 M e d i a n 3.077 2.768 3.090 3.182 z-statistici2 ^ 590 o . l31 (significance level) (6%) (45%) t-statistic^^ -0.709 0.038 (significance level) (24%) (49%) "Subsample containing firms whose announcement price reaction is below the sample's median. ' 'Ratio of market to book value of firm equity after issue. ' F r o m one-tailed Mann-Whitney U - test. ' 'From one-tailed *-test. the long mandatory retention firms are inc luded, the average scaled value is essentially equal for the two subsamples when considering only low information firms, while it is lower for short retention firms i n the ful l sample. Here again there is a contradiction between the results of the parametric and non-parametric tests. The M a n n - W h i t n e y test even detects a difference that is not only contrary to the prediction of Propos i t ion 5, but almost significantly so for the ful l sample, as is the case in Table 4.11. It must be noted that the descriptive statistics for the whole sample given in Table 4.4 indicate significantly higher average value for firms wi th short retention periods. T h i s , combined with the results obtained in this section suggests that firms for which /> < A < 1 are not very influential on the I P O market and that al l the previous attempts have been ineffective in isolating them. 4.5 Association between Time-Series Behaviour of Earnings and Ownership Re -tention P e r i o d . Earnings announcements often provide the single most important piece of information released by firms about their performance. Earnings are also considered by investors to be reliable because of the involvement of auditors i n their measurement. They may thus be a good proxy for the information signal y released at the end of the first per iod , in the model presented in Chapter 3. It was shown i n Corol lary 3 that i f the outcomes from the investment project are independent across periods, Two-Per iod retention is a dominant strategy, even for entrepreneurs who can separate w i t h the m i n i m u m retention period allowed. Coro l lary 4 shows, on the other hand, that i f the outcomes foUow a M a r k o v process, One-Per iod retention is a dominant strategy for a l l entrepreneurs. T h i s suggests that firms wi th outcomes following a Markov process would choose the shortest retention per iod allowed by regulations whereas firms wi th independent outcomes would choose long commitment . Unfortunately, the time-series behaviour of outcomes for I P O firms are difficult to determine because of the lack of historical data . Even using ex post quarterly data to estimate the time-series behaviour of earnings before the issue leads to problems, since few firms survive long enough to allow such an estimation.^"* The work of Col l ins and K o t h a r i (1989) and Easton and Zmijewski (1989) may provide a solution to this problem, however. B o t h studies find a l ink between f irms' earnings persistence and earnings response coefficients. W h e n a firm's earnings have a large permanent component, i.e. when they are close to a Markov process, the earnings response coefficient is large. Th i s result suggests that one could use earnings response coefficients as proxies for time-series be-haviour of earnings i n a test of Corollaries 3 and 4. A test of the association of E R C and retention period length would also be a test of Proposi t ion 5, as Table 4.8 suggests. F i rms with p > X are firms whose financial reports are very informative about their value. They should then have high E R C s . Propos i t ion 5 then suggests that firms wi th high stock price reaction to their earnings announcements choose short retention, and those whose earnings are not very informative about their value choose long retention periods. 4.5.1 Earnings Response Coefficients Earnings response coefficients measure the market 's reaction to unexpected earnings when they are disclosed by a f i rm. In order to compute these coefficients, one must measure unexpected earnings, which are not directly observable. Easton and Zmijewski (1989) note that , ideally, unexpected earnings should be measured as the difference between actual earnings and the market 's expectation of these earnings just before announcement, and that no other information should be released at the time of announcement. In practice, this data is not observable and proxies suffer from measurement error and omitted variables. M a n y proxies have been suggested i n the l iterature but the measure that seems to have given the best results is analysts ' forecast errors. Unfortunately, I P O firms are not followed by analysts and this measure is not available '* A cursory investigation suggests that less than 15% of the 464 firms in the sample were still listed in Moody's Industrial Manuals in 1991. The others had been merged into other companies or had disappeared one way or another. for the tests to be performed here. The only measure of expected earnings that is observable for some of the new firms is the previous period earnings number, which only allows use of a univariate mechanical forecasting model . Univariate models are l ikely to induce spurious correlation. Because of the great difference i n the number of shares outstanding between the previous period (before the issue) and the announcement period (after the issue), earnings per share ( E P S ) were collected from Moody ' s OTC Industrial Manual for both periods and unexpected earnings were calculated as the difference between current and previous E P S . The E P S numbers were deflated by the value of a share, to put the unexpected earnings measure on a common footing across firms of differing size. Gr inb lat t and Hwang (1989), among others, show that underpric ing of I P O s is important , but that the market price of newly issued shares adjusts quickly, so that it reflects their true value after only three days of t rad ing . In order to take underpric ing of I P O s into account, the closing price on the t h i r d day of t rading after the issue was used as the measure of share value. The earnings response coefficients were finally computed by an O L S regression of the form for each firm j, where Rjt is the stock return for the firm on day t, RMI is the value-weighted market return from the C R S P Tape, EPSjy is earnings per share for year y, Pj is the share price, êjt is equal to 1 on the date of the announcement and the preceding trading day and 0 otherwise, and f32j is the earnings response coefficient. For the first yearend earnings announcements, E P S data was unavailable for 34 firms, which left 163 firms for which E R C s could be computed. In the first announcement sample, previ-ous years' quarterly earnings were available for very few firms other than those whose first announcement was for annual earnings and which were included i n the other sample. It was thus impossible to compute earnings response coefficients for the first earnings announcements after the issue. The fact that the sample comprises firms that just went public complicates the measurement (4.4) of E R C s even further. The advent of an i n i t i a l public offering usually brings a change in the earnings generating process of a f i rm. The use of a univariate time-series model to measure unexpected earnings may be even more inadequate than for other firms. If the firm is formed a few months before the issue, as is often the case, the previous year's earnings number represents only pre-operations transactions and is inadequate as a proxy for the market's expectation of future earnings. The combination of the problems described above lead to anomalous results in the empirical analysis of the sample employed here. A lmost half of the E R C s computed for the first annual earnings announcements were negative and the estimates for /32j varied from -44.0 to -f-80.0. These extreme values would mean that each dollar of unexpected earnings per share brought a decrease of 44 dollars i n the price of the first f irm and an increase of 80 dollars for the second. In order to avoid inval idat ing the other analysis on the data set, the E R C estimates were el iminated from the tests. 4.5.2 Alternative React ion Measures In view of the failure i n est imating E R C s , alternative measures of market reaction to earnings announcements, suggested i n the l i terature, were computed for both first earnings announce-ments and first yearend announcements: raw returns over the two-day event window; excess returns, the difference between the firm's raw returns and market return over the two days; abnormal returns, the residuals of the market model regression summed over the two days; and announcement reaction coefficients, the coefficient of 6j i n Rjt = iQj + luRMt + 'f2j6jt + (jt (4.5) where variables are defined as i n (4.4). Th i s choice of measures is part ly based on B r o w n and Warner [1985] who show, w i t h simulations, that cruder measures like mean-adjusted returns and market-adjusted returns perform just as well as market model adjusted returns in detecting market reactions to specific events. Th i s is especially true wi th non-synchronous trading which part icular ly affects newly issued over-the-counter shares. Absolute values were used since the magnitude of the reaction, rather than its direction, is the measure of interest here. For both sets of f irms, those wi th a first earnings announcement date and those wi th a first yearend announcement, firms with long mandatory retention were dropped to l imit the noise introduced in the test. Each sample was split i n two subsamples, according to retention period and the firms of the subsamples were matched on market value of equity, measured by the issue price. B o t h announcements were used because the set of first announcements has fewer observations than the set of first yearend announcements, but the event is closer in calendar time to the issue and phenomena of information dissemination may be easier to detect at that time than later. O n the other hand, results of the new investment project may not yet appear i n f inancial statements produced a few months only after the issue. They have more chance of being included i n a later earnings number. Table 4.13 shows the comparison of the various market reaction measures between short and long voluntary retention periods, for the first earnings announcements following the pr imary issue. A g a i n , M a n n - W h i t n e y U-test and f-test were used, since the distr ibution assumptions underlying parametric tests do not seem to be supported by the data . Average price reactions i n Table 4.13 are lower for short retention firms but the contradiction between the results of M a n n - W h i t n e y and t-tests suggest that there are no significant differences in market reaction to earnings between firms wi th long and short retention periods. Table 4.14 presents the results of the same tests performed on the sample of first yearend announcements. Here a l l measures show a larger average reaction for firms with shorter re-tention per iod , but the difference between the subsamples are not significant, although both parametric and non-parametric tests agree on the direction of the difference.. In an effort to increase the power of the test, the firms w i t h long mandatory retention were added to the long retention subsample, i n the same manner as i n Section 4.4. Th is does nothing to ameliorate the results for the yearend announcements (see Table 4.16) and the firms that do not have long retention periods by choice seem to only increase the noise in the data . For the Table 4.13: Tests of price reaction to the first earnings announcement following the issue for short vs. long voluntary retention per iod . (80 firms matched on marliet value of equity) Pr ice reaction measure Retention period Short Long z-statistic" t- statistic*" (significance level) Announcement React ion CoeflRcient: |72j|'^  M e a n M e d i a n 0.0211 0.0131 0.0230 0.0238 0.351 (36%) -0.340 (37%) A b n o r m a l Returns : \uj\'^ Mean 0.0410 0.0448 Med ian 0.0256 0.0122 0.371 (36%) -0.347 (37%) Excess Returns : \Rj - RM\ M e a n Med ian 0.0430 0.0241 0.0485 0.0270 -0.183 (43%) -0.450 (33%) R a w Returns : \Rj\ M e a n M e d i a n 0.0413 0.0286 0.0433 0.0307 0.000 (50%) -0.158 (44%) " F r o m one-tailed Mann-Whitney U-test. ' 'From one-tailed <-test. 'Coefficient from regression Rjt = 7o> -I- 7 I J ^ M « -I- 72j*jt + £jt. ' 'Sum over announcement twro-day window of residuals from regression R,t = oi]+ PjRut -¥uj,. Table 4.14: Tests of price reaction to the first annual earnings announcement following the issue for short vs. long voluntary retention period on subsamples matched on f irm value (108 firms matched on market value of equity) Price reaction measure Retention period Short Long ^-statistic" ^-statistic*" (significance level) Announcement Reaction Coefficient: |72j|= M e a n Med ian 0.025 0.014 0.024 0.011 0.489 (31%) 0.179 (43%) A b n o r m a l Returns : \uj\'^ M e a n Med ian 0.048 0.026 0.046 0.022 0.519 (30%) 0.156 (44%) Excess Returns : \Rj - RM\ M e a n M e d i a n 0.051 0.031 0.048 0.021 0.550 (29%) 0.306 (38%) R a w Returns : \Rj\ M e a n Med ian 0.050 0.027 0.045 0.024 0.213 (42%) 0.376 (35%) " F r o m one-tailed M a n n - Whitney U-test. ""From one- tailed t-test. 'Coefficient from regression Rjt = joj + lijRMt + Taj^jt + tjt-' 'Sum of the residuab over the announcement two-day window from regression Rjt = a J + 0jRMt + tijt. Table 4.15: Tests of price reaction to the first earnings announcement following the issue for short vs. long retention period on subsamples matched on market value of equity. Price reaction Retention period ^-statistic" t- statistic*" measure Short Long (significance level) Sample size 47 65 Announcement React ion Coefficient: |72j|'^  Mean 0.020 0.029 -1.333 -1.800 Median 0.012 0.019 (9%) (4%) A b n o r m a l Returns : \uj\'^ Mean 0.038 0.057 -1.327 -1.677 Median 0.023 0.038 (9%) (5%) Excess Returns : \Rj - RM\ Mean 0.041 0.060 -1.418 -1.739 M e d i a n 0.024 0.041 (8%) (4%) R a w Returns : \Rj\ M e a n 0.039 0.058 -1.408 -1.636 Med ian 0.029 0.045 (8%) (5%) " F i o n i one-tailed Mann-Whitney U-test. ' 'From one-tailed ^test. 'Coefficient from regression Rjt = yoj + 1\jRMt + T2j*jt -I- (jt-' 'Sum over announcement two-day window of residuals from regression R,t = -(- ^JRMI + « j t -first announcement after the issue however, average price reaction is lower for short retention for al l measures of reaction, and the differences are close to significance. 4.6 Conclusion Three implications derived from the model developed in Chapter 3 have been tested here. These implications pertain to the relations between ownership retention level and length of retention per iod , between firm value and length of retention period, and between the time-series behaviour of earnings and retention period. A comparison of average retention level between short and long mandatory retention shows it to be higher for short retention as predicted by Proposit ion 3. The differences were not significant, however. The hypothesized relation between firm value and retention period is not supported by the tests performed. In most of them, the mean value was marginal ly higher for short retention firms, except when only voluntary commitment firms were matched on prior assets, i n which case it was marginal ly lower for short retention firms. Us ing various measures of price reaction to earnings announcements as measure of t ime-series behaviour of earnings, the comparison between short and long retention firms yields an ordering that is consistent w i t h the prediction for yearend announcements, when the long mandatory retention firms are excluded from the test. However, the ordering is reversed for first announcements following the issue when mandatory long retention firms are included. In al l cases, the differences are only marg ina l . T h e results presented i n Chapter 3, being very detailed and involving a large number of possible strategies, are difficult to test empirical ly because the difference between the situations that lead to these strategies are not observable ex post. One cannot dist inguish, for example, between firms that chose to make an issue while Rule 144 st i l l restricted t rad ing on their shares on the secondary market and firms that would have preferred short retention, had they had the choice. B o t h types of firms are observed as having made an issue while under restrictions of Ru le 144. Table 4.16: Tests of price reaction to the first annual earnings announcement following the issue for short vs. long retention period on subsamples matched on firm value. Price reaction measure Retention period Short Long ^-statistic" t-(significance statistic*" level) Sample size 58 80 Announcement Reaction Coefficient: |72j|'^  Mean Median 0.023 0.013 0.026 0.014 -0.080 (47%) -0.551 (29%) A b n o r m a l Returns : M e a n Med ian 0.045 0.025 0.051 0.026 -0.041 (48%) -0.580 (28%) Excess Returns : \Rj - RM\ M e a n Median 0.049 0.029 0.055 0.029 -0.252 (40%) -0.516 (30%) R a w Returns : \Rj\ M e a n Median 0.047 0.023 0.053 0.040 -0.583 (28%) -0.510 (31%) " F r o m one-tailed Mann-Whitney U-test. •"From one-tailed t-test. 'Coefficient from regression Rft = to, + HIRM* •\- lijSjt + (,f ' 'Sum of the residuals over the announcement two-day window from regression Rjt = oj -|-^jRut + The lack of available data typical of newly public firms is another factor affecting the pre-ceding tests. W h i l e i n i t i a l public offerings appear to be an appropriate population on which to study information dissemination, they are also a challenge because the researcher's information set is so l imi ted . Moreover, the firms for which there is more data available are different from the others in the I P O sample. A n y test involving data from periods beyond the issuance of the prospectus is affected by survivorship bias. The subtle signaling effects may also have been drowned i n the "hot issue" market of 1981. A l though none of the tests had results strong enough to reject the nul l hypotheses, the consistency i n the direction of the differences wi th predictions provides some support for i t . Given this consistency, i t may be worthwhile to seek refinements leading to more powerful tests. The use of a different set of pr imary offerings, outside of a "hot market" period could be another avenue for future research. Bibl iography [1] Albrecht , W . Steve, Larry L . Lookab i l l , and James C . M c K e o w n . 1977. The time-series properties of annual earnings. Journal of Accounting Research 15 (Autumn):226-244. [2] A l l e n , Frank l in and Gera ld R . Faulhaber. 1989. Signaling by underpricing in the I P O market. Journal of Financial Economics 23 (August) :303-323. [3] B a l l , Ray and Peter B r o w n . 1968. A n empir ical evaluation of accounting income numbers. Journal of Accounting Research 6:159-171. [4] B a n k s , Jeffrey S. and Joel Sobel . 1987. E q u i l i b r i u m selection i n signaling games. Econo-metrica 55 (May) :647-661. [5] B a r o n , D a v i d P. 1982. A model of the demand for investment banking advising and d is tr i -but ion services for new issues. Journal of Finance 37 (September):955-976. [6] B lackwel l , D a v i d . 1953. Equivalent comparisons of experiments. Annals of Mathematical Statistics 24 (June):265-273. [7] B r o w n , Lawrence D , , Robert L . Hagerman, and M a r k E . Zmijewski . 1987a. Security analyst superiority relative to univariate time-series models i n forecasting quarterly earnings. Journal of Accounting and Economics 9 (Apr i l : 61 -87 . [8] B r o w n , Lawrence D . , Robert L . Hagerman, and M a r k E . Zmijewski . 1987b. A n evaluation of alternative proxies for the market's assessment of unexpected earnings. Journal of Accounting and Economics 9 (July) :159-193. 9] B r o w n , Stephen J . and Jerold B . Warner. 1985. Us ing daily stock returns. The case of event studies. Journal of Financial Economics 14 (January) :3 -31 . [10] C h o , In -Koo and D a v i d Kreps . 1987. Signaling games and stable equi l ibr ia . Quarterly Journal of Economics 102 (May) :179-221. [11] C larkson , Peter. M . , A l e x Dontoh , Gordon Richardson, and Stephan E . Sefcik. 1991 Re-tained ownership and the valuation of i n i t i a l public offerings: Canadian evidence. Con-temporary Accounting Research 8 (Fall ) :115-131. [12] Co l l ins , Danie l W . and S.P. K o t h a r i . 1989. A n analysis of intertemporal and cross-sectional determinants of earnings response coefficients. Journal of Accounting Economics 11 (July)143-181. [13] Conroy, Robert and John S. Hughes. 1989. O n the observability of ownership retention by entrepreneurs wi th private information in the market for new issues. Contemporary Accounting Research 6 (Fall ) :159-176. [14] D a t a r , Shrikant M . , Gera ld A . Fe l tham, and John S. Hughes. 1991. T h e role of audits and audit quality i n valuing new issues. Journal of Accounting and Economics 14 ( M a r c h ) : 3 -49. [15] Downes, D a v i d H . and Robert Heinkel . 1982. Signaling and the valuation of unseasoned new issues. Journal of Finance 37 ( M a r c h ) : l - 1 0 . [16] E a s t o n , Peter D . and M a r k E . Zmi jewski . 1989 Cross-sectional variation i n the stock market response to accounting earnings announcements. Journal of Accounting and Economics 11 (July) :117-141. [17] F e l t h a m , Gera ld A . and John S. Hughes. 1988. Communicat ion of private information i n capi ta l markets: Contingent contracts and verified reports. In Economic Analysis of Information and Contracts: Essays in Honor of John E. Butterworth, ed. A m i n A m e r s h i and W i l l i a m Ziemba. Boston : K l u w e r Nijhoff Pub l i sh ing . [18] F e l t h a m , Gera ld A . , John S. Hughes, and D a n A . Simunic . 1991. E m p i r i c a l assessment of the impact of auditor qual ity on the valuation of new issues. Journal of Accounting and Economics 14 (December):375-399. [19] Foster, George. 1977. Quarter ly accounting data : Time-series properties and predictive-abi l i ty results. The Accounting Review 52 ( J a n u a r y ) : l - 2 1 . [20] Frome, Robert L . and V i c t o r M . Rosenzweig. 1975. Sales of Securities by Corporate Insid-ers. New York : Prac t i s ing L a w Institute. [21] Ga le , Ian and St ig l i t z , Joseph E . 1989. The informational content of in i t ia l public offerings. Journal of Finance 44 (June):469-477. [22] G r i n b l a t t , M a r k and C h u a n Y a n g Hwang. 1989. Signal l ing and the pric ing of new issues. Journal of Finance 44 (June):393-420. [23] Hughes, John S. 1989. Discussion of " T h e valuation of i n i t i a l public offerings". Contempo-rary Accounting Research 5 (Spring):519-525. [24] Hughes, P a t r i c i a J . 1986. Signal l ing by direct disclosure under asymmetric information. Journal of Accounting and Economics 8 ( June ) : l 19-142. [25] Ibbotson, Roger G . 1975. Pr ice performance of common stock new issues. Journal of Fi-nancial Economics 2:235-272. [26] Imhoff, Eugene A . J r . and Gera ld J . Lobo . 1992. T h e effect of ex ante earnings uncertainty on earnings response coefficients. The Accounting Review 67 (Apri l ) :427-439. [27] Koh lberg , E l o n and Jean-François Mertens. 1986. O n the strategic stabil ity of equil ibria. Econometrica 54 (September):1003-1037. [28] K o r m e n d i , Roger and Robert L i p e . 1987. Earnings innovations, earnings persistence, and stock returns. Journal of Business 60:323-345. [29] K r i n s k y , I. and W . Rotenberg. 1989. The valuation of in i t i a l publ ic offerings. Contemporary Accounting Research 5 (Spring):501-515. [30] L e l a n d , Hayne E . and D a v i d H . Py le . 1977. Informational asymmetries, financial structure, and financial intermediat ion. Journal of Finance 32 (May) :371-387. [31] L e v , Baruch . 1983. Some economic determinants of time-series properties of earnings. Jour-nal of Accounting and Economics 5 (Apr i l ) :31 -48 . [32] Moody ' s Investors Service. 1981-83. Moody's OTC Industrial Manual. New Yor l c Moody 's Investors Service. [33] Muscare l la , Chr i s J . and Michae l R . Vetsuypens. 1989. A simple test of Baron's model of I P O underpric ing. Journal of Financial Economics 24 (September):125-135. [34] N a n d a , V i k r a m . 1988. W h y firms go publ ic . W o r k i n g paper. Graduate School of Business, Univers i ty of Chicago. [35] O 'F laherty , Joseph S. 1984. Going Public: The Entrepreneur's Guide. New York: John W i l e y & Sons. [36] Ri ley , John G . 1979. Informational equi l ibr ium. Econometrica 47 (March) :331-359. [37] R i t t e r , Jay R . 1984a. Signaling and the valuation of unseasoned new issues: A comment. Journal of Finance 39 (September):1231-1237. [38] R i t t e r , Jay R . 1984b. T h e " H o t issue" market of 1980. Journal of Business 57:215-240. [39] R i t t e r , Jay R . 1991 The long-run performance of i n i t i a l public offerings. Journal of Finance 46 (March) :3 -27 . [40] R i t t e r , Jay. 1984. Signal ing and the valuation of unseasoned new issues: A comment. Journal of Finance 39 (September):1231-1237. [41] Rothsch i ld , M . and Joseph E . St ig l i tz . 1976. E q u i l i b r i u m i n competitive insurance markets: A n essay on the economics of imperfect information. Quarterly Journal of Economics 90:629-650. [42] S imunic , D a n A . and Michae l T . Ste in . 1987. Produce Differentiation in Auditing: Au-ditor Choice in the Market for Unseasoned New Issues. Vancouver: C G A Research Foundat ion . [43] Standard and Poor 's Corporat ion . 1981-83. Daily Stock Price Record OTC. New York: Standard and Poor 's Corporat ion . [44] T i t m a n , Sheridan and Brett Trueman. 1986. Information quality and the valuation of new issues. Journal of Accounting and Economics 8 (June):159-172. [45] Welch, Ivo. 1989. Seasoned offerings, imi tat ion costs, and the underpricing of in i t ia l public offerings. Journal of Finance 44 (June):421-449. [46] W i l s o n , C . 1977. A model of insurance markets wi th incomplete information. Journal of Economic Theory 16:167-207. [47] W i n t e r , E lmer L . 1972. Complete Guide to Making a Public Stock Offering. Englewood Clif fs :Prentice H a l l . A p p e n d i x A List of Variables z = {P,a,p) = Contract offered by the entrepreneur in the prospectus. P = Issuing price. at — Percentage of the firm's shares retained by entrepreneur in period t. at{p) = O p t i m a l level of under-diversification at t for entrepreneur wi th f irm of value p. a{p,T) = O p t i m a l retention level for entrepreneur wi th f irm of value p, i f the length of the retention per iod is r . p = Probab i l i ty of exogenous revelation of f irm value at ti. z{p,T,p) = O p t i m a l l inear separating contract to be offered by entrepreneur wi th a f irm of value p for retention period r , i f the probabi l i ty of exogenous revelation is p. ZQ = " N u l l " contract i n which the entrepreneur retains a l l her firm's shares and the project is financed by debt. p = F i r m ' s value at <0) used to characterize f irm type. ^ = Lowest possible f i rm value. d{z) = Probab i l i ty that investors wiU reject z. K = Investment necessary for the firm to undertake the project. il)t = Information reported at t about the project outcome for the preceding period. y = Representation of the information reported at ti.. X = Terminal value of the project at the end of the longest retention period. W2 = Entrepreneur's wealth at ^2-Lis t of Variables (continued) b Entrepreneur's risk aversion measure. X = Measure of j/'s informativeness about p. P = Corre lat ion between y and x. H-) = Dist r ibut i on function. Vt{-) F i r m value inferred by investors from information revealed at or before t. Uiz,p,d) Entrepreneur's expected ut i l i ty function. Biz,p,d) = Investors' expected ut i l i ty function. H = Set of a l l possible f i rm values in the economy. H{z) Set of f i rm types whose owner would weakly prefer offering contract z to offering their opt imal contract2(/i). H'{z) = T y p e of f irm whose owner would be most l ikely to offer contract z in preference to opt imal contract p. u{z,p) — M i n i m u m probabi l i ty of rejection of contract z by investors that would deter entrepreneur wi th f irm of type p from offering i t . A p p e n d i x B Proofs B . l Proposit ion 1 L e m m a 1 There exists a separating solution to maximization problem (3.8). Proof: The first-order condit ion for tlxe maximizat ion of (3.8) is: {l-a)p'{z) + p-p{z)-b(T^a = 0. ( B . l ) Including equi l ibr ium condition (3.7) into ( B . l ) yields p'(z) = bcT'j^. (B.2) For the solution of this differential equation, a boundary condit ion must be determined. E n -trepreneurs w i t h projects of the lowest qual ity have nothing to gain by bearing risk since investors are always wi l l ing to purchase shares at a price of /£ or less. Hence it can be assumed that / x ( P , 0 ) = £ V P . (B.3) The solution to (B.2) is then p{z) = -b(7^a+lnil-a)] + p (B.4) and the opt imal level of retained ownership for a f irm of type p is given by a{p) + ln[l-aip)] = ^ . (B.5) The opt imized level of expected ut i l i ty is derived from (B.4 ) , (B.5) , and (3.8): U{z{p),p) = p - K - l ba'a\p). (B.6) 87 It must be verified that this solution leads to separation of types. Th is is done by totally differentiating (B.5) . ^ = ( i ^ > 0 V O < a < l (B.7) dp aba^ ^ ' Hence the signal is increasing in type, allowing investors to correctly infer the type of any firm from the number of shares offered i n the prospectus. It is also decreasing in firm-specific rislc: dcr^ aba'^ ^ ' The situation specific to each firm depends on the value of ^ , p, b, and cr^ characterizing i t . It is important to ensure that a l l firms have access to the opt imal signaling strategy. For an entrepreneur to succeed i n separating w i t h Two-Per i od Commitment , there must exist an a between zero and one for which (B.5) holds. Such a level of ownership exists if, and only if, 0 + l n ( l ) > > 1 + ln(0) 0 < ^ ^ < o o . (B.9) The first inequality i n (B.9) holds for a l l firms since £ is the lowest type. The second holds i f neither the entrepreneur's risk aversion nor the project variance is zero. Hence, al l games with the structure assumed here can lead to a separating equi l ibr ium. Q.E.D. It remains to be shown that this solution leads to a unique stable equi l ibr ium. It is necessary to first define certain types of contracts that can be offered by entrepreneurs. z = ( P , a ) = Contract by which an entrepreneur offers (1 - a) of her firm's shares for a price P} z{p) = (p, a{p)) = O p t i m a l contract for firm of type p. ZQ = T h e null contract by which the entrepreneur retains a l l of her firm's shares ( a = 1). * P is defined as the price for the whole firm. Acceptation of z by investors will generate proceeds of (1 — a) P. In order to keep the following analysis as clear as possible, further variable definitions w i l l prove useful. The entrepreneur's and the investor's expected ut i l i ty functions are denoted, respectively, U{z, p,d) = Uiz, p)(l - diz)) + Uizo, p)d{z) (B.IO) and B{z,p,d) = {l-a){p-P){l-d{z)). The following definitions w i l l also be used i n subsequent proofs: H = [p,p] H{z) = {p\U{z,p)>U{z{p),p),peH} ( B . l l ) (B.12) (B.13) i^iz,p) = u'iz) = H*{z) ^ 0 otherwise max u(z, p) arg max i^{z, p) d\z) (B.14) (B.15) (B.16) (B.17) = 0 i f 2 = z{p) for some p £ H, oi iî P < p 6 [u'(z), 1] i f z # z{p) e and \f P > p The objective is to determine whether [z{p), d*{z)] is a stable equi l ibr ium for the invest-ment game given by (3.8). T h i s set of strategies is one where a l l entrepreneurs offer the opt imal contract z{p) = {p, a ( / i ) ) , given their type p, and investors accept such contracts w i th proba-b i l i ty (1 - d*{z)). The set H{z) defined i n (B.13) is the set of types who would weakly prefer off-equilibrium contract z to their separating contract z{p). u{z, p) is the m i n i m u m rejection probabi l i ty which would deter a firm of type p from oflfering contract z. O f the types i n H{z), the most l ikely to oflfer contract z would be those w i t h the highest m i n i m u m rejection proba-bi l i ty viz). Hence H*{z) is the set of types which would benefit most by offering z instead of z{p), and thus would be the most l ikely to do so. In order to show that a set of strategies is part of a stable equi l ibr ium, one must first show that it is an equi l ibr ium. The definition of equi l ibr ium most often used in the signaling l iterature is that of a Nash equi l ibr ium. A set of strategies is said to be a Nash equi l ibr ium i f none of the players has any incentive to change his strategy, given that al l other players stick to theirs. Clear ly [z(p), d'(z)] as defined above is a Nash equi l ibr ium. Stabi l i ty as defined by Koh lberg and Mertens (1986) obtains i f investors' strategy d''{z) is rational when faced wi th an off-equilibrium contract z, considering the type most l ikely to be offering i t . L e m m a 2 gives an intermediate result needed to complete the stabil ity proof. L e m m a 2 u{z, p) is strictly concave in p and decreasing at p = P. Proof. From ( B . 1 4 ) we know that : where U{z,p) = {l-a)P-K+ ap-^ ba^a^ from (3.8) ( B . 1 9 ) U{z{p), p) = p - K - i b(T^ a^{p) from ( B . 6 ) Uizo,p) = p - K - ^ b ( T ^ . ( B . 2 0 ) Combin ing ut i l i ty functions ( B . 1 9 ) , ( B . 6 ) , and ( B . 2 0 ) w i th ( B . 1 8 ) yields i/(z, M) = 1 - Diz, p) ( B . 2 1 ) where D(., ,) . ^ ^ " ' ( ' - " ' W ) . ( B . 2 2 ) (1 - a) (P - ^) + 1 (.<,"(! - a^) In the following derivations, it is useful to remember that for any function of the form 9{x) f{x) = h{xy fix) = fix) 9\x)_h\x) gix) hix) The first derivative of i>{z, p) w i th respect to p is 2 1 i/^ (ar, p) = D{z, p) ba^{l + a{p)) ( P - + 1 6tr2( l + a) Evaluated at p = P, (B.23) becomes 2 2 (B.23) (B.24) .60-2(1+ a ( P ) ) 6^2(1+ û ) j ' Expression (B.24) is negative, since a < a{P). Indeed no entrepreneur, whatever her firm type, would prefer to hold more than a{P) to signal a firm value of p = P. The second derivative of v{z, p), is found by restating (B.23) as u^(z, p) = D{z, p)[F{p) - Giz, p)] which yields u,,{z, p) = Diz, p) [[F'ip) - G,{z, p)] - [F{p) - G{z, p)f) . (B.25) For any offer price P greater than the value of a firm of type p, (B.25) is negative i f [F'{p) — G^i{z, p)] is negative, since D{z, p) is positive for P > p. From (B.23) and (B.7) , and hence {/{z, p) is a str ict ly concave function. Q.E.D. P r o o f of Proposit ion 1 L e m m a 1 shows that a unique solution exists to the entrepreneur's decision problem (3.8), the opt imal level of ownership is given by (3.9), and the maximized expected ut i l i ty is given by (3.10). It now remains to be shown that this solution leads to a stable equi l ibr ium. Kohlberg and Mertens's (1986) stabi l i ty criterion has been chosen because the conditions it imposes on strategies and beliefs have intuit ive appeal. Moreover, several authors (Cho and Kreps (1987), Banks and Sobel (1987), and Datar , Fe l tham, and Hughes (1991), for example) have developed necessary and sufficient conditions for tii is type of stabil ity in signaling games. The proof uses Datar , Fe l tham, and Hughes's (1991) Proposi t ion C 2 : For a generic investment game, an equi l ibr ium is stable if, and only if, for unoffered contract z, either (a) H{z) = 0 or (b) P > p for some p e H*(z). If H{z) = 0 then there is no off -equil ibrium contract which is even weakly preferred to its opt imal contract by any f irm type. T h e equi l ibr ium is thus stable. If H{z) ^ 0 then there exists a contract z such that U(z,p) > U(z{p),p) ÎOT some p e H and H*(z) is the set of f i rm types which are most l ikely to move from their opt imal contract z{p) to contract z. L e m m a 2 shows that v{z,p) is str ict ly concave and hence has a unique m a x i m u m . Moreover, this m a x i m u m is attained for type p < P since i'{z,p) is decreasing at p = P. Hence, H*{z) contains only one f irm type p and its value is lower than the offer price P. Investors would always refuse contract z = (P,a) because i t would imp ly a negative expected return for them, given the f irm that is most l ikely to offer i t . Hence, z would never be offered. The unique separating equi l ibr ium is thus stable. It remains to be shown that no pool ing equi l ibr ium is stable.^ Since the intuit ive criterion of C h o and Kreps (1987) is a necessary condition for stabil ity, it can be used to eliminate unstable equi l ibr ia . A n equi l ibr ium is said to fai l the stabi l i ty criterion i f there exists another contract which is weakly preferred to the equi l ibr ium contract by some firm types and if investors would make a non-negative expected return by accepting the off- equi l ibr ium contract from all of those types. ^Welch (1989) and Allen and Faulhaber (1989) both have pooling equilibria for some parametrizations of signaling games with underpricing. In these models the two types of entrepreneurs, who are risk neutral, have to issue shares to finance the firm's operation for the first period. This imposes a minimum level of a > 0. Define a pool ing contract as i = {P,à) for al l firm types, equi l ibr ium [z,d''{z)] is said to fai l the Cho Kreps criterion i f there exists an off-equilibrium contract z such that H{z) ^ 0 and B{z,p) > 0 for al l G H{z). Consider z = z(p) as the off-equilibrium contract. Then H{z{p)) is the set of all types that weakly prefer their opt imal separating contract to pool ing contract z. Because z{p) is opt imal for type p and 7^ > 0, the set H{z{p)) contains a l l types p > p{z). Moreover, investors would accept z{p) since B{z{p), p) > 0 for any type offering i t . O n l y entrepreneurs with firms of quality better than p(z) would have an incentive to defect from the pool ing equi l ibr ium. Hence equi l ibr ium [z,d*(z)] fails the intuit ive criterion and thus is not stable. Q.E.D. B.2 Proposit ion 2 The solution of the entrepreneur's problem is reached by backward induct ion . First the opt imal percentage of equity to be retained in Per iod 2 is determined, for each percentage possibly retained in Period 1 and earnings number possibly announced at the end of that period. The first-order condition for maximizat ion of (3.14) is -b(T^{l- p'^)a2 = 0 (B.28) which implies 02 = 0 for a l l values of o j and y. It is opt imal for the entrepreneur to sell al l her remaining shares at the end of the first period, whatever the level of earnings announced or the number of shares she had retained at to-Her decision problem at the beginning of Per iod 1 is thus reduced to max {1 - ai) piz) - K + ai [p{z) + (p - piz)) f ] - ^ ba^p'^af (B.29) and the first-order condit ion leads to differential equation / ! , , ( . ) = 6 a V ' Y 3 y ^ . (B.30) Th i s differential equation can be solved by apply ing boundary condition p{P,0,0) = p V P , piz) = -b(j^ A2 a i + In (1 - £ a j ] + p. (B.31) T h e opt imal levels of ownership for the two periods are given by a^(p)-i-In ( l - i a,{p)) = f - ^ (B.32) a2i^l,y) = 0 (B.33) and the entrepreneur's expected ut i l i ty at the op t imum is U{zip), p) = p - K - \ bcr'p' alip). (B.34) Such a solution exists if, and only if, there exists a level of a\ between zero and one which satisfies (B.32) . 0 + M l ) > > f a x + l n ( l - f a i ) (B.35) 0 < 0^ < - a a i + l n ( l - ^ a i ) ) . (B.36) which goes to (3.16) as a i goes to 1. If p = A then, as a j goes to 1, (3.16) becomes and a solution always exists. If p > A the left hand side of (3.17) goes to —oo as a j goes to ^ < 1. There is thus always an a i < 1 which satisfies (3.17) and a solution always exists. W h e n a solution does exist for (3.15), i t is a separating solution i f i t leads to a different opt imal level of ai for each type of f i rm. Tota l ly differentiating (3.17) w i t h respect to p yields dai _ 1 - f ai > 0 for aU 0 < ^ a i < 1.^  (B.37) dp ba'^p'^ai Hence ai{p) is a monotonical ly increasing function. Investors can infer f irm type by observing the percentage of shares offered in its prospectus. The opt imal retention level is decreasing in firm-specific r isk: da ( l _ ^ \ f ^ ^ ^^^^^ d(T^ ^For f a i > 1, it would be necessary that p > A. In that case the level of retention that satisfies (3.17) need never exceed ^ . There remains to verify whether this opt imal solution leads to a credible equi l ibr ium in the case of One-Period Commitment . We do this first by testing equi l ibr ium [z{p),d''(z)] (where d'{z) is as defined i n (B.17)) against the Cho -Kreps intuit ive criterion. E q u i l i b r i u m [z{p),d*{z)] fails the intuit ive criterion i f there exists a contract z such that p>P V / i G H(z) and (B.39) H(z) f 0. (B.40) From (3.15) and (3.18), C/(2, p) = P-K\OL^{p-P)\ - \h o^p^al (B.41) Uiz{p),p) = p - K - \ bcr'p'aiip). Let the difference between the two levels of expected ut i l i ty be M{z,p) = U{z,p)-U{z{p),p) = {P-p){\-fa,)-\ba^p\a\-a\{p)). (B.42) If condit ion (B.40) holds, then a l l types i n H{z) must have p> P ioi condition (B.39) to also ho ld . O f the types i n H{z), choose the type that would benefit most from offering off-equi l ibr ium z rather than z(p). It is the level o{p which maximizes M{z, p) and hence satisfies first-order condit ion M^{z, p) = - ( 1 - ^ a i ) ^ { l - i a i (M) ) = 0. (B.43) E q u a t i o n (B.43) holds i f , and only if , a j = ax{p). For the type chosen, the opt imal level of ownership is the same i n both contracts. The entrepreneur of such a f irm would prefer z only i f P > ^. B u t P = p means that z = z(p) and is not an off-equilibrium contract. Hence, condit ion (B.39) above does not hold for at least one type in H{z) i f condition (B.40) holds. E q u i l i b r i u m [z{p),d*{z)] does not fai l the intuit ive criterion and , hence, is possibly stable. One-Per iod Commitment may not always lead to a stable equi l ibr ium. Whether it actually is stable depends on the specific parameters of the firm. The intuit ive criterion used here is a necessary condit ion for stabil ity, but there may exist situations where the equi l ibr ium is unstable even i f the criterion is not violated. There may exist an off-equilibrium contract in which the stock is underpriced for some of the firm types that would prefer it and for which investors assess the probabi l i ty of underpric ing to be high enough to accept the contract. For p > X, the equi l ibr ium can be shown to be stable, however. The proof follows that of Proposi t ion 1. The levels of expected ut i l i ty attained by the entrepreneur for the different contracts are U{z,p) = P - K + a,{p-P){ - Iba^p'ai U{2(p),p) = p - K - \ ba'^p'^a\{p) from (B.6) U{zQ,p) = p - K - \ b(7\ (B.44) (B.45) The m i n i m u m rejection probabi l i ty that would deter an entrepreneur wi th firm type p from oflfering off-equilibrium contract z is where Diz, p) = u{z,p) = l-D{z,p) \ ba^l-p-'alip)) (B.46) (B.47) ( 1 - f a i ) {P-p) + \ ba^{l-p^a\y The next step is to show that v{z,p) is decreasing at = P and str ict ly concave in p. The first derivative w i t h respect to p is l-±a,ip) I - { a . u^{z, p) = D{z, p) \ ba^\-p^a\{p)) ( l - £ a a ) ( P - ^ ) + i ba\l-p^a\)\ Evaluated at /x = P , (B .48) becomes . (B.48) _ 1 - p'a\{P) 1 - i a,{P) 1 - I Q i [(1 - p^a\[P)) (1 - p^a\)\ • (B.49) The function fiZjp) is decreasing at P = ^ i f the last term of (B.49) is negative. Let W ( a ) = l - a 2 • (B.50) Then >V'(a) = - 1 - p2a2 2 p 2 a 1 - ^ a 1 - /j2a2 I ( l - p a ) 2 + 2 p a ( ^ -p) ( l - ^ a ) ( l - p 2 « 2 ) (B.51) 1 - /j2a2 which is negative for p > X. Thus , W is decreasing i n a which implies that W ( Q I ( P ) ) < W ( a i ) , since a i < a i ( P ) . It follows that the last term of (B.49) is negative and that ^^(z, P) is negative for p> X. The second derivative of v{z,p) is u^^{z, p) = i5 (z , p) [[F'ip) - G,{z, p)] - [F{p) - G{z, p)f) (B.52) where = ( , - . „ . ) ( P - ; H T > ^ ' ( I - . ' » J ) -v{z,p) is str ict ly concave i n /z i f , and only if , (B.52) is str ict ly negative. It wi l l be if F'{p) -G^,{z,p) < 0. for p > A and 6a2 G ^ ( ^ , M) = i 2 ( l - i a i ( / . ) ) p'^aiip) l - p 2 a f ( / i ) •f ( l - p ^ a i ( / x ) ) ^ + 2 p a i ( M ) ( ^ - p ) p 2 a i ( / i ) ( l - p 2 a î ( / i ) ) < 0 > 0 [ ( l - ^ a i ) ( P - ; i ) + i 6 a 2 ( l - p 2 a 2 ) ] 2 since ^ a i is always less than 1. Stabi l i ty follows from this as i n Proposit ion 1. (B.55) (B.56) (B.57) Q.E.D. B.3 Proposit ion 3 Let OA = a{p,2), the op t ima l retention level for Two-Per i od Commitment , and as = a(p,l), the opt imal level for One-Per iod Commitment . From (3.9) and (3.17) comparison can be made between the opt imal levels of ownership retention for each of the strategies: ^ = a ^ + l n ( l - a ^ ) = A2 a f l + l n ( l - ^ ag)] . Let F ( A , p , a s ) = [£. as + In (l-fag)] G ( Q ^ ) = OA+ ln(l - oiA). Tota l ly differentiating (B.58) w i t h respect to A and ag gives Fx{X,p,aB)dX + Fa{X,p,ag)dag = 0 and doiB ^ Fx{X,p,ag) dX Fa{X,p,aBy The first derivative of F(-) w i t h respect to A is Fx{X,p,ag) = X B y Taylor 's expansion, 1 -f 2 In (1 - £ a s ) ^ " « ( ' + r ^ ) = 2 [ ^ a B + l {iaBf^\ {{^Bf^h {{ agf + and 2 In (1 - £ ag) = - 2 a s + i agf + \ (£ aB? + \ ( f CCB)' + Replac ing (B.64) and (B.65) into (B.63) yields Fx{X,p,aB) > 0. The first derivative of F ( - ) w i t h respect to a g is Fa{X,p,aB) = p 2 / - " B , 1 - A « B / < 0. Results (B.66) and (B.67) imp ly For p = X, (B.58) becomes das dX > 0 (B.68) aA + l n ( l - aA) = X^ [ag + l n ( l - a s ) ] (B.69) which implies that a ^ < a g , since A < 1, A s A increases from X = p, (B.68) indicates that Qfl increases and the retention level for Two -Per i od Commitment is lower than the level under One-Per iod retention. For p > X, signaling is possible under both regimes for a l l firms. The boundary conditions used i n constructing the necessary retention levels assumes that , at = a ^ = a g = 0. We also know that , as p approaches oo, approaches 1 and as approaches ^ < !• Hence there exist some types for which ag < a ^ . The following analysis shows that there exist a type p' such that OCA < ocB for p e [li,p') OA > OCB for p e {p',p] Let (B.70) F ( a ) = X^ia + l n { l - i a ) ) G(a) = a - l - l n ( l - a ) (B.71) (B.72) and let A ( a ) denote the difference i n the value inferred by investor observing a and r = 1 versus r = 2. A ( a ) = ba'[-F{a)-{-G{a))] = a ( l - pX) -I- l n ( l - a ) - A 2 l n ( l - { a ) (B.73) (B.74) A s a approaches A ( a ) approaches -|-oo. Hence, for large p, ajg < a ^ . A t a = 0, A ( a ) = 0. Its first derivative is pX which , for a = 0 is equal to 0 . The second derivative is _ Q ) 2 - 1 ( B . 7 6 ) M ( Q ) . ( B . 7 7 ) - ( l - a ) 2 -A t a = 0 , A " ( a ) < 0 , so A ( Q ) is concave around this point. Since A ( 0 ) = 0 and A ' = 0 , A ( a ) has to be negative for a close to zero. If one shows that A ( a ) is concave for low values of a and convex for high values, with à separating the two groups, it implies that there is one a ' > 0 such that A ( a ' ) = 0 , and one p' for which ( B . 7 0 ) holds. Concavity of A ( Q ) depends on the sign of M ( a ) . A t a = 0 , A f ( 0 ) = p2 - 1 < 0 ( B . 7 8 ) and The first derivative of M{a) is l i m Mia) = oo > 0 . ( B . 7 9 ) Hence, M ( a ) is an increasing function which is negative for low values of a and positive for high values of a. Th is implies that there exist an â such that A ( Q ) is concave for a < â and convex for a > â. Q.E.D. ) B.4 Proposit ion 4 Let UA be the m a x i m u m expected ut i l i ty level attainable w i t h Two -Per i od Commitment , as given by ( 3 . 1 0 ) , and UB the level attainable w i t h One-Period C o m m i t m e n t , as given by ( 3 . 1 8 ) . UA = p - K - \ ba^a\ i ba'p-'as UB = l i - K - \ ba^ ^ j Adopt ion of One-Per iod mandatory commitment leads to a Pareto improvement i f en-trepreneurs expect to at ta in a higher level of ut i l i ty than wi th Two-Per i od Commitment , i.e., iî UB > UA- Th is holds if, and only [{, OA > pots-B y Taylor 's expansion. a ^ + l n ( l - a ^ ) = (B.81) (pagy 1 (pagf 1 (pag)^ (B.82) 2 A 3 A2 4 Equal i ty of (B.81) and (B.82) implies that aA> pag if, and only if, 0 < A < I. ' ' If A > 1, oiA ^ poiB and Ug < UA and there is no Pareto improvement. Hence, if p > X, Ug > UA for a l l types and i f p < A, ^7^ > UA if , and only if , A < 1 for a l l types below p*. For types in [p*,p], Ug=p-K-\b a which is less than UA- Q.E.D. B.5 Proposit ion 5 For a given information and risk structure (p. A, cr^, 6), define p* as the upper bound on the types that can sell some of their shares at ^ i . It is , thus, the lowest type that w i l l use r = 2 and the entrepreneur w i t h f irm type p* w i l l offer to retain a* so that she is indifferent between retaining ful l ownership for one period and offering z* = {p*,a'*,2). Th is implies that a * < a{p*,2), the level she would have retained under Two-Per i od mandatory retention. Proposi t ion 4 shows that a l l types p € [/£,/^*) are better off w i th shorter commitment i f a{p,2) is defined as i n (3.9). For entrepreneur wi th type p*, the lowest type to choose r = 2, the cost of separating is lower than under the Two-Per iod mandatory regime, so a* < a{p*,2) is sufficient to communicate her private information. *I am grateful to Jim Xie for his help with this proof. The following demonstrates that there is no measurable subset ip^,p^ + e) C [p,p'] that prefers to offer r = 2, even though a l l [p,p^] offer r = 1. Let be the retention level that would make p^ indifferent between r = 1 and r = 2. T h a t is U\ = p^-K-\ ba\a^f (B.83) and Ul=p^-K-'^ bcT'p'a\p^,l). (B.84) are equal. Entrepreneur type p^ is indifferent between the two i f pa{p\l) = a''. (B.85) Types above p^ w i l l continue to choose One-Per iod Commitment if , and only i f UB > UA- Th i s holds if, a.t p = p^, dUA ^ dUg dp dp (B.86) Total ly differentiating (B.83) and (B.84) yields ^ = l - 6 a V ^ (B.87) dp dp ^ ^ ^ = l - 6 . V W , l ) ^ ^ ^ . dp dp (B.88) Hence, (B.86) holds if , and only if . ^ 2 „ ( ^ t , 1) da{É2ll < a t 1 ^ . at M = /^t. (B.89) dp dp Using (B.7) and (B.37) , and the fact that pa(p^, 1) = yields = " T T T = pa(/|t,l) / ' / (B.90) and The first equality i n (B.90) results from replacing the derivative by (B.7) and the second follows from replacing by pa{p^, 1). Comparison of (B.90) and (B.91) yields ^ V ^ t , i ) M ^ < « t ^ . V A < 1 . (B.92) dp dp Hence, shorter commitment signaling strategies are preferred by types p > p^, even with the lower retention level resulting from choice. Hence, a l l types i n the interval {p^,p^ + e) prefer r = 1, and p^ has measure zero. A l l types p G [p,p*) choose short commitment , i f A < 1, and aU other types have no choice but to commit for two periods. The ir level of retention is different from the level necessary when T w o - P e r i o d Commitment is mandatory for a l l f irms, however. The boundary condition necessary to solve (B.2) is p{p*,a',2) = -bo^ia* + \nil - a*)) + C = p* (B.93) where a* is the level of retention that would make p* indifferent between {p*,a*,2) and (p*, 1,1). T h a t is , the level for which p * - K - \ ba^p^ = p * - K - l ba\a*)\ (B.94) Thus , a* = p and the level of retention necessary for efficient signaling of type p w i th r = 2 is given by a + l n ( l - a ) = - (p + l n ( l - p)). (B.95) If A > 1, a l l types prefer Two -Per i od C o m m i t m e n t , so there is no change i n the retention level since the worst type to offer that sort of contract is fi. Q.E.D. B.6 Proposit ion 6 The first-order condition for maximizat ion of (3.20), combined wi th equi l ibr ium condition (3.7), yields diflTerential equation p'{z) = b<T^r^j^. (B.96) where r2 = p2^ + ( l - p ) 2 Solving (B.96)and impos ing boundary condit ion M ( P , 0 , 2 , P ) = £ (B.97) yields the schedule of inference p{z) = -ba^r^ia + ln(l - a)) + ^. (B.98) The opt imal retention level is given by aip,2,p) + \n(l-aip,2,p)) = f ^ and the expected ut i l i ty level by (B.99) Uiz{p,2,p)) = p - K - \ b(T'r'a\p,2,p). (B.lOO) Equat ion (B.99) can be satisfied for a l l < oo so Two-Per i od Commitment is available for al l f irm types. It also leads to separation since da 1 — a > 0 V O < p < l . ( B . l O l ) dp ha'^r'^a The level of retention defined by (B.99) is higher than the level necessary when p = 0 since da_ _ in-p) f a \ ^2 (1 - p ) - p ^ ^ l - a ) J dp 6(7^ \^ - ^ which is negative i f 1 - p < p^/2 and positive i f the reverse is true. Stabi l i ty is shown i n the usual way wi th expected ut i l i ty levels U{z,p,p) = {l-a)P-K + ap-^ ba^r^a"^ U{z{p),p,p) = p - K - \ ba'r'a\p,p) Uizo,p,p) = p - K - l ba^. (B.102) (B.103) (B.104) (B.105) From these definition, D(z,p,p) = Ui4t^),l^,P)-Uizo,P,p) U{z,p,p) - U(zQ,p,p) 1 ba'il-T'a^p,p)) and i^ /x(^ >M>P) = D{z,p,p) {P-p){l-a) + \ 6 ^ 2 ( 1 - r 2 a 2 ) 1 - a ( ^ , p ) (B.106) (B.107) l - a \ ba^{l-r^a^{p,p)) {P - p){l - a) + I bcr^{l - r^a^) ' (B.108) At p = P, i 0cr2 ( l - r 2 a 2 2 6 C T 2 ( l - r 2 ) is negative i f the bracketed term is negative. Let l - a ( P , p ) l - a l - r 2 Q 2 ( p , p ) 1-7-2^^2 W ( a ) = 1 - a then W ' ( a ) = -l - a 1 - r2a2 l - r 2 a 2 ' ( l - r a ) 2 - i - 2 r ( l - r ) a ( l - Q ) ( l - r 2 a 2 ) < 0. where 1 - a{p,p) G{z,p,p) = i 6 a 2 ( l - r 2 a 2 ( ; z , p ) ) 1 - a and F'{p,p) = -F{p,p) ( P - / i ) ( l - a ) + i 6 a 2 ( l - r2a2) ( l - r Q ( / x , p ) ) 2 + 2Q( / x ,p ) ( r - - p 2 ) da dp {l-a{p,p)){\-r^a^p,p)) ( l - a ) 2 {P-p){l-a)+l 6 a 2 ( l - r 2 a 2 ) Hence, i/^^(z,/x,p) < 0 and stabi l i ty follows as i n previous proofs. (B.109) ( B . l l O ) ( B . l l l ) Th i s implies that W ( a ( P , p ) ) < W ( a ) , since a < a{P,p), and that i/^{z,P,p) < 0. The second derivative of i/(z,p,p) w i th respect to p is iy^^tiz,p,p) = Diz,p,p) {[F\p,p) - G^iz,p,p)] - [F{p,p) - Giz,p,p)]^) (B.112) (B.113) (B.114) < 0 (B.115) (B.116) Q.E.D. B,7 Proposit ion 7 Let Qc = a{p,2,p), the op t imal retention level for entrepreneur of type p under Two-Per iod mandatory commitment when there is a probabi l i ty p of f i rm value revelation, and Uç = U{z{p),p,2,p). From Proposit ions 1 and 6, Uc = t i - K - \ ba^r^al. (B.117) (B.118) There is a Pareto improvement wi th random value revelation if, and only if, Uc > UA for aU p with strict inequality for at least one. T h i s w i l l hold if , and only if. aA > rac. (B.119) We know, from Proposit ions 1 and 6 that = aA + ln(l - aA) = r^{ac + ln(l - ac)). 0 (T' B y Taylor 's expansion aA + ln(l-aA) = - a . + r 2 ( a c + l n ( l - a c ) ) = - r ^ 2 3 4 ^ [roc]^ [racf [raç]* 2 3r ^ 4r2 which implies that a A > rac-(B.120) (B.121) (B.122) Q.E.D. B.8 Proposit ion 8 The first-order condition for maximizat ion problem (3.23), and imposi t ion of equi l ibr ium con-dit ion (3.7) y ie ld differential equation p,(z) = ba^p'j-^ (B.123) where u ; = l - ( l - p ) ( l - ^ ). Introduct ion of boundary condit ion M ( P , O , I , P ) = ^ yields schedule fJ-iz) = — ^ ^ [ w a - | - l n ( l -ua)] + p. The opt imal level a{p, l , p ) is given by u;Q(^,l ,p)-|-ln(l - u;a(/i ,l ,p)) = and the maximized expected ut i l i ty is U{z{p),p,p) = p - K - \ bcr'p'a'ip, l,p). (B.124) (B.125) (B.126) (B.127) The opt imal level of retained ownership is increasing i n firm value for al l values of p between zero and one, ensuring separation: da 1 -ua > 0 dp ba'^p^a It is also decreasing i n firm-specific r isk: da fl -ua\ ( - p for a l l 0 < w a < 1. \ ua ) KbaHpIXy) ^ (B.128) (B.129) da^ ua J Kbo'^ip/Xy, There remains to be shown that the solution satisfies C h o - K r e p s ' Intuitive Cr i ter ion for stabifity. U{z,p,p) = P-K^ua{p-P) (B.130) The difference between expected ut i l i ty attained wi th the opt imal contract z{p,l,p) and wi th an off-equilibrium contract z is given by M{z,p,p) = U{z,p,p)- U(z{p,p),p,p) = ( l - a . a ) ( P - / i ) - l ba'[{l-f)'p{l-p)(P-p)' - 1 6 C T V V - « ' ( / ^ , P ) ) . (B .131) Condit ions (B.39) and (B.40) must both hold for an equi l ibr ium to fail the intuitive stabil ity criterion. If condition (B.40) holds, then there is at least one f irm type for which M{z,p) > 0. Choose one of these types, one for which M{z,p,p) attains a m a x i m u m . First-order condition M^iz,p,p) = u{a - aip,p)) + ba^ ( l - ^ ) ' p ( l - p) ( F - M) = 0. (B .132) holds i n three types of situations: (1) a = a{p,p) and P = p, (2) a < a{p,p) and P > p, or (3) a>a{p,p) and P < p. In situation (1) z is equal to z{p,p), the equi l ibr ium contract, so there is no defection. In situation (2), P > p violates (B.39) and no investor would accept such a contract. In s ituation (3), M{z,p,p) < 0 at its m a x i m u m , so H(z) is empty, i n vio lat ion of (B.40). Hence, there does not exist a contract which could lead to a vio lat ion of the intuit ive stabil ity criterion. Stabi l i ty of the equi l ibr ium depends on the relative value of the parameters i n the specific case faced by the entrepreneur. Q.E.D. B.9 Proposi t ion 9 Let a£) = a{p,l,p), the opt imal ownership retention level defined i n Proposit ion 8, and Up = U{z{p),p,2,p). F r o m Proposit ions 2 and 8, we know that UB = p - K - \ bo^p^al UD = P - K - I ba'^p'^al. A Pareto improvement requires that [/"£>> (7b for a l l types and t / ^ > i / s for at least one type. Th is holds if, and only if, Propositions 2 and 6 i m p l y that ^ = A2 a B + l n ( l - ^ aB)) = ^,{uaD + lnil-uaD)). B y Taylor 's expansion, ( I ae + l n i l - i ag)) = V (B.133) 2 ^ ^ 3 ^ A 2 4 ^ and (wayj -1- l n ( l - a;a£)) = -p^ a D -I 3 4 (B.134) If p < A then f < w and equality (B.133) holds if, and only if, ag > ap. If /» > A, f > a; and OB < a£). Hence, i f /> < A, < a g , and entrepreneurs are better off w i th random revelation. If p > A, > a g . A l l entrepreneurs are made worse off by random revelation, because they have to bear more risk. Up = A, ao = CUB and entrepreneurs are indifferent between One-Per iod retention regimes w i t h and without random revelation. Q.E.D. B.IO Corol lary 1 W i t h p = 0, condition (3.16) for existence of a short commitment separating equi l ibr ium be-comes 0 < < 0. (B.135) One-Period Commitment is not possible if p = 0. Q.E.D. B . l l Corol lary 2 B y Proposi t ion 2, efficient signaling is possible for a l l f irms, i f p = A. The level of retention is lower for r = 2 by Proposi t ion 3 but r = 1 is preferred and chosen by entrepreneurs, i f A < 1, from Proposit ions 4 and 5. Q.E.D. B . l 2 Corol lary 3 Subst i tut ing P = and X = y/2 into equations (3.17) and (3.18), the opt imal retention level i n the case of independent outcomes is i aip, 1) + In ( l - 1 a{p, 1)) = (B.136) which implies condition (3.43) for the existence of a solution where 0 < a{p,l) < 1, and the m a x i m u m expected ut i l i ty Uiz{p,l),p) = M - A ' - ^ 6 a V ( / i , l ) . (B.137) It was shown in Propos i t ion 5 that U{z{p,2),p) > U{z(p,l),p) for a l l A > 1. So Two-Per iod Commitment is preferred to One-Per iod Commitment when cash flows are independent across periods. Q.E.D. B . l 3 Corol lary 4 Subst i tut ing p = X = into (3.17) and (3.18) a{p,l) + ln{l-aip,l) = ^-^, (B.138) which implies existence condit ion - 6cr2 0 < ^^T-ê < (B-139) and expected ut i l i ty U(zip,l),p) = p - K - -^ba-'a^p, 1). (B.140) Stabi l i ty follows from Propos i t ion 2 and the fact that p = X. Q.E.D. A p p e n d i x C List of Sample F i r m s Table C . l : No . F i r m Name Issue Date (1981) 188 A B F E N E R G Y C O R P 12/24 300 A C A D I A P E T R O L E U M C O R P 1/23 301 A C C U T E S T S Y S T E M S I N C 8/12 189 A D I E L E C T R O N I C S 9/14 302 A D V A N C E D C H E M I C A L C O R P 11/16 190 A D V A N C E D F U E L S Y S T E M S 12/10 303 A D V A N T C O R P 12/9 191 A E R O S E R V I C E S I N T E R N A T I O N A L 4/14 192 A G G I E O I L C O 8/12 194 A I M E X C O 5/14 195 A I R C H A P A R R A L I N C 7/8 196 A L D E B A R A N D R I L L I N G C O 6/5 305 A L E M B I C 11/19 197 A L E X A N D E R E N E R G Y C O R P 11/19 306 A L F A R E S O U R C E S 11/6 198 A L L E G H E N Y A N D W E S T E R N E N E R G Y C O R P 7/1 307 A L P H A M I C R O S Y S T E M S 6/18 308 A M E R I C A N D I A G N O S T I C S C O R P 5/7 1 A M E R I C A N E L E C T R O M E D I C S C O R P 6/18 309 A M E R I C A N F I B E R O P T I C S C O R P February 2 A M E R I C A N N A T I O N A L P E T R O L E U M C O 6/4 310 A M E R I C A N P H O N E M E T E R 2/5 3 A M E R I C A N S P O R T S A D V I S O R S I N C 2/20 311 A M E R I C A N S Y N - F U E L S I N C 2/11 312 A M E R I C A N V A S C U L A R I N T E R N A T I O N A L 8/4 313 A M E R I C A N W E L L S E R V I C I N G C O R P 6/26 314 A M P L I C A 6/22 315 A M P O W E R I N S T R U M E N T C O J u l y 4 A N D R O S A N A L Y Z E R S I N C 5/21 5 A N E F C O I N C 8/12 No. F i r m Name Issue Date (1981) 316 A P P L I C A T I O N S S Y S T E M S G R O U P 2/25 6 A Q U A N A U T I C S 7/15 7 A R R O W H E A D E N E R G Y C O R P 8/21 8 A S K C O M P U T E R S Y S T E M S I N C 10/1 317 A S T R A D Y N E C O M P U T E R I N D U S T R I E S 11/10 9 A S T R O D R I L L I N G C O M P A N Y 5/14 10 A T O U R S I N C 3/10 318 A U T O M A T I C V O T I N G M A C H I N E C O R P 11/9 319 A V I A T I O N G R O U P I N C 12/17 11 A Z T E C E N E R G Y C O R P 5/26 193 A . H . B E L O C O R P 12/9 12 B A L A N C E C O M P U T E R C O R P 2/5 321 B A L B O A E X P L O R A T I O N 3/31 322 B A L C O E N E R G Y C O R P 5/20 354 B A L T I M O R E C A B L E T V I N C February 13 B A N K E R ' S N O T E I N C 11/12 323 B A R L E Y P R O D U C T S I N T E R N A T I O N A L I N C 5/21 324 B A R T O N V A L V E C O I N C 6/2 14 B E D F O R D C O M P U T E R C O R P 7/28 199 B E L L P E T R O L E U M S E R V I C E S 8/13 320 B G S E N E R G Y I N C June 325 B I G B I T E I N C 9/1 327 B I O C E L L T E C H N O L O G Y C O R P 8/21 200 B I O N C O R P 8/6 201 B I O S E A R C H M E D I C A L P R O D U C T S I N C 7/24 202 B I O S O N I C S I N C 10/9 204 B I O T E C H R E S E A R C H L A B S I N C 3/11 326 B I O - E N E R G Y S Y S T E M S I N C 3/6 203 B I R D V I E W S A T E L L I T E C O M M U N I C A T I O N S I N C 10/21 328 B I S C O M M U N I C A T I O N S C O R P 11/13 205 B I W C A B L E S Y S T E M S 4/15 207 B L U E J A Y E N E R G Y C O R P 5/12 329 B O B O E X P L O R A T I O N I N C 9/21 206 B O L T T E C H N O L O G Y C O R P 9/2 208 B O N R A Y D R I L L I N G C O R P 6/4 209 B R A C K E N E X P L O R A T I O N C O 11/5 210 B U F F T O N O I L & G A S 5/1 211 B U L B M I S E R C O R P O F A M E R I C A 12/23 212 B U R T O N E N E R G Y & S O L A R T E C H N O L O G Y I N C 11/12 No. F i r m Name Issue Date (1981) 331 B U S I N E S S C O N C E P T S M A R K E T I N G C O R P M a r c h 213 B U S I N E S S E X C H A N G E I N C 5/8 332 C C O R E L E C T R O N I C S I N C 2/26 333 C A B L E T V I N D U S T R I E S 5/13 334 C A M B R I D G E A C A D E M Y I N C 6/1 214 C A R A V A T T C O M M U N I C A T I O N S I N C 11/2 215 C A R D I L L O T R A V E L S Y S T E M S 9/10 216 C A R L K A R C H E R E N T E R P R I S E S I N C 10/15 217 C A R T E R E D W A R D S P R O D I N C 12/2 218 C A S I N O A N T I Q U E S 7/8 335 C A S I N O T E C H N O L O G Y G R O U P 8/7 336 C A S S C O C O R P 7/6 219 C E N T R A L C O R P O R A T E R E P O R T S S E R V I C E S I N C 4/30 220 C E T U S C O R P 3/6 338 C H A T F I E L D O I L & G A S 4/27 339 C H I L D R E N ' S P L A C E I N C 4/28 221 C H I P O L A O I L C O R P 4/8 340 C H O Y F O O D S C O R P 10/15 341 C H R O N A R 8/6 222 C I B O L A E N E R G Y C O R P 5/28 342 C I N E M A S T A R C O R P June 223 C I P H E R D A T A P R O D U C T S I N C 10/6 224 C I R C L E S E V E N O I L & G A S 5/29 343 C O A L T E C H N O L O G Y C O R P 11/17 344 O O G E N I C E N E R G Y S Y S T E M S I N C 5/21 345 C O L L A G E N C O R P 10/23 346 C O L L E C T O R S G U I L D I N T E R N A T I O N A L 2/12 347 C O L O R A D O G O L D & S I L V E R I N C 9/3 225 C O M S Y S T E M S I N C 11/17 226 C O M A I R 7/16 348 C O M B U S T I O N E L E C T R O M A G N E T I C S I N C 11/5 349 C O M B U S T I O N R E S E A R C H & T E C H N O L O G Y 11/23 227 C O M M U N I C A T I O N S S Y S T E M S I N C 11/18 228 C O M P U T E R A S S O C I A T E S I N T E R N A T I O N A L 12/9 541 C O M P U T E R D E S I G N E D S Y S T E M S 7/15 229 C O M P U T E R E N T R Y S Y S T E M S C O R P 4/15 350 C O M P U T E R M A G N E T I C S C O R P 4/14 351 C O M P U T O N E S Y S T E M S I N C 11/4 352 C O M T E X S C I E N T I F I C C O R P 7/22 No. F i r m Name Issue Date (1981) 353 C O N S O L I D A T E D P E T R O L E U M I N D U S T R I E S 3/4 230 C O N T R A C A P I N C 12/31 355 C O R B O E N T E R P R I S E S I N C 12/14 231 C O R V U S S Y S T E M S 10/2 233 C P A C I N C 3/30 356 C P U C O M P U T E R C O R P 6/18 232 C R A C K E R B A R R E L O L D C O U N T R Y S T O R E I N C 11/5 234 C R A W F O R D E N E R G Y I N C 4/28 235 C Y B E R D I A G N O S T I C S I N C 4/8 15 C Y C A R E 9/23 358 D A L L A S O I L & M I N E R A L S I N C 1/22 16 D A T A I / O C O R P 5/5 17 D A T A L A W C O 2/9 18 D A T A M E A S U R E M E N T C O R P O R A T I O N 9/15 19 D A T A P O W E R I N C 10/21 359 D A T A F L E X C O R P September 360 D A T A S P E E D I N C 12/22 361 D A W S O N G E O P H Y S I C A L C O 4/23 20 D E L T A D R I L L I N G C O 3/17 362 D E S T R O N I N C 12/11 21 D E T E C T O R E L E C T R O N I C S C O R P 6/2 22 D I A B L O O I L C O 8/21 23 D I O G E N E S S Y S T E M S I N C 11/6 24 D N A M E D I C A L I N C 9/9 363 D O R A D O M I C R O S Y S T E M S 4/21 25 D O T R O N I X I N C 5/7 364 D R I L L W E L L D E V E L O P M E N T C O R P 7/20 365 D U N H A L L P H A R M A C E U T I C A L S 10/16 26 D U R A L I T H C O R P 3/24 27 D Y N A S T Y O I L & M I N E R A L S I N C 12/9 366 D Y N A T R E N D I N C 11/16 28 D Y S A N 1/27 367 E E S I N C 3/23 368 E I K O N I X C O R P 12/2 369 E L D O R A D O G O L D & E X P L O R A T I O N 5/13 370 E L E C T R O N I C F U N D S T R A N S F E R S Y S T E M S 11/10 30 E L E C T R O - B I O L O G Y I N C 2/18 371 E M E R E X O I L C O 6/5 373 E M S E N E N E R G Y I N C 10/30 No. F i r m Name Issue Date (1981) 375 E N E R G Y D Y N A M I C S I N T E R N A T I O N A L C O R P 2/24 376 E N E R G Y G A S t O I L C O R P 9/2 31 E N E R G Y O I L I N C 5/14 33 E N E R G Y S O L U T I O N S I N C 4/10 34 E N E R G Y S Y S T E M S I N C 6/15 35 E N E R S E R V P R O D U C T S I N C 4/23 36 E N G I N E E R I N G M E A S U R E M E N T S C O 1/21 377 E N T E R P R I S E R A D I O 2/3 378 E Q U I N E T I C S 9/15 37 E S S E X C O R P 12/23 38 E S T E B A N ' S M E X I C A N F O O D S I N C 8/6 379 E T I I N C August 39 E X P L O R A T I O N S U R V E Y S I N C 4 /9 29 E . I . L . I N S T R U M E N T S I N C 4/8 40 F A F C O I N C 6/23 380 F A S T F O O D O P E R A T O R S I N C 4/9 41 F E R R O F L U I D I C S C O R P 7/16 42 F I A T R O N S Y S T E M S I N C 6/2 43 F I D E L I T Y M E D I C A L S E R V I C E S I N C 1/2 382 F I R S T M A T A G O R D A C O R P 6/23 44 F L A R E I N C 11/10 45 F L I G H T D Y N A M I C S I N C 5/20 383 F L O A T T O R E L A X I N C 1/23 384 F O N A R C O R P 10/23 46 F U N D S N E T I N C 2/18 385 F X C I N V E S T M E N T G R O U P I N C 11/12 386 G A R C I A ' S O F S C O T T S D A L E 10/16 387 G E N E R A L W A R R A N T Y C O R P 7/24 388 G E N E T I C E N G I N E E R I N G I N C 1/14 389 G E N E T I C S Y S T E M S C O R P 6/4 47 G E N T E X 12/8 48 G E O P H Y S I C A L F I E L D S U R V E Y S I N C 8/5 390 G I B R A L T A R E X P L O R A T I O N 5/11 49 G L O B U S C O P E I N C 7/21 50 G O L D O R E L I M I T E D O F C R I P P L E C R E E K 5/1 51 G R A N T I N D U S T R I E S I N C 7/29 52 G R A Y H I L L E X P L O R A T I O N C O 12/21 391 G R E A S E M O N K E Y H O L D I N G C O R P 3/24 53 G R E A T A M E R I C A N C O A L I N C 12/8 No. F i r m Name Issue Date (1981) 392 G R E A T E A S T E R N E N E R G Y & D E V E L O P M E N T 7/28 393 G R E A T O U T D O O R A M E R I C A N A D V E N T U R E I N C 8/18 394 G R E A T W E S T E R N M I N E R A L S C O R P 10/22 54 G R E A T W E S T H O S P I T A L S I N C 4/22 395 G U L F A M E R I C A N F I N A N C I A L C O R P 11/10 55 G U L F N U C L E A R I N C 11/14 56 H & H O I L T O O L C O 12/9 57 H A N F O R D S I L V E R I N C 7/1 58 H B O & C O M P A N Y 6/30 59 H E A L T H C A R E A N D R E T I R E M E N T C O R P O F A M E R I C A 12/10 60 H E A L T H D Y N E 12/8 61 H E I I N C 3/24 62 H E I Z E R C O R P 5/7 63 H E L I O N E T I C S I N C 6/16 69 H E M O K I N E T I C S I N C 7/27 64 H E N R Y E N E R G Y C O R P 3/31 65 H I N D E R L I T E R E N E R G Y E Q U I P C O R P 11/5 397 H I N G E L I N E O V E R T H R U S T O I L & G A S I N C 4/6 66 H O M E D E P O T I N C 9/22 398 H O M E P A R T N E R S O F A M E R I C A I N C 9/16 67 H Y B R I T E C H I N C 10/28 68 I C O I N C 7/29 400 I D E N T I P R I N T I N C 9/25 71 I K E L O V E L A D Y I N C 4/29 401 I L L I N O I S I N D E P E N D E N T A L C O H O L P R O D U C E R S I N C 2/2 72 I M M U N O G E N E T I C S I N C 6/30 403 I M P A C T E N E R G Y I N C 1/16 404 I N F O R M A T I O N R E T R I E V A L S Y S T E M S C O R P 1/9 73 I N F O T R O N S Y S T E M S 3/26 74 I N P U T B U S I N E S S M A C H I N E S I N C 5/13 76 I N S I T U F O R M E A S T I N C 10/20 405 I N S I T U F O R M O F N O R T H A M E R I C A 8/27 406 I N S O L A R I N C 12/14 75 I N S T A C O M I N C 11/4 407 I N S T R U M E N T D E V E L O P M E N T C O R P 12/17 77 I N T E G R A T E D M I C R O C I R C U I T S I N C 7/21 78 I N T E G R I T Y G R O U P I N C 8/17 408 I N T E L E P L E X C O R P 11/10 80 I N T E R A C T I O N S Y S T E M S I N C 5/11 No. F i r m Name Issue Date (1981) 81 I N T E R F E R O N S C I E N C E S I N C 5/12 82 I N T E R G R A P H C O R P 4/7 83 I N T E R M A G N E T I C S G E N E R A L C O R P 4/14 84 I N T E R M O U N T A I N R E S O U R C E S I N C 1/26 409 I N T E R N A T I O N A L E Q U I N E T I C S I N C 12/31 85 I N T E R N A T I O N A L G A M E T E C H N O L O G Y 10/22 86 I N T E R N A T I O N A L I N S T I T U T E F O R M E D I C A L S C I E N C E S 3/24 410 I N T E R N A T I O N A L M O B I L E M A C H I N E S C O R P 11/12 411 I N T E R N A T I O N A L T H O R O U G H B R E D B R E E D E R S I N C 3/24 87 I N T E R N A T I O N A L T O T A L I Z A T O R S Y S T E M S I N C 11/17 88 I N T E R T E C D A T A S Y S T E M S C O R P 4/16 79 I N T E R T E L I N C 2/5 89 I P L S Y S T E M S I N C 5/12 413 I S S C I N D U S T R I A L S O L I D S T A T E C O N T R O L S I N C 1/6 70 I V I E E L E C T R O N I C S I N C 2/3 90 J A C K P O T E N T E R P R I S E S I N C 6/23 91 J E C L A S E R S I N C 10/13 92 J E F F E R S O N - W I L L I A M S E N E R G Y C O R P 9/1 415 J E G E R O I L C O R P M a r c h 416 J E T A M E R I C A A I R L I N E S I N C 11/12 417 J E T I N D U S T R I E S I N C 4/2 418 J I F F Y J O H N S I N C 5/20 419 J O N E S S P A C E L I N K L T D 8/11 414 J . M . R E S O U R C E S I N C 2/12 420 K A L B R O C O R P 6/3 421 K E E B E E O I L & G A S C O 10/5 423 K E L L Y J O H N S T O N E N T E R P R I S E S I N C 7/1 93 K E N C O P E E N E R G Y C O 4/8 94 K E N T U C K Y H O R S E C E N T E R I N C 10/23 95 K I M B A R K O I L & G A S C O 6/4 424 K I N G J A M E S S H R I M P I N C 8/7 96 K L O S S V I D E O C O R P 6/17 97 K Y L E T E C H N O L O G Y C O R P 6/18 100 L E X I D A T A C O R P 12/23 425 L E Z A K E N E R G Y G R O U P I N C 4/29 236 L I E B E R T C O R P 7/1 426 L I F E C E N T E R S I N C 2/20 237 L I N E A R I N S T R U M E N T S C O R P 8/12 238 L I O N R E S O U R C E S C O R P 8/12 No. F i r m Name Issue Date (1981) 239 L I T T L E F I E L D A D A M S k C O 6/4 427 L I Z C L A I B O R N E I N C 6/9 240 L Y N X E X P L O R A T I O N C O 5/26 428 L Y - L I N E P R O D U C T S I N C 6/22 99 L . B . F O S T E R & C O 6/9 241 M A C H I N E T E C H N O L O G Y I N C 1/7 429 M A I N S T R E A M E N G I N E E R I N G C O 6/16 430 M A J O R E X P L O R A T I O N 3/6 431 M A N A G E M E N T S C I E N C E A M E R I C A I N C 4/8 432 M A S T E R S E N E R G Y C O R P 5/12 242 M A T R I X S C I E N C E C O R P 1/7 243 M C C O Y I N D U S T R I E S I N C 5/22 244 M E D I C A L G R A P H I C S C O R P 6/2 245 M E L T O N D R I L L I N G k E X P L O R A T I O N 6/26 434 M E T A L A R T S C O 1/22 246 M E T R O A I R L I N E S I N C 10/30 435 M I C O M S Y S T E M S I N C 6/19 247 M I D W E S T E X P L I N C 6/1 248 M I N C O M P C O R P 5/28 249 M I N E X R E S O U R C E S I N C 4/14 437 M I O C E N E R E S O U R C E S 5/28 250 M I Z E L P E T R O R E S O U R C E S I N C 4/14 101 M O N C H I K - W E B E R C O R P 11/10 438 M O N O C L O N A L A N T I B O D I E S 8/4 439 M O N O S I L I N C 4/16 440 M O N T E J A S E N E R G Y R E S O U R C E S 6/25 102 M O U N T A I N M E D I C A L E Q U I P M E N T I N C 5/13 441 M O U N T A I N S T A T E S O V E R T H R U S T 0 & G 4/27 103 M U S E A I R C O R P 4/30 104 M U S T A N G D R I L L I N G & E X P L O R A T I O N I N C 9/8 105 N A H A M A & W E A G A N T E N E R G Y C O 2/24 442 N A T I O N A L M O T O R C O N V E R S I O N S C O R P 8/13 106 N A T I O N A L R O Y A L T Y C O R P 3/11 444 N A T I O N A L V I D E O C E N T E R S I N C 12/1 107 N A U G L E S I N C 10/29 445 N C A C O R P 8/27 446 N E I G H B O R H O O D R E A L T Y G R O U P U S A I N C 4/13 447 N E L S O N R E S E A R C H & D E V E L O P M E N T C O 4/30 448 N E T W O R K S E C U R I T Y C O R P 9/15 No. F i r m Name Issue Date (1981) 449 N E W U N I T E D B U S I N E S S I N V E S T M E N T S A p r i l 450 N E W Y O R K A I R L I N E S I N C 2/20 108 N E W P O R T P E T R O L E U M S I N C 5/15 109 N O R P A C E X P L O R A T I O N S E R V I C E S I N C 5/6 452 N O R T H E A S T I N S U R A N C E C O 6/16 453 N O R T H S T A R M I N E R A L S I N C 7/22 110 N O V A R E L E C T R O N I C S C O R P 5/13 114 N R G D Y N A M I C S I N C 11/5 111 N U C L E A R S U P P O R T S E R V I C E S I N C 12/15 113 N U C L E A R & G E N E T I C T E C H N O L O G Y 10/28 454 N U C L E O N I C S C O R P October 112 N U T R I S Y S T E M I N C 1/8 455 N U T R I E N T C O S M E T I C L T D 4/13 456 O B J E C T R E C O G N I T I O N S Y S T E M S I N C 3/19 457 O C E A N I C M I N E R A L S C O R P A p r i l 458 O C I L L A I N D U S T R I E S I N C 6/18 459 O D E T I C S I N C 7/14 460 O I L M O P I N C 5/15 461 O K O B O J I P A R K L T D 7/20 116 O M M I D E N T I X S Y S T E M S C O R P 9/2 463 O M N I T R O N I C S R E S E A R C H C O R P 3/26 117 O R T H O M O L E C U L A R N U T R I T I O N I N S T I T U T E 7/7 466 O R Y X C O M M U N I C A T I O N S I N C 6/30 467 O U T B A C K O I L k M I N E R A L E X P L O R A T I O N 7/21 115 O V E R T H R U S T R E S O U R C E S L T D 6/9 468 P A C I F I C P O W E R k P R O T E I N I N C 4/29 118 P A C O P H A R M A C E U T I C A L S E R V I C E S I N C 8/5 469 P A T H F I N D E R P E T R O L E U M C O R P 6/8 120 P E R S O N A L D I A G N O S T I C S I N C 5/13 121 P E T R A R E S O U R C E S I N C 6/10 122 P E T R O Q U E S T I N C 9/24 472 P E T R O S Y S T E M S I N T E R N A T I O N A L 11/4 123 P E T R O L E U M A C R E A G E C O R P O F T E X A S 4/15 124 P E T R O M A X E N E R G Y C O R P 7/10 471 P E T R O N O M I C S I N C 12/2 125 P H O T O G R A P H I C S C I E N C E S C O R P 6/1 473 P H O T O V O L T A I C S I N C 5/27 126 P I E Z O E L E C T R I C P R O D U C T S I N C 6/2 127 P I N N A C L E P E T R O L E U M I N C 4/22 No. F i r m Name Issue Date (1981) 128 P I P E R H Y D R O I N C 8/21 474 P I Z Z A E N T E R T A I N M E N T C E N T E R S I N C 12/16 475 P I Z Z A T I M E T H E A T R E I N C 4/16 476 P I Z Z A V E N T U R E S I N C 10/15 477 P L A S M A - T H E R M I N C 10/13 129 P O L A R I S G O L D C O R P 11/10 478 P O L I C Y M A N A G E M E N T S Y S T E M S C O R P 12/16 130 P O S I T E C H C O R P 10/19 480 P R A B R O B O T S I N C 9/17 481 P R A I R I E P R O D U C I N G C O 4/8 482 P R I C E C O M M U N I C A T I O N C O R P October 483 P R O D I G Y S Y S T E M S I N C 4/7 484 P R O G R A M S U N L I M I T E D I N C 9/9 485 P R U D E N T I A L G O L D & S I L V E R C O R P 9/13 131 Q U E S T M E D I C A L I N C 4/28 486 Q U I C K P R I N T O F A M E R I C A I N C 7/23 487 R A M E N E R G Y I N C 10/6 488 R A M P A N T E X P L O R A T I O N & D R I L L I N G I N C 12/16 132 R E A D I N G A V I A T I O N S E R V I C E S I N C 5/12 489 R E E F E N E R G Y C O R P 4/22 490 R E P U B L I C R E S O U R C E S C O R P 5/4 133 R E S E R V E E X P L O R A T I O N C O 9/10 134 R E S O R T & U R B A N T I M E S H A R E S I N C 8/20 491 R E S O U R C E S E Q U I P M E N T C A P I T A L C O R P 7/27 135 R I B I I M M U N O C H E M R E S E A R C H I N C 5/27 492 R I O G R A N D E D R I L L I N G C O 10/14 493 R I O O I L k M I N E R A L S I N C 10/4 494 R I V A L R E S O U R C E S I N C 4/24 495 R O B E R T S O I L k G A S I N C 10/9 496 R O G U E O I L k G A S I N C 11/9 497 R O L F I T E C O 6/24 498 R O S E B R A N D P R O D U C T S I N C 11/3 136 R O Y A L T Y V E N T U R E S C O R P 5/1 137 S A G E D R I L L I N G C O 3/17 499 S A N D I E G O B A N C O R P January 138 S A N A N C O E N E R G Y C O R P 11/6 139 S A R A T O G A M I N E S I N C 12/24 140 . S A T E L L I T E I N D U S T R I E S I N C 11/23 141 S C H A G R I N ' S I N C 5/19 No. F i r m Name Issue Date (1981) 142 S C I E N C E D Y N A M I C S C O R P 4/22 143 S C I E N T I F I C L A B O R A T O R I E S I N C 7/31 144 S C I E N T I F I C L E A S I N G I N C 2/17 501 S C O T T I N S T R U M E N T S C O R P 4/2 502 S E A G A T E T E C H N O L O G Y 9/24 145 SEIS P R O S I N C 7/30 146 S E I S D A T A S E R V I C E S I N C 10/28 147 S E P A R E X C O R P 6/24 148 S E V E N O A K S I N T E R N A T I O N A L I N C 5/22 503 S I G L E R P E T R O L E U M C O R P 12/1 505 S I L I C O N E L E C T R O - P H Y S I C S I N C 4/16 149 S I L I C O N S Y S T E M S I N C 1/29 150 S I P P I C A N O C E A N S Y S T E M S I N C 10/15 151 S K I P P E R S I N C 5/19 152 S O C C E R C I T Y 7/14 507 S O F T W A R E A G I N T E R N A T I O N A L I N C 6/9 506 S O F T W A R E T E C H N O L O G Y C O 8/27 153 S O L V - E X C O R P 6/3 154 S O U T H T E X A S D R I L L I N G k E X P L O R A T I O N I N C 2/4 155 S O U T H E R N C A L I F O R N I A B A N C O R P 9/17 508 S O U T H E R N M E D I C A L & P H A R M A C E U T I C A L C O R P 8/18 509 S O U T H W E S T T E X A S D R I L L I N G C O 9/8 156 S P E C T R U M C O M M U N I C A T I O N S C O R P 2/25 510 S P U D N U T S I N C 5/15 511 S T A R R E S O U R C E S I N C 7/10 157 S T A R B R I T E C O R P 3/26 512 S T E R L I N G P I P E k S U P P L Y C O 4/1 513 S U N C O A S T P L A S T I C S I N C 11/12 514 S W E E T N L E G A L U S A I N C 5/21 515 S W I F T E N E R G Y C O 6/24 158 S W I T C H C O I N C 9/22 159 S Y N T E C H I N T E R N A T I O N A L I N C 6/2 516 S Y N T H E M E D C O R P 2/25 160 S Y S C O N C O R P 11/17 517 S Y S T E M A T I C S I N C 8/12 161 T A R G E T O I L k G A S I N C 2 /2 519 T E A N E C K H O L D I N G G R O U P 7/30 162 T E C H N O L O G Y M A R K E T I N G I N C 3/24 520 T E L E S P H E R E I N T E R N A T I O N A L 4/23 No. F i r m Name Issue Date (1981) 163 T E T R A S Y S T E M S I N C 5/8 521 T E X A S G L O B A L O I L C O R P November 164 T E X O I L I N C 10/13 165 T H O R A T E C L A B O R A T O R I E S C O R P 5/14 166 T I M E S F I B E R C O M M U N I C A T I O N S I N C 3/18 522 T O K A L O T G O L D & S I L V E R I N C September 167 T O P A I R M A N U F A C T U R I N G I N C 10/13 524 T R A N S G L O B A L A I R L I N E S 11/18 525 T R I H I E N E R G Y C O December 526 T R I A D E N E R G Y C O R P 1/28 527 T R I N I T Y O I L & G A S I N C 7/8 168 T R P E N E R G Y S E N S O R S I N C 8/20 169 T V I E N E R G Y C O R P 6/19 518 T . E . W I L L I A M S P H A R M A C E U T I C A L S 10/8 171 U L T I M A T E C O R P 4 /7 531 U L T R A S Y S T E M S I N C 5/28 172 U N I M A T I O N I N C 11/25 532 U N I O I L 9/17 530 U N I T A H E N E R G Y C O R P 2/27 174 U N I T E D M E D I C A L C O R P 6/25 175 U N I T E D S T A T E S A I R C R A F T C O R P 4/28 176 U N I T E D S T A T I O N E R S I N C 11/24 177 U N I T E L V I D E O I N C 5/28 529 US E X P L O R A T I O N C O R P 5/15 533 U T V C A B L E N E T W O R K 12/9 170 U . S . D E S I G N C O R P 7/6 534 V A C A T I O N T I M E S H A R I N G A L L I A N C E J u l y 178 V E C T O R E N E R G Y C O R P 5/27 179 V E C T O R G R A P H I C I N C 10/14 180 V E N T R E X L A B O R A T O R I E S I N C 3/26 535 V I A B L E R E S O U R C E S I N C 2/24 536 V I D E O C A S S E T T E R E V I E W 11/24 537 V I R A T E K I N C 5/7 538 V I S U A L T E C H N O L O G Y I N C 11/7 181 W E N T E X I N T E R N A T I O N A L I N C 4/7 539 W E S T E R N C O N S O L I D A T E D M I N E S I N C 11/12 540 W E S T E R N S I L V E R D E V E L O P M E N T C O R P October 542 W H I T E M A N M E D I C A L C O R P 6/17 182 W I C K L U N D P E T R O L E U M C O R P 5/18 N o . F i r m Name Issue Date (1981) 183 W I L D E R N E S S E X P E R I E N C E I N C 4/29 184 W I N D B A R O N 6/23 185 W O M E T C O C A B L E T V I N V 5/5 186 Z O E P R O D U C T S I N C 4/2 187 Z O N I C C O R P 4/2 

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:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0086536/manifest

Comment

Related Items