... they actually appear in the data Since factor loadings and covariance matrices used to simulate individual firm returns are unknown, I also incorporate estimation risk (e.g., Klein and Bawa (1976)... vq and small diagonal elements in '&~1 result in low amount of shrinkage and large variation across the factor lo a d in gs- T he parameter values for the diagonal elements in &-1 are set as... S a m ple X ? fr o m p(Ai | Aj , , A* ) p(Aj | A, 1+1, A3 , , A* ) p{Xd | Aj+1, A} t.) T he vectors A , A1 , , A1 , are a realization from a Markov Chain It can be shown (Geman and Gem an
IN F O R M A T IO N T O U S E R S This manuscript has been reproduced from the microfilm master UMI films the text directly from the original or copy submitted Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer The quality of this reproduction is dependent upon the quality of the copy submitted Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted Also, if unauthorized copyright material had to be removed, a note will indicate the deletion Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps Each original is also photographed in one exposure and is included in reduced form at the back o f the book Photographs included in the original manuscript have been reproduced xerographically in this copy Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge Contact UMI directly to order UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 R e p r o d u c e d w ith p e r m issio n o f th e co p y r ig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n Reproduced with permission of the copyright owner Further reproduction prohibited without permission TH E UNIVERSITY OF CHICAGO INFERENCE IN LONG-HORIZON EVENT STUDIES: A BAYESIAN APPROACH A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF BUSINESS IN CANDIDACY FOR TH E DEGREE OF DOCTOR OF PHILOSOPHY BY ALON BRAV CHICAGO, ILLINOIS AUGUST 1998 R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n UMI Number: 84149 Copyright 1998 by Brav, Alon All rights reserved UMI Microform 9841496 Copyright 1998, by UMI Company All rights reserved This microform edition is protected against unauthorized copying under Title 17, United States Code UMI 300 North Zeeb Road Ann Arbor, MI 48103 R e p r o d u c e d with p e r m issio n o f th e co p y r ig h t o w n e r F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n Copyright © 1998 by Alon Brav All rights reserved R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n ACKNOWLEDGMENTS I thank my committee members George Constantinides, Mark Mitchell, Nick Poison, Richard Thaler and especially Eugene Fam a for their guidance and encouragement In addition, I would like to thank J.B H eaton for his invaluable insights throughout the writing of this dissertation iii R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n TABLE OF CONTENTS A C K N O W LED G M EN TS iii LIST OF F IG U R E S vi LIST OF T A B L E S vii A B S T R A C T viii Chapter IN T R O D U C T IO N 1.1 B ackground M ETH O D O LO G Y 2.1 D ata D e sc rip tio n 2.2 Basic Setup and ModelE s tim a tio n 2.3 Predictive Distribution for Long-Horizon R e tu rn s 2.4 Statistical Inferen ces 2.4.1 Do the ResidualCovariations M a tte r ? 2.4.2 A check on Simulation E r r o r 7 18 19 21 21 EMPIRICAL R E SU L T S 3.1 Initial Public Offerings 3.1.1 Sample Description 3.1.2 Statistical Inferences 3.1.3 Do the Residual Covariations M a tte r ? 3.1.4 A check on Simulation E r r o r 3.1.5 Comparison with an Alternative M e t h o d 3.2 Stock R ep u rch a ses 3.2.1 Sample Description 3.2.2 Statistical In fe re n c e 3.2.3 Are “Value” Repurchasing Firms U ndervalued? 3.2.4 Explaining the Difference in Computed R e t u r n s 3.3 Dividend I n itia tio n s 3.3.1 Sample Description 3.3.2 Statistical In fe re n c e 3.4 Dividend O m is s io n s 3.4.1 Sample Description 3.4.2 Statistical In fe re n c e 23 23 23 25 26 26 27 30 30 31 32 33 35 36 37 39 39 40 iv R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 42 CONCLUSION Appendix A P R O O F S A l Positive-Definiteness of R A.2 Sampling from the conditional distributions for p and crl 44 44 45 B F IG U R E S 47 C T A B L E S 52 R E F E R E N C E S 66 v R e p r o d u c e d w ith p e r m issio n o f th e co p y r ig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n LIST OF FIGURES Figure Page Shrinkage Estim ation of Factor L o a d in g 48 Shrinkage Estim ation of Residual Standard D e v ia tio n s 49 Shrinkage Estim ation of the common correlation c o e f fic ie n t 50 Comparison of EPO and Replacing Firms Residual Standard Deviations 51 vi R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n LIST OF TABLES Table Page D ata description for computer and d ata processing I P O s 53 Aftermarket performance of computer and data processing I P O s 53 Regression results for computer and d ata processing I P O s 54 Predictive densities for the computer and data processing I P O s 54 Predictive densities assuming independence for the com puter and data process ing I P O s 55 Simulation sensitivity c h e c k 55 IPO data d e s c rip tio n 56 EPO aftermarket p e rfo rm a n c e 56 Predictive densities for IPO average abnormal r e t u r n 57 10 Predictive densities assuming independence for IPO average abnormal return 57 11 Simulation sensitivity c h e c k 57 12 IPO sample bootstrap d is tr ib u tio n 58 13 Industry Classifications for EPO A n a ly sis 58 14 IPO Excess R eturn Relative to the NYSE-AMEX value-weight i n d e x 59 15 Stock repurchases d a ta d e s c rip tio n 60 16 Predictive densities for stock repurchases average abnorm al r e tu r n 60 17 Predictive densities for repurchase sample sorted by book-to-m arket 61 18 Comparison of abnorm al return calculations for repurchase s a m p l e 61 19 Industry classifications for stock repurchase an aly sis 62 20 Repurchasing firms excess return relative to the NYSE-AMEX value-weight index 62 21 Dividend initiations data d e s c rip tio n 63 22 Regression results for the dividend initiation s a m p le 63 23 Predictive densities for dividend initiations average abnorm al r e t u r n 64 24 Dividend omissions d ata description 64 25 Regression results for the dividend omission s a m p l e 65 26 Predictive densities for dividend omissions average abnorm al r e t u r n 65 vii R e p r o d u c e d w ith p e r m issio n o f th e co p y r ig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 56 Table IPO data description The table gives the distribution of the 1521 sample firms by size and book-to-market For each IPO I use the pre-issue book value reported by Ritter (1991) while size is determined using the first closing price available from CRSP The 5x5 size and book-to-market cutoffs were determined using NYSE firm breakpoints Each IPO was first allocated to a size quintile and then allocated to a book-to-market quintile Panel (a) reports the number of observations in each cell The last row in this panel gives the number of missing book-to-market observations.1 Panel (6) reports the mean market capitalization within each size quintile Panel (c) reports the mean book-to-market for each cell P a n e l (a ): Number of IP O s Size Smallest Book-to-Market 21 Low 65 990 183 41 39 22 0 26 High Missing book 106 Largest 0 0 P a n e l (b ): Mean Size (mS) Smallest 24.6 Size 104.7 223.1 451.8 Largest 1099.5 P a n e l (c): Mean Book-to-M arket Size Book-to-Market Smallest 0.07 low 0.12 0.12 0.11 0.73 0.70 0.70 0.63 1.04 0.93 0.98 — 1.37 1.33 High 1.91 - Largest 0.11 - Table IPO aftermarket performance The table provides descriptive statistics regarding the five-year aftermarket return performance of the 1521 IPOs relative to the NYSE-AMEX value-weight index If a firm delists prematurely I calculate the buy and hold return until the delisting month both for the sample firm and the benchmark Also given is the cross-sectional standard deviation of abnormal returns (Std) and the skewness (Skew) of the abnormal return distribution N um ber of IPOs 1521 IPO Return Avg (%) Median (%) 27.2 -37.1 NYSE-AMEX Avg return (%) 92.9 Year Abnormal Retum (% ) Avg S td Skew -65.7 245.9 11.9 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 57 Table Predictive densities for IPO average abnormal return The table reports descriptive statistics of the predictive densities for the IPO sample average abnor mal return under different shrinkage scenarios Reported are the 1st, 5th, 50th and 95th percentiles, as well as the mean Panels (t) and (ii) give the properties of these densities for two different levels of B shrinkage Within each panel I report the effect of residual variance shrinkage The rightmost column gives the sample abnormal performance calculated using the firms’ factor loadings P a n e l (i): “Mild” shrinkage of B (elements in 'k equal 1/2) Shrinkage Sim ulated Distribution Abnormal R eturn Of C i 5% 50% 95% Mean 1% -1 -1.4 24.1 0.7 -47.0 Mild -2 5 0.4 Strong -2 -1 -0.9 22.1 -46.9 P a n e l (ii); “Strong” shrinkage of B (elements in 'k equal 1/4) Mild -2 -1 - 0.6 1.5 -45.0 27.0 - 1.1 Strong -2 -1 22.0 0.3 -45.3 Table 10 Predictive densities assuming independence for IPO average abnormal return The table reports descriptive statistics of the predictive densities for the IPO sample average ab normal return assuming independence under different shrinkage scenarios Reported are the 1st, 5th, 50th and 95th percentiles, as well as the mean Panels (i) and (it) give the properties of these densities for two different levels of B shrinkage Within each panel I report the effect of residual variance shrinkage P a n e l (i): Shrinkage Of ffi Mild Strong P a n e l (ii): Mild Strong “Mild” shrinkage of B (elements in 'k equal 1/2) Simulated D istribution 5% 50% 95% Mean - 20.1 -15.8 -1.8 21.5 0.4 -13.9 -0.7 17.1 -19.1 0.2 “Strong” shrinkage of B (elements in ,k ~ t equal 1/4) 1% -20.7 -18.9 -15.5 -14.1 - 1.6 -0.5 18.7 17.0 0.0 0.5 Table 11 Simulation sensitivity check The table reports the sensitivity of the predictive distributions for the IPO sample average abnormal return to simulation error For each shrinkage scenario in table I use the simulated means and resample 100 times, with replacement, samples of abnormal mean returns each containing 2000 observations Then, for each such sample, I calculate the 1st, 5th, 50th and 95th percentiles Summary statistics regarding the variation of these statistics across the different simulations are presented below Shrinkage of B «r, Mild Mild Mild Strong Strong Mild Strong Strong 1% Mean -25.2 -24.6 -24.3 -24.1 S td 0.2 0.3 0.2 0.2 5% Mean Std -18.8 0.1 -18.2 0.1 -18.0 0.1 -17.9 0.1 50% Std Mean 0.2 - 1.1 -0.7 0.1 -0.5 0.1 -0.7 0.1 95% Mean 24.6 22.4 26.1 21.9 Std 0.3 0.3 0.4 0.2 R e p r o d u c e d w ith p e r m is s io n o f th e co p y r ig h t o w n e r F u rth er re p ro d u ctio n p roh ib ited w ith o u t p e r m issio n 58 Table 12 IPO sample bootstrap distribution The table presents the bootstrapped distribution for the IPO sample The distribution is created as follows Since each EPO has been assigned to a size and book-to-market portfolio allocation (see section 3.1.5) I randomly select from that allocation a replacement firm with the same return horizon as the original firm If a replacement firm delists prematurely, I invest the proceeds from the delisting firm in another randomly selected firm from the same portfolio, for the remaining period This replacement is repeated for all IPOs in the sample, resulting in a new “pseudo” sample I proceed to calculate the latter sample abnormal performance relative to the original size and bookto-market portfolios Repeating this replacement 2000 times results in 2000 average abnormal returns which are used to construct the bootstrapped density for the sample mean The table reports the 1st, 5th, 50th and 95th percentiles as well as its standard deviation, mean and skewness coefficient The abnormal return adjusted by size and book-to-market is given in the last column 1% -1 S im ulated D istribution (2000 Bootstraps) 5% 50% 95% Mean Std Skewness -8 -0.75 11.86 0.24 6.71 1.49 Abnorm al R eturn -6 Table 13 Industry Classifications for IPO Analysis The main source for the industry d efinitio n s is Ritter (1991) and Spiess and Affleck Graves (1995) The column “Added” lists the additional SIC codes added to some of these industries In d u stry 10 11 12 13 14 15 16 17 Electronic equipm ent Computer M anufacturing Financial In stitu tio n s Oil &: Gas Com puter a n d d a ta processing services Optical, m edical an d scientific equip’ Retailers Wholesalers Health care & HM Os R estaurant chains Drug and genetic engineering Business Services Airlines Communications Metal and m etal products Insurance O ther Total SIC Codes Added R itter 369 366, 367 357 620-628 602-603, 612, 671 131, 138, 291, 679 492 737 381-384 520-573,591-599 501-519 800-804 805-809 581 283 — 739 452,458,372 451 — 480-489 351-356, 358-359 — 631-641 — - R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n N um ber of IPO s 146 144 139 129 113 111 70 63 57 54 44 42 32 29 24 17 307 1521 59 Table 14 IPO Excess Return Relative to the NYSE-AMEX value-weight index Based on the industry classification given in table 13, I allocate the 1521 IPOs into 17 industries and then calculate their five year abnormal return relative to the NYSE-AMEX value-weight index For each industry I report the number of firms, the average and median industry return, and the corresponding average market return The last three columns give the average abnormal return (Avg) as well as the cross-sectional standard deviation (Std) and skewness (Skew) of excess returns In the last row I report these statistics for the full sample Industry Electronic Equipm ent C om puter M anufacturing Financial Institutions Oil & Gas Com puter & d a ta p ro c ’ Optical &: medical equ ip ’ Retailers Wholesalers Health care & HM Os R estaurant chains Drug genetic eng’ Business Services Airlines Communications Metal Insurance O ther Total Number of IPOs 146 144 139 129 113 111 70 63 57 54 44 42 32 29 24 17 307 1521 IPO R eturn Avg (%) Median (%) -48.3 3.9 -47.7 19.3 52.6 90.6 -50.7 -86.1 -47.2 24.5 -53.5 -2.3 -16.4 35.2 -48.5 -10.9 -27.3 19.9 -71.8 166.4 72.7 41.8 -35.3 0.0 61.1 -11.9 -55.6 -15.8 5.9 -50.6 84.9 101.3 36.1 -26.1 27.2 -37.1 NYSE-AM EX Avg re tu rn (%) 97.6 99.1 93.7 93.5 90.2 96.2 91.9 86.8 84.0 89.1 100.7 90.3 82.1 79.3 90.5 96.4 91.2 92.9 Abnormal Return(% ) Avg Std Skew -93.7 152.2 3.8 -79.8 201.1 3.8 150.3 -3.1 0.8 -144.2 7.9 152.9 -65.7 185.0 2.8 -98.5 150.7 3.4 -56.7 154.4 2.2 -97.7 93.6 1.2 -64.1 146.9 1.4 77.3 971.8 5.0 -28.0 142.3 1.8 134.4 -90.3 2.1 -21.0 180.1 2.0 -95.1 83.1 0.3 -84.6 136.8 1.7 159.4 4.9 0.8 207.7 5.9 -55.1 -65.7 245.9 11.9 R e p r o d u c e d w ith p e r m issio n o f th e co p y r ig h t o w n e r F u rth er r ep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 60 Table 15 Stock Repurchases data description T he table presents the distribution of the sample firms by m arket capitalization (size) and book-to-market Size and book-to-m arket cutoffs were determ ined using NYSE firm breakpoints Each repurchasing firm was first allocated to a size quintile a n d th en allocated into a book-to-m arket quintile Panel (a) reports the num ber of observations in each cell T he last row in this panel gives the num ber o f missing book-to-market observations Panel (b) reports th e m ean m arket capitalization within each size quintile Panel (c) reports th e mean book-to-m arket for each cell P a n e l (a): Number of Firm s Book-to-M arket Low Smallest 92 101 High Missing 101 Smallest 37.64 85 78 87 58 74 65 42 26 33 Size 54 53 42 30 25 16 56 56 38 50 21 22 P a n e l (b ): Mean Size (mS) Size Q uintile Quintile3 Quintile 978.40 150.26 398.29 P a n e l (c): Mean Book-to-M arket Size Smallest Book-to-M arket Low 0.37 0.36 0.35 0.35 0.62 0.64 0.64 0.66 0.86 0.84 0.87 0.91 1.21 1.24 1.20 1.23 High 2.00 1.75 1.79 1.63 Largest 90 7564 44 25 18 Largest 5701.18 Largest 0.34 0.64 0.85 1.20 1.62 Table 16 Predictive densities for stock repurchases average abnorm al return T he table reports descriptive statistics of the predictive densities for the repurchase sam ple average abnormal re tu rn under different shrinkage scenarios R eported are th e 1st, 5th, 50th, 95th and 99th percentiles, as well as the mean The first and second rows give the properties of these densities for two different levels of B shrinkage The rightm ost colum n gives the sample abnorm al performance calculated using the firms’ factor loadings B Shrinkage Strong Mild 1% -15.1 -14.9 5% - 12.1 - 11.6 50% -1.3 - 1.1 95% 16.9 19.3 99% 3.3 5.9 Mean 0.9 1.7 Abnorm al R eturn 6.3 6 R e p r o d u c e d with p e r m issio n o f th e co p y r ig h t o w n e r F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 61 Table 17 Predictive densities for repurchase sample sorted by book-to-market Using book-to-m arket information available prior to the event, I sort repurchasing firms into book-to-market quintiles The average four year performance of these firms is reported in the table below along with th e average factor loadings for each subsam ple and the percentiles needed in order to conduct statistical inferences Quintile Low High N um ber of firms 299 298 298 298 300 Factor Loadings RM RF HML SMB - 0.1 0.6 1.0 1.0 0.0 1.1 0.2 0.6 1.0 0.3 0.4 0.6 1.0 0.6 0.7 yr Avg R etu rn (%) Rep' Bench Diff 69.9 - 0 45.9 73.0 7.4 65.6 86.0 12.5 73.5 99.2 14.0 85.2 114.7 2 137.5 Percentiles 5% 95% -24.9 42.1 -16.8 25.0 -17.6 23.4 -17.1 22.5 -26.8 45.0 Table 18 Comparison of abnom m al return calculations for repurchase sample T he table presents abnorm al return calculations for the repurchase sam ple employing either buy and hold or annual rebalancing m ethods T he six rows correspond to the full repurchase sam ple (first row) and to th e book-to-m arket quintiles (second through sixth rows) Repurchase Firms B u y -a n d -H o ld Size and Bookto-M arket 89.2 82.3 47.8 71.5 74.1 66.2 88.5 75.4 102.0 87.2 139.2 116.0 P o r tfo lio R e b a la n c in g Abnorm al Abnormal Repurchase Size an d BookFirms to-M arket R eturn R eturn Full Sample Results 6.9 99.9 93.6 6.3 Low Book-to-M arket Quintile -2 46.8 2nd Book-to-M arket Quintile 7.9 74.0 3rd Book-to-M arket Quintile 90.8 13.1 4th Book-to-M arket Quintile 14.8 111.2 High Book-to-Market Quintile 23.2 160.3 76.1 -2 72.0 79.7 11.1 92.7 18.5 114.5 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 62 Table 19 Industry classifications for stock repurchase analysis T he main source for th e in d u stry definitions is R itte r (1991) and Spiess and Affleck Graves (1995) The column “A dded” lists th e additio n al SIC codes a d d ed to some of these industries In d u stry 10 11 12 13 14 Com puter M anufacturing Communications and electronic equip’ Oil & Gas Financial Institutions Com puter and d a ta processing services Optical, medical an d scientific equip’ Retailers Wholesalers R estaurant chains Food Drug and genetic engineering Metal and m etal pro d u cts T ransportation E quipm ent O ther Total SIC Codes Added R itte r 357 369, 481-489 366, 367 131, 138, 291, 679 492 620-641 602-603, 612, 671 737 381-384 520-573,591-599 501-519 581 — 200-209 283 351-356, 358-359 371-379 — — - N um ber of R ep' firms 42 94 130 273 34 31 88 63 21 68 42 53 58 623 1620 Table 20 Repurchasing firms excess return relative to the NYSE-AMEX value-weight index Based on th e industry classification given in table 19 I allocate the 1620 repurchasing firms into 14 industries and then calculate their four year excess return relative to the NYSE-AMEX value-weight index For each industry I report the num ber of firms, the average a n d median industry retu rn , and th e corresponding average market return The last th ree colum ns give the average excess return (Avg) as well as th e cross-sectional standard deviation (Std) and skewness (Skew) of excess returns In the last row I report these statistics for the full sample Industry Computer M anufacturing Communications Oil & Gas Financial Institutions Computer & d ata proc’ Optical & medical equip’ Retailers Wholesalers R estaurant chains Food Drug & genetic eng’ Metal Transportation Equipm ent O ther Total N um ber of firms 42 94 130 273 34 31 88 63 21 68 42 53 58 623 1620 F irm R eturn M edian (%) Avg (%) 1.1 48.4 27.4 49.8 9.3 17.7 119.7 98.5 79.5 126.8 94.5 118.4 71.3 104.2 48.9 79.3 47.6 62.8 136.4 155.8 91.4 109.8 46.1 50.2 37.9 79.2 62.6 85.7 64.2 87.0 NYSE-AMEX Avg (%) 73.0 71.4 79.6 72.3 54.7 74.4 63.3 71.2 59.4 68.8 68.2 70.6 74.9 70.9 71.1 A bnorm al R eturn(% ) Avg S td Skew 151.2 1.9 -24.6 101.1 - 21.6 1.0 99.9 -61.9 0.6 47.4 128.2 1.8 156.7 72.0 0.8 170.0 2.2 44.0 148.4 40.9 1.9 170.2 3.7 8.0 3.4 96.7 0.9 163.7 87.0 3.5 94.1 41.6 0.1 -20.4 0.7 89.3 4.3 109.6 1.5 14.8 117.3 1.8 129.0 2.0 15.9 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 63 Table 21 Dividend initiations data description T he table provides descriptive statistics for the 560 firms th a t initiated dividends over th e period 1964-1988 Q uarterly size and book-to-m arket breakpoints were created using NYSE firm s only Then, each firm was allocated to a size quintile in th e q uarter before its dividend initiation F irm s were further allocated into book-to-m arket quintiles w ithin each size sort In Panel (a) I report the allocation of these firms into the size and book-to-market quintiles T he last line in this panel reports the num ber of missing book value firms w ithin each size quintile Panel (b) rep o rts the mean size w ithin each quintile Panel (c) reports the mean book-to-m arket ratio for each of th e 25 possible allocations P a n e l (a ): Num ber of firms Initiating Size Book-to-M arket Smallest Low 26 13 38 14 11 56 44 19 72 11 74 14 High Missing 18 10 98 Dividends Largest 1 1 P a n e l (b): Mean Size (m$) Sm allest 17.14 78.62 Size 171.58 378.25 Largest 2001.04 P a n e l (c): Mean Book-to-Market Size Book-to-M arket Smallest low 393 0.485 0.394 0.352 0.834 0.677 0.850 0.813 1.127 1.088 0.987 1.140 1.622 1.504 0.958 0.984 2.254 2.385 2.064 2.676 High Largest 0.347 0.591 1.163 0.907 NaN Table 22 Regression results for the dividend initiation sample T he table gives the regression results for the 560 dividend initiating firms I report th e average of the posterior means for th e factor loadings and residual standard deviations R esults are presented both for the C A PM and the Fam a and French three-factor model Factor Loadings and Residual Standard Deviations CA PM F am a & F re n c h Factor Loading Factor Loading Market Residual Std Market HML SMB R esidual Std 1.49 0.12 1.12 0.17 1.33 0.11 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 64 Table 23 Predictive densities for dividend initiations average abnormal return The table reports descriptive statistics of the predictive densities for th e dividend initiation average abnorm al return R eported are th e 1st, 5th, 50th, 95th and 99th percentiles, as well as the mean, standard deviation and skewness T he last colum n gives the abnormal return calculated using the firms’ factor loadings Model CAPM Fama-French 1% -9.69 -17.6 5% -6.34 -13.5 50% -0.47 -0.62 95% 10.32 14.78 99% 15.77 30.19 Mean 0.46 -0.18 Std 5.38 9.30 Skewness 0.88 0.58 Abnormal R eturn 59.41 -0.28 Table 24 Dividend omissions data description The table provides descriptive statistics for the 885 firms th a t om itted dividends over the period 1964-1988 Q uarterly size and book-to-m arket breakpoints were created using NYSE firms only Then, each firm was allocated to a size quintile in th e quarter before its dividend omission Firm s were further allocated into book-to-m arket quintiles w ithin each size sort In Panel (a) I report th e allocation of these firms into the size and book-to-m arket quintiles T he last line in this panel reports the num ber of missing book value firms within each size quintile Panel (b) reports the mean size within each quintile Panel (c) reports the mean book-to-m arket ratio for each of th e 25 possible allocations P a n e l (a): Number of Firm s O m itting Dividends Size Largest Book-to-M arket Smallest Low 29 15 36 13 74 22 18 3 23 14 113 High 208 40 25 20 Missing 137 30 16 P a n e l (b): Mean Size (m$) Size Smallest 20.56 94.49 216.89 600.32 Largest 2572.17 P a n e l (c): Mean Book-to-M arket Size Book-to-M arket Smallest 0.316 low 0.379 0.357 0.353 0.600 0.700 0.769 0.658 1.027 0.763 1.030 1.075 1.187 1.397 1.314 1.432 2.170 High 2.219 2.542 2.399 Largest 0.489 0.753 - 0.893 2.413 R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 65 Table 25 Regression results for the dividend omission sample The table gives th e regression resui r~- for the 885 dividend initiating firms I report the average of the posterior m eans for th e factor loadings and residual standard deviations Results are presented both for the CAPM and th e Fam a a n d French three-factor model Factor Loadings and Residual S tandard Deviations F a m a & F ren ch CA PM Factor Loading Factor Loading M arket HML SMB Residual Std M arket Residual Std 1.03 0.57 1.43 0.12 1.33 0.13 Table 26 Predictive densities for dividend omissions average abnormal return The table reports descriptive statistics of the predictive densities for th e dividend omission average abnormal return R eported are th e 1st, 5th, 50th, 95th and 99th percentiles, as well as th e mean, standard deviation and skewness T he last colum n gives the abnormal retu rn calculated using th e firms’ factor loadings Model CAPM Fama-French 1% -1 -1 5% -8 -1 50% -1.28 - 0.86 95% 8.02 13.85 99% 13.55 19.64 Mean -0.34 -0.18 S td 6.61 7.75 Skewness 4.13 0.38 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n Abnormal R eturn -5.19 -44.95 R EFER EN C ES Barber M Brad and John D Lyon, 1997, “Detecting Long-Run Abnormal Stock Returns: The Empirical Power and Specification of Test-Statistics,” Journal o f Financial Eco nomics, 43(3) Barnard, John, R obert McCulloch and Xiao-Li Meng, 1997, “Modeling Covariance Matrices with Application to Shrinkage," Working paper Bernard, Victor L., 1987, “Cross-Sectional Dependence and Problems in Inference in Market-Based Accounting Research," Journal of Accounting Research, 25(1) Blattberg, C Robert and Edw ard I George, 1991, “Shrinkage Estim ation of Price and Promotional Elasticities: Seemingly Unrelated Equations,” Journal of the American Sta tistical Association, 86(414), 304-315 Blume, Marshall E and Robert F Stambaugh, 1983, “Biases in Com puted Returns An application to the Size Effect,” Journal of Financial Economics, 12, 387-404 Box, George E P., 1980, “Sampling and Bayes’ Inference in Scientific Modelling and Ro bustness (with discussion),” Journal o f the Royal Statistical Society A, 143(4), 383-430 Brav, Alon and Paul Gompers, 1997, “M yth or Reality? The Long-Run Underperformance of Initial Public Offerings: Evidence from Venture and Nonventure Capital-backed Com panies,” Journal of Finance, 52(5), 1791-1821 Collins, Daniel W and W arren T Dent, 1984, “A Comparison of A lternative Testing Methodologies Used in C apital M arket Research,” Journal o f Accounting Research, 22(1), 48-84 Cowan, Arnold R and Anne M.A Sergeant, 1997, “Interacting Biases, Non-Normal Return Distributions and the Performance of Parametric and Bootstrap Tests for Long-Horizon Event Studies,” Working paper, Iowa State University Davidson, Russell and James G MacKinnon, 1993, Estimation and Inference in Economet rics Oxford University Press Fama, Eugene F and K enneth R French, 1993, “Common risk factors in the returns on stocks and bonds,” Journal o f Financial Economics, 33, 3-56 Gelfand A E., D K Dey and H Chang, 1992, “Model Determ ination Using Predictive Distributions w ith Im plem entation via Sampling-Based Methods,” in Bayesian Statistics, ed by J.M Bernardo, J.O Berger, A.D Dawid and A.F.M Smith Oxford University Press, vol 4, pp 147-167 66 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 67 Gelfand, Alan E and Adrian F M Smith, 1990, “Sampling-Based Approaches to Cal culating Marginal Densities,” Journal o f the American Statistical Association, 85(410), 398-409 Gelfand, Alan E., Susan E Hills, Amy Racine-Poon and A drian F M Smith, 1990, “Illus tration of Bayesian Inference in Normal D ata Models Using Gibbs Sampling,” Journal of the American Statistical Association, 85(412), 972-985 Gelman, Andrew, John B Carlin, Hal H Stern and Donald B Rubin, 1995, Bayesian Data Analysis Chapman & Hall Gelman, Andrew, Xiao-Li Meng and Hal Stem , 1996, “Posterior Predictive Assessment of Model Fitness Via Realized Discrepancies,” Statistica Sinica, 6, 733-807 Geman, S and Geman D., 1984, “Stochastic Relaxation, Gibbs distributions and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741 Gibbons Michael, 1982, “M ultivariate Tests of financial models: A new approach,” Journal of Financial Economics, 10, 3-27 Gilks, W R., S Richardson and D.J Spiegelhalter, 1996, Markov Chain Monte Carlo in Practice Chapman & Hall Ibrahim G Joseph and Purushottam W Laud, 1994, “A Predictive Approach to the Anal ysis of Designed Experiments,” Journal of the American Statistical Association, 89(425), 309-319 Hcenberry, David, Josef Lakonishok and Theo Vermaelen, 1995, “M arket underreaction to open market share repurchases,” Journal of Financial Economics, 39, 181-208 Jorion Philippe, 1991, “Bayesian and CAPM estimators of the means: Implications for portfolio selection,” Journal of Banking and Finance, 15, 717-727 Kent, Daniel, Mark Grinblatt, Sheridan T itm an and Russ Wermers, 1997, “Measuring M utual Fund Performance with Characteristic Based Benchmarks,” Journal of Finance Klein, R W and V.S Bawa, 1976, “The effect of estim ation risk on optimal portfolio choice,” Journal of Financial Economics, 3, 215-231 Kothari, S P and Jerold B Warner, 1997, “Measuring Long-Horizon Security Perfor mance,” Journal of Financial Economics, 43(3) Kothari, S.P and Jay Shanken, 1997, “Book-to-Market, Dividend Yield, and Expected Market Returns: A Time-Series Analysis,” Journal of Financial Economics, 44(2), 169203 Laud W Purushottam and Joseph G Ibrahim , 1995, “Predictive Model Selection,” Journal of the Royal Statistical Society B, 57(1), 247-262 R e p r o d u c e d w ith p e r m issio n o f th e co p y r ig h t o w n e r F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 68 Lindley D V and A F M Smith, 1972, “Bayes Estimates for the Linear Model,” Journal of the Royal Statistical Society B , 34, 1-41 Lintner, John, 1965, “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budjets,” Review of Economics and Statistics, 47, 13—37 Loughran, Tim and Jay R Ritter, 1995, “The new issues puzzle,” Journal o f Finance 50, 23-51 Lyon, D John, Brad M Barber and Chih-Ling Tsai, 1998, “Improved Methods for Tests of Long-Run Abnormal Stock R eturns,” Forthcoming, Journal of Finance Metrick Andrew, 1997, “The Equity Performance of Investment Newsletters,” Working paper, Harvard University Michaely, Roni, Richard H Thaler and Kent L Womack, 1995, “Price Reactions to Dividend Initiations and Omissions: Overreaction or Drift?,” Journal of Finance, 50, 573-608 Olkin Ingram, 1981, “Range Restrictions for Product-Moment Correlation Matrices,” Psychometrika, 46(4), 469-472 Paparodotis Efstathios, 1996, “A Frequency Domain Bootstrap-Based M ethod for Checking the Fit of a Transfer Function Model,” Journal of the American Statistical Association, 91(436), 1535-1550 Priest H F., 1968, “Range of Correlation Matrices,” Psychological Reports, 22, 168-170 R itter, Christian and M artin A Tanner, 1992, “Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler,” Journal of the American Statistical Association, 87(419), 861-868 R itter, Jay R., 1991, “The long-run performance of initial public offerings.” Journal of Finance, 46, 3-28 Roll, Richard, 1983, “On Computing Mean Returns and the Small Firm Prem ium ,” Journal of Financial Economics, 12, 371-386 Rubin, Donald B., 1984, “Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician,” The Annals of Statistics, 12(4), 1151-1172 Sefcik, Stephan E and Rex Thompson, 1986, “An Approach to Statistical Inference in Cross-Sectional Models with Security Abnormal Returns as Dependent Variable,” Journal of Accounting Research, 24(2) Shan ken Jay, 1990, “Intertemporal asset pricing: An empirical investigations,” Journal of Econometrics, (45), 99-120 Sharpe, William F., 1964, “Capital asset prices: a theory of market equilibrium under conditions of risk,” Journal of Finance, 19, 425-442 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n 69 Speiss, Katherine D and John Affleck-Graves, 1995, “Underperformance in the long-run stock returns following seasoned equity offerings,” Journal o f Financial Economics, 38, 243-267 Stambaugh, Robert F., 1997, “Analyzing Investments W hose Histories Differ in Length,” Journal o f Financial Economics, 45(3), 285-331 Stangl Dalene and Gabriel Huerta, 1997, “Using Bayesian Hierarchical Models to Assess The Im pact of Managed-Care Strategies,” Working Paper, In stitu te of Statistics and Decision Sciences, Duke University Stevens, Ross L., 1996, “New Methods in Asset Pricing Model Estim ation,” University of Chicago w o rk in g paper Tanner, M artin A., 1996, Tools for Statistical Inference: Methods fo r the Exploration of Posterior Distributions and Likelihood Functions Springer-Verlag, third edn Tsay, Ruey S., 1992, “Model checking via parametric bootstraps in time series analysis,” Applied Statistics, 41(1), 1-15 Womack, L Kent, 1996, “Do Brokerage Analysts’ Recommendations Have Investment Value?,” Journal o f Finance, 51(1), 137-167 Zellner Arnold, 1962, “An efficient m ethod of estim ating seemingly unrelated regressions and tests for aggregation bias,” Journal o f the American Statistical Association, 57 348368 , 1971, A n Introduction to Bayesian Inference in Econometrics John Wiley and Sons, New York R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n IMAGE EVALUATION TEST TARGET ( Q A - ) 1.0 |2j8 ill Ih 2.2 £ Urn 2.0 yo Ui l.l 1.8 1.25 1.4 1.6 150mm IIVWGE Inc 1653 E ast Mam S treet R ochester NY 14609 USA Phone: 716/482-0300 Fax: 716/288-5989 R e p r o d u c e d w ith p e r m issio n o f th e co p y rig h t o w n er F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n