Essays in financial economics and applied econometrics

For exam ple, sm all stocks dow ngraded from “b uy” have negative abnorm al returns until 60 trad in g days after the ratin g change, while large stocks do not have significant post-even

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R e p r o d u c e d with p e r m i s s i o n o f t h e co p y r ig h t o w n e r F u r t h e r r e p r o d u c t i o n p ro h ib ite d w ith o u t p e r m i s s i o n

ESSAYS IN FINANCIAL ECONOMICS AND

A Craig MacKimay, Co-s§pcrvisui TjFDisS5Rati'0TT

Francis X Diebold, Co-supervisor of Dissertation

Steven A Matthews, Graduate Group Chairperson

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To my parents, my husband and my children

a

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First, I wish to thank the four people who have been guiding and supporting me in completing this dissertation My greatest debts are to Craig MacKinlay and Frank Diebold, my Dissertation Supervisor and Co-supervisor, from whom I learned how to do research and teaching in financial economics I also appreciate their insightful comments, patience and continuing encouragement throughout the process Gary Gorton and Petra Todd have been enormously helpful in giving me illuminating comments and directions o f my research I could not have had a better team of advisors

M any faculty and staff members and fellow graduate students (former and current) at Penn have helped me in different ways In particular I am grateful to Professor Phillip Stocken for his gracious help with the first chapter o f the dissertation I thank Sean Campbell, Jun (QJ) Qian, Canlin Li and Brett Norwood for their helpful discussions and support I would also like to thank Professor Neil Wallace who taught me the first graduate class in economics at University of Miami Neil is a great economist, and an even better mentor

I am indebted to University o f Science and Technology o f China (USTC) for its rigorous training and academic freedom I had the best experience as an undergraduate at USTC

I would like to say thanks to my loving parents, Peiping Peng and Shengli Cheng You gave

me the best home and the best education M ore importantly you have always shown me the enormous courage and strength I also want to thank my older sister, Hongmei You have always been on my side I am grateful to your confidence

I want to thank my dear husband, Tianming Zhang, and my beautiful children, Jimmy and Karina You have made me a better person You make me happy, gentle, and strong I am grateful

to have you three in my life every day

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ABSTRACT

ESSAYS IN FINANCIAL ECONOMICS AND APPLIED ECONOMETRICS

Yingmei Cheng

A Craig MacKinlay

In the first chapter, Informativeness o f Analysts’ Recommendations, we investigate the

informativeness o f sell-side analysts’ recommendations by examining abnormal stock returns before, during and after changes in analysts’ ratings First, we show that the market derives different information from the similar recommendations by different brokerage firms, especially

in the case of downgrading from “ buy” The brokerage firms in the sample differ in terms of the impact o f their analysts’ recommendations on subsequent stock returns, although they are all ranked highly Second, we document that the market reacts quickly to the analysts’ recommendations, which contradicts the continuation of abnormal returns for months after recommendations, i.e., the so-called “ post-recommendation drift”, documented by the literature

In the second chapter, A Model o f Inside and Outside Experts-the Example o f Buy-side and

Sell-side Equity Analysts, we model the information transmission from multiple equity analysts to

a mutual fund manager The buy-side analyst has the same preference as the manager while the sell-side has different preference If the fund manager relies on only sell-side analysts, a subgame equilibrium always exists in which the analysts’ opinions are independent of their private signals and thus the information content is totally lost With one buy-side analyst in the panel, however, truth-telling is the only subgame equilibrium under a certain range o f parameters The equilibrium outcome is that the manager relies on both sell-side and buy-side equity analysts to make investment decisions

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In the third chapter, Evaluating Preschool Programs when Length o f Exposure to the

Program Varies—A Nonparametric Approach, we develop a nonparametric multi-dimensional

matching method and apply this method to a large, non-experimental data set to evaluate the effects o f a preschool enrichment program This generalized version of the matching method is able to control for nonrandom selectivity into the program or into alternative program duration by matching the group of interest to a comparison group on more than one dimension It minimizes the impact o f distributional assumptions The third chapter is intimately related to the first two in that it develops the nonparametric multi-dimensional matching method which is applicable to a variety issues in corporate finance

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C o n t e n t s

3.3.2 Comparison between Matching Methods and Traditionai

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Program Impacts After Adjusting for Selectivity Using

Mean Program Impacts After Adjusting for Selectivity Using

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21 Estimated Marginal Impacts by Duration and Age Classes: Group P,

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to b e r 23, 2000, inform ation th a t a publicly tra d e d com pany knows to be “m aterial’-

m ust be disclosed to th e professional and th e public a t the sam e time This regulation

is designed to make th e inform ation of public com panies as accessible to investors as

it is to well-known analysts It shows th a t the SEC tru ly believes th a t analysts have privileged access to inform ation We know th a t one task of equity analysts2 is to issue recom m endations (buy, sell, etc.) on stocks If S E C ’s belief is tru e, how does the

an aly sts’ private inform ation affect th e m arket th ro u g h th eir recom m endations?

T h e lite ra tu re has m ainly focused on sh o rt periods aro u n d recom m endations Stickel (1985) an d o th er work3 report evidence th a t T h e Value Line Investm ent Survey and

l I am gratefu l to C raig M acK inlay and Frank D ieb o ld for th eir encou ragem en t and guidance I

a p p reciate co m m en ts an d in sigh ts from Gary G orton , P etr a T od d and participan ts a t Penn E con om et­ rics W orkshop an d W h arton F in ance Sem inar I also ap p reciate su ggestion s from sem in ar participan ts

a t U n iversity o f O regon, U n iversity o f S ou th C arolina, F lorida S ta te U niversity and C harles R iver

A sso c ia te s I am in d eb ted to Sean C am pbell an d P h illip S tocken for th eir generous help an d ex ten siv e com m en ts I th a n k F irst C all for providing H istorical R eco m m en d a tio n D atab ase an d K en n eth French for access to h istorical factor returns A ny errors a re m y ow n responsibility.

'U n le s s oth erw ise n oted, th e a n a ly sts refered to in th is p aper are sell-sid e eq u ity a n a ly sts, i.e., those work for brokerage firms and p u b licly issue earn in gs forecasts and sto ck ratings.

3For ex a m p le, L loyd-D avies and C anes (1978), Liu, S m ith an d S yed (1990) and Francis and Soffer (1997).

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security analysts have private inform ation th a t, when revealed, results in small b u t statistically reliable price adjustm ents in a short period after th e recommendations, e.g., th ree o r five days around the events More recently, Womack (1996) examines stock retu rn s m onths after recom mendations He not only finds significant abnorm al retu rn s d u rin g th e three-day event window, b u t also docum ents evidence of the con­tin uatio n of abnorm al retu rn s for up to six months following the recom m endations

T his is the so-called “post-recom m endation d rift” T h e existence of longer-term post­recom m endation abnorm al returns is a puzzle It su pports the idea th a t the m arket

is slow to incorporate inform ation tra n sm itte d by the recom m endations and thus, the initial price reactions to these recom m endations are incom plete It is striking evidence against th e sem i-strong form of m arket efficiency hypothesis4

In this ch ap ter, I investigate the informativeness of seil-side equity analysts’ recom­

m endations by exam ining both the short- and longer-term abnorm al stock returns after changes in an aly sts’ ratings I construct a unique d a ta set th a t consists of recommen­dations hand-collected individually from F irst Call an d th e n combined w ith earnings inform ation from I / B / E / S and COM PUSTAT Industrial Q uarterly T h e paper makes two m ajor contributions

F irst, I show th a t th e m arket possibly derives different inform ation from the same

or sim ilar recom m endations by top brokerage firms To examine th e im pact of the brokerage firms on m arket reactions, I control for m arket capitalization of the stock, concurrent earnings news and other factors T h e results show th a t th e brokerage firms

l S in ce th e 1960s, there has been em pirical research in acad em ia ch allen gin g the m arket efficiency hy­

p o th esis T h e d eb a te has h istorically been con centrated on tests for th e weak form o f m arket efficiency,

or m ore generally, te sts for return pred ictab ility (Fam a, 1991) For th e sem i-stron g form, tests o f how quickly secu rity prices reflect public inform ation announcem ents, th ere has recently been su bstan tial work d o cu m en tin g overeaction /u n d erreaction o f sto ck prices to certain events For the strong-form ,

te sts o f w h eth er an y in vestors have private inform ation th a t is n ot fully reflected in m arket prices, or

te sts for p rivate inform ation, there is work on inside trading (Jaffe,1974; S eyhun,19S6), professional

p ortfolio m an agem en t (J e n se n ,1968; Ip polito,1989) an d security an alysis (Stick el,1985).

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differ in term s o f th e im pact of their an aly sts’ recom m endations on subsequent stock returns, although all th e brokerage firms in th e sam ple are ranked inside the top 20 by

Institu tio na l In v e sto r d uring th e sam pling period T he difference is m ost prom inent

in th e case of dow ngrading from “b u y ’ One explanation is t h a t the brokerage firms differ in term s of th e degree of interest conflicts between th em an d th e investors, yet

an o th er explanation is th a t the m arket has unobservable belief a b o u t how accurate the recom m endations are an d th e belief varies across different brokers

D istinguishing recom m endations from individual brokers is new in the literaturệ Since an individual analyst usually needs to o b ta in approval from a research oversight com m ittee in his or her firm before issuing ra tin g changes, especially in the case of dow ngrading, it is worthwhile to analyze th e recom m endations by different brokerage firms

Second, I docum ent th a t the m arket generally reacts quickly to th e an aly sts’ rec­

om m endations, which contradicts the existence of longer-term post-recom m endation abnorm al retu rn s docum ented by Womack (1996) One possible explanation for the drift is th a t th e m arket does not fully incorporate the inform ation em beđed in ana­

ly sts’ recom m endations, ịẹ, the m arket is inefficient A nother possibility is th a t the drift is due to bias in m easured abnorm al return s Still an o th er possible explanation is

th a t the post-recom m endation drift is sample-specific, ẹg., it m ight be sensitive to the tim e period or certain characteristics of th e firms I show th a t th e existence of “post­recom m endation d rift” is not robust to th e sam pling period T h e d a ta I use is from

1995 to 1997 in stead of 1989-1991 as in W omack (1996) T h e results do not provide evidence of significant post-event abnorm al retu rn s, except w hen firms are downgraded from “b u y ’ In th e case where it is supported, th e post-recom m endation drift is fragile

in th a t it is sensitive to the m agnitude of ra tin g change, th e m arket capitalization of

°S tickel (1995) ex a m in es w heth er the an alysts, w h o are selected in to A ll-S ta r A m erican first and

secon d team s by I n s titu tio n a l In vesto r, have m ore in fluence on sto ck reaction s th an oth er an alysts

However, he d id n ot con sid er different brokerage firm s.

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th e su bject company, an d th e broker issuing th e recom m endation For exam ple, sm all stocks dow ngraded from “b uy” have negative abnorm al returns until 60 trad in g days after the ratin g change, while large stocks do not have significant post-event abnorm al retu rn s Thus th e results question th e existence of “post-recom m endation drift” and show th a t in general th e m arket quickly incorporates inform ation tra n sm itte d from the recom m endations.

T h e above results are obtained using the size-adjusted model, which assum es th e expected retu rn of a stock to be th e re tu rn of th e m arket portfolio in th e sam e firm-size decile To exam ine th e sensitivity of th e results to different models, two o th e r models axe adopted to m easure th e expected returns: th e restricted m arket m odel an d th e nonparam etric local linear regression m ethod (LLR) Different from the size-adjusted model, these two models derive each sto ck’s specific expected returns by using param e­ters employing an estim ation period T he two models are different from th e widely used

m arket model T he nonparam etric local linear regression m ethod is ad o p ted to control for nonlinearity and reduce th e bias caused by outliers since it imposes fewer function form restrictions th a n th e m arket model6 However, the existence of pre-event abnor­

m al returns makes it difficult to specify the estim ation period for the m arket model

or th e nonparam etric LLR T hus, I propose a restricted m arket model as an altern a­tive when significant abnorm al retu rn s exist during the pre-event period R esults from these models are close to each other in th e short-run In the longer-run, th e restricted

m arket model and th e nonparam etric LLR have results generally consistent w ith those from the size-adjusted model In some cases, th ey further reject the existence of the post-recom m endation d rift

T h e rem ainder of th e chapter is organized as follows Section 1.2 outlines a frame­work for interpreting th e em pirical results in fight of inform ation transm ission from stock analysts to investors Section 1.3 presents d a ta construction and sam ple descrip­tion Section 1.4 describes th e em pirical methodology Section 1.5 examines th e im pact

fiT h e market m odel a ssu m es a linear relationship b etw een the stock return and th e m arket return.

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of different brokerage firms on short-run stock returns Section 1.6 studies the longer- term retu rn s Section 1.7 examines robustness of th e results to altern ativ e models of expected retu rn s Section 1.8 discusses th e results and Section 1.9 sum marizes the paper.

1.2 Information Transmission from Analysts to Investors

P rio r to issuing recom m endations, the analyst gathers inform ation on the individual stock from firm m anagers, custom ers and suppliers, and analyzes these d a ta to form

an opinion on w hether to buy or sell the stock T hen, he issues his recom m endation usually after o b taining approval by a research oversight com m ittee in his firm

It is reasonable to assum e th a t the analyst decides w hether a stock is overvalued

or undervalued by in p u ttin g his information, b o th public and private, into a valuation model P ublic inform ation includes earnings of the subject com pany and other types

of inform ation gathered, for example, from reports to the shareholders T he analyst may also have some private inform ation th a t the investors do no t have T he private inform ation m ay come from th e selective disclosure of inform ation from th e subject com pany to th e analysts, as the SEC believes is th e case For exam ple, the informa­tion m ay come from private m eetings with high-level m anagem ent or from information conferences held by the com pany exclusively for analysts7 T he stock price movements around th e recom m endations can thus be rationalized as investors infer and react to

th e p o ten tial private inform ation embedded in stock recom m endations

However, would th e recom m endation necessarily reflect the an aly ses tru e opinion?

T he a n a ly st’s objective is not necessarily to make th e m ost accurate recom m endation

T h ere are m ultiple forces pulling him in o th er directions For exam ple, an analyst faces pressure not only from the m anagem ent of th e com pany he covers, but also from the investm ent banking d ep artm en t in his brokerage firm (Balog, 1991) T he analyst may

‘ T h is w ould ch an ge in th e p resence o f R egu lation F D (Fair D isclosure) T h e sam ple in this stud y

d oes not go b eyon d D ecem ber 1997.

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have incentive to cultivate m anagem ent relations Interest conflicts also arise when the

a n a ly st’s firm provides investm ent banking services for th e com pany he is following

(M ichaely Sz W omack, 1999).

T herefore, inferring inform ation from an aly sts’ recom m endations is not an easy task A few theoretical papers, such as M organ and Stocken (2000) and Cheng (2000) show how th e interest conflicts could reduce th e inform ation content of the recom­

m endations issued by equity analysts Different brokerage firms m ight have different degrees of interest conflicts and valuation models of differing accuracy Thus investors

m ay respond differently to th e sam e recom m endation by different brokers In Section 1.5, stock reactions to recom m endations are com pared across brokerage firms and the results show th a t the brokerage firms indeed have different influence on stock reactions

A n o th er question is: how quickly do th e investors react to th e inform ation? If

a post-recom m endation drift exists, it would show th a t the m arket slowly takes the inform ation into account In Section 1.6, I show th a t in general, th e m arket reacts quickly to th e analysts’ recom m endations

1.3 Data Construction and Sample Description 1.3.1 Data Construction

D a ta from a variety of sources, including T h e Value Line Investm ent Survey, Zacks Investm ent Research, Investext, and F irst Call, have been used in em pirical work inves­tig a tin g a n aly sts’ recom m endations8 I use th e F irst Call Historical R ecom m endation

D atab ase I t is a com pilation o f individual recom m endations from more th an 220 ana­lysts a t leading Wall Street a n d regional research firms First Call distributes analy sts’ recom m endations to its subscribers through an on-line system As brokerage firms

'’For ex a m p le, Francis and Soffer (1997) u se In vestext; Francis and Philbrick (1993) and Stickel (1985) use T h e V alue Line In vestm en t Survey; S tickel (1995) and Barber, Lehavy, M cN ichols & True­

m an (1999) u se Zacks; W om ack (1996) u ses F irst Call.

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issue recom m endations from th e ir “m orning calls”3 electronically, F irst Call makes it available alm ost im m ediately to its subscribers who are also custom ers of th e broker­age firms T h e advantage o f th e F irst Cali R ecom m endation D atab ase to researchers

is th a t th e brokerage firms have an incentive to verify th e accuracy of the inform ation

on F irst Call since F irst Call is sold to professional, in stitu tio n al investm ent m anagers

T h e sam ple analyzed in th e current research comes from recom m endations issued betw een O ctober 1, 1995 and Decem ber 31, 1997 by six top brokerage firms identified

by Institutional In v e sto r (I I) I I annually ranks security analysts an d research d e p art­

m ents of m ajo r brokerage firms, m ainly according to polls of in stitu tio n al investors,

on th e basis of stock picking, earnings forecasts, w ritten rep o rts an d overall service I

have access to six brokerage firms am ong th e top 20 ranked by II Since some brokerage

firms en ter agreem ents w ith F irst Call which preclude F irst C all from d istrib u tin g their recom m endations to anyone o th er th a n th e brokerage houses’ clients, th e recom m enda­tions of several brokerage houses, including M errill Lynch and G oldm an Sacks, are not included in the d a ta s e t10 Table 1 presents th e list of brokerage firms in th e sample

a n d shows their ran k in g as rep o rted in II.

D uring the p eriod betw een O ctober 1995 and D ecem ber 1997, I read th e headlines

an d docum ents individually to collect the following inform ation for every observation:

th e d a te th e recom m endation is dissem inated by F irst Call, th e d a te on the underlying docum ent, the old ratin g , th e new rating, the brokerage firm issuing the recom m enda­tion and th e stock’s ticker symbol

Daily stock retu rn s are obtained from CRSP CO M PU STA T In d u strial Q uarterly

is used to search for d ates of q u arterly earnings announcem ents and values of quarterly earnings I use In stitu tio n a l Broker E stim ation System ( I /B /E /S ) Sum m ary History

to find consensus earnings forecasts and I /B / E /S Daily D etail H istory to find earnings

9T h e m orning research conference calls are held at m ost brokerage firm s a b o u t two hours before the sto c k m arket op en s for trad in g in N ew York A n a ly sts and p ortfolio str a te g ists sp eak a b o u t, interpret

a n d p o ssib ly ch an ge o p in io n s on firms or sectors th e y follow.

l0 Zacks d a ta has th e sa m e problem (Barber, Lehavy, M cN ich ols & T ruem an (19 9 9 )).

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e stim ate s by individual analysts11 E arnings surprise is th e difference between th e

a c tu a l q u a rte rly earning and th e q u arterly earnings forecast consensus T he earnings forecast revision is th e difference betw een th e newly issued earnings forecast and the consensus A nalysts usually forecast earnings for different tim e horizons, for exam ple,

c u rre n t year, n ext year, quarters of a year, etc A m ajority (m ore th a n 53%) of them are for th e curren t year and th e next year It is also common th a t multiple analysts issue earnings forecasts on a certain stock If th ere is only one earnings forecast revision for th e c u rren t year, I use it as th e earnings revision If th ere are m ultiple revisions occu rrin g around th e sam e tim e12, I take th e average If there is no revision for th e

c u rre n t year, I consider the revision in th e ord er of next year a n d then this q u arter,

For Prudential, who has a three-rank system , I take its “hold” as “n eu tral” P u ttin g

different ratings in to one ratin g system requires some subjective judgem ent

E xcluding th e 21 U.S companies whose stock prices are no t available on C R SP

a n d all non-U S com panies, there are 1209 ratin g changes on 942 stocks Only new changes in ratings are included R eiterations of ratin g changes are excluded, because

th e y are usually rep eated several times an d have been shown to have less im pact th a n

11 I / B / E / S also has records o f earnings an n ou n cem en t d a tes, b u t th ey are th e d a te s w hen th e earnings are rep o rted to I / B / E / S

12H ere it m ean s th e y occu r w ithin five days arou n d th e ratin g changes.

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new changes of ratings (Francis and Soffer, 1997) There are 19 types of ratin g changes

w ith non-zero observations The frequency of observations for different categories is sum m arized in Panel A of Table 3

It is well known th a t very few “sell” recom m endations are m ade, an d this d a ta set

is no exception: “sell” recom m endations app ear in only 16 out of 1209 observations

an d new coverage was never initiated w ith a “sell” rating T he m anagem ent has been known to penalize analysts who issue “sell” recom mendations and pessimistic reports

on a company Some offended firms punish these analysts by excluding them from con­ference calls, meetings an d other forms of direct contact w ith m anagem ent (Siconolfi, 1995)13 Several o th er explanations have also been proposed for this bias McNichols

an d O ’Brien (1997) find th a t analysts ten d to cover companies about which they are optim istic; D ugar and N athan(1995) show th a t financial analysts of brokerage firms

th a t provide investm ent banking services to a company (investm ent banker analysts) are optim istic relative to other (noninvestm ent banker) analysts when making earn­ings forecasts and investm ent recom m endations; Michaely & Womack (1999) provide evidence of bias of analysts towards “b u y ” ratings on the stocks their brokerages un­derw rite In this d a ta set, the lack of “sell” recommendations is more prom inent than all previous studies Since there are so few “u n attractiv e” an d “sell” ratings, I combine them into one category in the analysis In doing so, the two upgrades from “sell” to

“u n a ttra c tiv e ” an d one downgrade from “u n attractiv e” to “sell” in the d a ta set are discarded Thus, th e sam ple has 1206 observations

Term inations of coverage are not included in the sample because there are too few

of th em for m eaningful analysis To com pare w ith the literature, I also construct four additional types of recommendations: “added to buy” , “removed from buy” , “added

to u n a ttra ctiv e/se ll” and “removed from un attractiv e/sell” These recom m endations are the com binations of certain ratin g changes For example, “added to buy” is the com bination of “from neutral to buy” , “from attractive to buy” and “in itiated as buy”

l3T h is m ight change after R egulation F D is im plem en ted.

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T he four cases have 369, 274, 38 a n d 53 observations respectively.

P anel B of Table 3 shows th e frequency of recom m endations issued on individual stocks in th e sample M ore th a n 77% of th e stocks only have one ra tin g change and less

th a n 4% of th e stocks have th ree or m ore14 Thus, although m ultiple recom m endations

of th e sam e stock occur in th e sam ple, they are few a n d should not m aterially change the results Among th e stocks who have multiple ratin g changes, a b o u t 53% have more th a n one brokerage firm am ong th e six following them a n d a b o u t 61% have

m ultiple recom m endations issued by th e same firm15 For recom m endations by multiple brokerage firms on th e sam e stocks, only 12% of th em are less th a n one m onth ap art from th e ratin g change issued by a different brokerage firm

Table 4 summarizes th e m arket capitalization of the stocks T hey are predom inantly large-capitalization com panies M ore th a n 50% of th e sample are from th e two largest

m arket capitalization deciles16 I call stocks in deciles 9-10 large, deciles 6-8 medium and deciles 1-5 small

Table 5 sum m arizes th e frequency of recom m endations occurring aro u n d quarterly earnings surprises and earnings forecast re-visions A sm all percentage o f stocks (about 5%) can not be found in C O M PU STA T or I /B /E /S A bout 10% (com bination of pos­itive an d negative surprises) of th e recom m endations have some q u a rte rly earnings surprises w ithin days -5 to + 5 For “added to buy” , “removed from b uy” , “added to

u n a ttra ctiv e/se ll” , an d “rem oved from u n attractiv e/sell” , there are a b o u t 9%, 13%,

11 T h e sto ck w ith seven ratin g ch an ges is D ell.

toT h e average duration o f th e recom m en dation s is about 11 m onths roughly c a lcu la ted from the

su b set o f m ultip le recom m en dation s issu ed by the sam e brokerage firms.

t6C R S P ranks all N Y SE com p an ies b y th eir market cap italization and d ivid es th em in to 10 equally

p o p u la ted portfolios A M E X a n d N A S D A Q stocks are th en placed into d eciles accord in g to their resp ective cap italization s, d eterm in ed b y N Y SE breakpoints T h e portfolios are rebalanced each year,

u sing th e security m arket ca p ita liz a tio n a t the end o f the previous year to rank th e secu rities T he largest secu rities are p laced in p ortfolio 10 and sm allest in p ortfolio 1 If a se cu rity sta r ts trad ing in

th e m id d le o f a year, its first ca p ita liz a tio n o f the year is used in th e ranking I take th e d ecile to which each sto ck b elon gs at th e b egin n in g o f th e pre-event period as its size.

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19% and 12% of recom m endation issued around quarterly earnings surprises respec­tively A pparently th ere is an asym m etry ab ou t w hat recom m endations are m ore likely

to be issued around q u arterly earnings surprises, i.e., upgrades seem to be less driven

by earnings surprises th an dow ngrades M ore than 30% (com bination o f positive and negative revisions) of recom m endations are around some earnings forecast revisions Upgrades are more likely to be associated w ith positive earnings surprises or positive earnings forecast revisions th a n negative earnings surprises o r negative earnings forecast revisions Downgrades act similarly

1.4 The Empirical M ethodology

I use the size-adjusted model to derive th e m ain results In Section 1.7, I adopt a restricted m arket model and n o np aram etric local linear regression m eth o d to examine the robustness of th e results

According to the size-adjusted model, th e abnorm al re tu rn of stock i a t tim e t is:

A R i t — R i t R s iz e ,t- >

where £ is the trad in g day relative to th e recom m endation d ate (£ = 0), R it is the return

of stock 2 on day £ and R Size,t is th e re tu rn of value-weighted C R SP portfolio for the

sam e firm-size decile on day £ T h e size decile index portfolios are form ed from stocks listed on the NYSE, AMEX, and NASDAQ Stocks w ith retu rn s for any given day are com pared to the decile portfolios based on th eir m arket capitalization a t th e beginning

of the pre-event period

Using term inology from C am pbell, Lo and M acKinlay (1997), th e Average Abnor­

mal R eturn across N stocks a t tim e £ is:

T h e f-statistic is:

A C A R

t — V n ■

a (A C A R ) ’

w here a ( A C A R ) is th e cross-sectional standard deviation of A C A R 1‘

K o th ari an d W arner (1997) an d Lyon, B arber an d Tsai (1999) p o in t out th a t long- horizon param etric te st statistics do not satisfy the assum ed zero m ean and unit nor­

m ality assum ptions a n d over-reject the null hypothesis of no ab no rm al performance

T h e ir sim ulation results show th a t the distribution of stan d a rd te st sta tistic has a pos­itive m ean an d it is fat-tailed relative to a unit-norm al d istrib u tio n For this reason I use a b o o tstra p p ed t-sta tistic distribution in this p a p er18

F irst Call provides th e specific d ate and tim e when it dissem inates information to its clientele T his inform ation is recorded in the headline We th u s know the date

1 ‘ F am a (1998) argues th a t th eoretical and statistical con sid erations su g g est th a t form al inferences

a b o u t lon g-term returns sh ou ld b e based on averages or su m s o f sh ort-term ab n orm al returns rather

th a n th e b u y-an d -h old ab norm al returns C um ulative A bnorm al R eturn (C A R ) is less likely to yield

sp u riou s rejection s o f m arket efficien cy than m ethods th a t ca lcu la te b u y -an d -h old returns by com ­

p ou n d in g sin gle p eriod returns F irst, th e buy-and-hold m eth o d can m agn ify underperform ance or overperform ance, even if it occurs in o n ly a single period, d ue to th e nature o f com p ou n d in g single­

p eriod returns Secon d , d istrib u tion al properties and te st sta tistic s for C A R s are b ette r understood

B arber an d Lyon (1997) an d K othari k Warner (1997) d ocu m en t th a t test s t a tis tic s of long-horizon

b u y-an d -h old abnorm al returns are m ore significantly right-skew ed th a n cu m u la tiv e abnorm al returns L8T h e b o o tstra p p in g p roceed s as follows: Draw 1,000 b o o tstra p p e d resam ples from th e original sam p le o f th e sam e size N In each resam ple, calculate th e sta tistic:

b /77 A C A R b

~ a ( A C A R b) ’

w here A C A R b and a { A C A R b) are the A C A R and its cross-section al stan d ard d ev ia tio n in the b oot­

stra p p ed resam ple I reject th e null h yp oth esis that the m ean ab norm al return is zero if £<Xi or £ > x u- From th e 1,000 resam ples, I calcu la te th e two critical valu esfyj an d x u ) f ° r th e t-sta tistic , £, to reject

th e null h yp oth esis a t th e a sign ifican ce level by solving:

P r(£ 6 < X I) = P r ( £ fc> x J = |

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(and even tim e of th e day) th a t th e inform ation was sim ultaneously m ade available

to th e entire clientele of F irst Call I call it th e dissem ination d a te and use it as the event date For each event in the sample, th ere axe b o th benchm ark and individual stock returns for th e period from 261 days before until 261 days after the event date, generally a b o u t two years in calender time

1.5 Brokerage Firms and Short-run Market Reactions

1.5.1 Three-day Event Window

Column 1 of Table 6 lists th e ACARs o f th e three-day event window for all th e types

of rating changes using th e size-adjusted model Most of th e ACARs are statistically

significant a t least a t a = 0.10 Upgrades lead to positive abnorm al returns and

downgrades lead to negative abnorm al returns, which is consistent w ith th e literature.Downgrades lead to larger re tu rn movements th an corresponding upgrades For example, “from buy to n eu tral” leads to a three-day A C A R o f -2.64%, while “from neutral to buy” only has a three-day ACAR of 4-1.08% Downgrades of sm aller mag­nitude lead to sm aller re tu rn movements, for example, “from buy to a ttractiv e” has

a three-day A CAR o f -1.23%, while “from buy to neutral” has a three-day ACAR of -2.64% O n th e o th e r hand, upgrades of sm aller m agnitude do not necessarily result in

sm aller re tu rn m ovem ents, for example, “from a ttra ctiv e to buy” and “from neutral to buy” display sim ilar re tu rn movements

Table 7 presents results for “added to b uy” , “removed from buy” , “added to

u n attra ctiv e/se ll” , “rem oved from u n attra ctiv e/se ll” and th eir subsets stratified by size Except for “rem oved from u n a ttractiv e/sell” , all other types of recom m endations result in significant three-day ACARs “A dded to u n a ttra ctiv e/se ll” has an ACAR of -3.76% during the three-d ay window By co n trast, “removed from u n attractiv e/sell” results in m uch sm aller abnorm al returns, +0.52%

The recom m endations seem to have bigger im pacts on sm aller stocks Large stocks

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have ACARs of sm aller m agnitude th a n th e m edium a n d sm all stocks for all th e four types of recom m endations Small stocks show ACARs of -4.65% a n d -8.15% for “re- moved from buy” and “added to u n a ttra c tiv e /se ll” respectively T his result is consis­ten t w ith differences in firm s’ inform ation environm ents: th ere is less publicly available inform ation a b o u t sm aller firms, possibly increasing th e inform ation content o f the recom m endation.

1.5.2 Impact of Brokerage Firms

T he question of interest is: do different brokerage firms have different influence with

th e sam e recom m endations? Since th ere are not enough observations for each rating change to divide th e sam ple am ong th e brokers, I only focus on two cases: “added to buy” and “removed from buy”

Table 8 contains th e three-day ACARs for different brokerage firms For “added to

buy” , D L J results in a positive abnorm al re tu rn of 2.10% P rudential, Paine Webber and J.P Morgan recom m endations have abnorm al re tu rn s betw een +1% and +1.5%

Morgan Stanley and B ear S te a m s have abnorm al retu rn s less th a n 1%: for “removed

from buy” , D L J and J.P Morgan cause negative abnorm al retu rn s of -4.31% and -4.48% respectively Prudential an d B ear S te a m s have abnorm al retu rn s around - 1.7% Morgan Stanley and Paine Webber result in abnorm al re tu rn s o f much sm aller

m agnitude: -0.10% and -0.40% respectively

T he results from Table 8 show th a t the recom m endations from th e brokerage firms cause abnorm al retu rn s of different m agnitude N ote th a t th e stocks followed by the six brokerage firms do not have exactly the sam e d istrib u tio n s of m ark et capitalization

(Table 9) For exam ple, for “added to buy” , M organ Stanley has th e highest percentage

of large com panies, 52.3%, and lowest percentage of sm all com panies, 15.4 %, while

D L J has th e opposite p a tte rn T h e frequency of concurrent earnings news also exhibits

differences across brokerage firms (Table 10) Morgan Stanley has lower percentage of concurrent positive (negative) earnings surprises and forecast revisions th a n D L J in

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“added to b uy” ( “rem oved from buy”) Previous results suggest th a t stocks of different sizes have different price reactions to th e sam e recom m endations T he concurrent earnings news m ay also contribute to stock price changes For these reasons, I control for m arket cap italizatio n , concurrent earnings forecast revisions and qu arterly earnings surprises when analyzing th e three-day A C A R cross-sectionally I use dum m y variables

to control w h eth er th e re is a positive q u a rte rly earnings surprise, a negative q u arterly earnings surprise, a positive earnings forecast revision or a negative earnings forecast revision w ithin five days of a recom m endation

As I specified before, I use the dissem ination d a te on F irst Call as the event date However, th is is not necessarily th e only d a te investors learn of th e recom m endations

T here is also an o th er d a te available, which is th e d a te appearing on the underlying detailed rep o rt w ritte n by th e analyst I call it th e docum ent d ate T h e docum ent date

is no la te r th a n th e dissem ination date In a b o u t 20% of th e sam ple, these two dates are the sam e In a b o u t 50% of th e sam ple, th e differences betw een these two are no more th a n 3 days O n average the docum ent d ate precedes th e dissem ination d a te by

a b o u t 4 days T h ere are several possibilities for th e gap between th e two dates One

is th a t a n an aly st m ay w rite up a report and then, for som e reason, wait la te r to issue the re p o rt A n o th er possibility is th a t an analyst m ay have dissem inated his o r her report in o th e r ways before electronically d istrib u tin g it th ro ug h F irst C all19,20 The

gap betw een th e two dates varies across brokers For Morgan Stanley, th e docum ent

d ate precedes th e dissem ination d a te by a b o u t 2 days on average For D LJ, Paine

Webber an d B ear S te a m s, the differences are about 7, 6 and 5 days respectively For

191 talk ed to p eo p le a t F irst C all and a cou p le o f a n a ly sts at M organ S tanley T h ese are th e two

p o ssib ilities th e y agree u p o n U nfortu nately th ey can not sp ea k for oth ers and I can n o t id en tify the reason b eh in d every ev en t.

■°I a n a ly ze d th e retu rn s during the three-day even t w indow u sing each o f the two d ates as th e event

d ate W ith th e d o cu m e n t d a te being th e event d a te , the three-d ay A verage C um ulative A bnorm al

R eturns (A C A R s) are o f sm aller m agnitude than th o se ob ta in ed by u sing the d issem in ation d a te as

th e even t d a te.

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P rudential and J.P Morgan, th e difference is on average around 1 day The different

p a tte rn across th e brokers indicates th a t th e brokers may differ from each other in term s of th e way th ey dissem inate their recom m endations Tim ing is an im portant issue Suppose some investors get to know ab o u t th e recom m endations on one date while th e others a t a la te r date If b o th sets o f investors react to th e recom m endations,

th e stock reactions around the recom m endations would be bigger if th e two dates are closer to each other Therefore, the discrepancy between th e dissem ination d ate and

th e docum ent d ate is also controlled for in analyzing abnorm al return s associated with recom m endations issued by different brokerage firms

T h e resuits concerning the im pact of different brokerage firms on stock reactions are presented in Colum ns 1 and 4 o f Table 11 T he dependent variable is the three-

d ay cum ulative abnorm al returns for individual events obtained using th e size-adjusted

m odel T h e independent variables include brokerage firms, stock sizes, w hether the

ra tin g change skips a rank, concurrent earnings news and the num ber of days between

dum m y variable for th e brokers I use W h ite’s procedure (W hite, 1980) to estim ate heteroscedasticity-robust stan d ard errors

B o th earnings surprises and earnings forecast revisions affect A CAR significantly

T he stock price reaction is reinforced by the same-sign earnings surprises/revisions

G ood earnings news apparently fu rth er increases abnorm al stock retu rn s in "added to

b uy” (m arginal effect of +1.67% and +1.45% for positive earnings surprises and positive earnings forecast revisions respectively) while bad news further reduces abnorm al stock

re tu rn s in “removed from buy” (m arginal effect of -1.62% and -1.25% for negative earnings surprises and negative earnings forecast revisions respectively)

T h e reaction around the dissem ination d ate is reversely related to the num ber of days betw een the docum ent d ate and th e dissem inate date However, th e effect is not significant For one e x tra day th e docum ent d a te preceding the dissem inate date, the abnorm al retu rn for “added to buy” on average decreases 0.06% an d the abnorm al

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re tu rn for “removed from buy’’ increases 0.08%.

T he m arginal effect of D L J issuing “added to buy” is an additional 4-1.03% d uring

th e three-day window beyond th a t associated w ith Morgan Stanley T he recom m enda­

tions of “added to buy” by the o th er four brokerage firms has a lower m arginal effect

For “removed from buy” , it is a different story D L J and J.P Morgan seem to be significantly m ore influential th a n M organ Stanley T hey have the m arginal effect of -4.03% ( £-statistic=-1.98) and -4.22% ( t-statistic= -2 6 2 ) respectively Bear S te a m s and Prudential have a m arginal effect of -1.74% and -1.67% respectively Therefore

the difference across the brokerage firms is asym m etric w ith respect to upgrades and downgrades

I exam ine th e robustness of th e results by doing th e same analysis for the two subperiods of th e sample tim e frame O ne period is from O ctober, 1995 to November

1996 and the o th er is from Decem ber, 1996 to December, 1997 T he results in the subperiods axe generally consistent w ith those for th e whole sample (Columns 2, 3, 5 and 6, Table 11)

T hus th e analysis docum ents th a t the brokerage firms have different degrees of influence on stock reactions around th e recom m endations, especially in the case of

dow ngrading from “buy” It seems surprising th a t J.P Morgan has more influence

th a n Morgan Stanley if we consider th e fact th a t J.P Morgan is ranked consistently and significantly behind Morgan Stanley by Institu tio n a l Investor in every year during

th e sam ple period (see Table 2) However, only one of the ranking criteria used by I I

is based on how accurate the recom m endations are, i.e., “stock picking” One possible explanation for th e difference is th a t th e m arket has unobservable belief about how ac­

cu rate an individual brokerage firm ’s recom m endations are The belief varies across the

brokerage firms and may not agree w ith the ranking of II A nother explanation is th a t

th e difference is caused by some o th er factors we have not controlled for One p o ten tial factor is th e possible investm ent banking or corporate financing relationship betw een

th e brokerage firm and the subject com pany For example, an investm ent bank m ight

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be involved w ith th e security issuance o r m erger/acquisition for a su b jec t com pany on which its analysts are m aking stock recom m endations If such a relationship induces bias in th e recom m endations, th e m arket will take this into account Therefore the

m arket will react differently if th e brokerage firms in the sam ple differ in term s of the

“severity” of the relationship

1.6 Stock Returns Before and After the Recommendations

In th e previous section, I exam ined ACARs over the three-day event window, and found

th a t th e m arket reacts differently to th e top brokerage firms around th e recom m enda­tions, especially in th e case of dow ngrading from “buy” In this section, I exam ine the stock retu rn s before and after the ra tin g changes

1 6 1 P r e - e v e n t a n d P o s t - e v e n t A b n o r m a l R e t u r n sFigures l a and lb graph ACARs for “added to buy” , “removed from b u y ” , “added to

u n a ttra c tiv e /se ll” , and “removed from u n a ttractiv e/sell” Table 12 lists ACARs for stocks in the four cases before and a fte r the recommendations For “added to buy” ,

th e re is significant running up before th e event T he cum ulative abnorm al return

th ro u gh o u t the pre-event period is a b o u t +12% W hile the abnorm al re tu rn is still positive until 90 days after stocks are added to “buy” , it is not sta tistic a lly significant (Table 12) For “removed from b u y ” , th e abnorm al retu rn has been close to zero

th ro u g h th e pre-event period; th e significantly negative abnorm al re tu rn continues

u n til 60 days after th e recom m endation (Table 12)

T h e case of “added to buy” raises questions about the tim ing of recom m endations

an d th e stock-picking abilities of th e analysts It seems as if th e analy sts add stocks

to th e list o f “b uy” after a t least one year of price running up, b u t sto ck prices return

to th e ir pre-event level w ithin one y ear after the event Overall, th e A C A R across the event and post-event periods is close to zero, which is in sharp c o n tra st to th e running

up in th e year before the event

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For b o th “ad d ed to u n a ttra ctiv e/se ll” an d “removed from u n attra ctiv e/se ll” (Figure

lb ) , th e re is significant running down before th e event The overall pre-event abnorm al

re tu rn s are a ro u n d -16% an d -17% respectively From Section 5, we see th a t “added

to u n a ttra c tiv e /se ll” causes a three-day A CA R o f -3.76% while th e three-day ACAR arou n d “rem oved from u n a ttra c tiv e /se ll” is of much smaller m agnitude, +0.52% The existence o f pre-event ru nning down m ay help explain the difference W hen th e analysts upgrade th e stocks from “u n a ttra c tiv e /se ll” following a large running down, th e m arket sees it as th e result of th e “price pressure", and does not derive much inform ation from it; when th e analysts dow ngrade th e stocks to “u n a ttra ctiv e/se ll” following the

ru n n in g down, th e dow ngrading is unexpected in light of the “price pressure" and thus,

th e m arket infers ab o u t and reacts significantly to the private inform ation driving the dow ngrades

For “added to u n attra ctiv e/se ll” , the negative post-event abnorm al retu rn continues after th e event, however is not statistically significant (Table 12) For “removed from

u n a ttra c tiv e /se ll” , th e size-adjusted model does not give significantly positive post­event ab n o rm al retu rn s during th e first 30 days after the event and th e additional abnorm al re tu rn tu rn s negative after day 31 (Table 12)

Therefore, for “added to buy” , “added to u n attractiv e/sell” and “removed from

u n a ttra c tiv e /se ll” , the results do no t su p p o rt th e existence of post-event drift: only for

“rem oved from buy” , there is continuation of significantly negative abnorm al returns

u ntil 60 tra d in g days after th e recom m endation

1.6.2 Sensitivity of Pre- and Post-event Returns

In this section, I exam ine how sensitive th e pre- and post-event results are to the old

an d new ratings, th e m arket capitalization, an d th e brokers

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Old and New Ratings

Are longer-term post-event returns as sensitive to the m agnitude of ratin g changes as

sh o rt-ru n retu rn s are? I examine th e three subsets of “added to buy” : “from, neutral

to buy” , “from a ttra ctiv e to buy” , and “in itiated as buy” Figure 2a shows the results.For “from a ttra c tiv e to buy” , and “in itiated as buy” , th e running-up before the event is large, over 15% and 25% of th e abnorm al re tu rn during the pre-event period respectively For “from neutral to buy” , there is no running up before th e event There are no significantly positive post-event abnorm al return s for any of th e three cases

In fact, for “in itiated as buy” , the abnorm al retu rn d uring th e first 30 days after the recom m endation is negative, although n o t significantly

Figure 2b presents results for th e tw o subsets of “removed from b uy” : “from buy

to a ttractiv e” an d “from buy to n e u tra l” For b o th o f them , the abnorm al returns before the recom m endations are close to zero For “from buy to a ttra c tiv e ” , there is no negative post-event abnorm al returns For “from buy to n eu tral” , th ere are significantly negative retu rn s until 60 trading days a fter the event window

Therefore th ere is no post-recom m endation drift for any of th e subsets of “added

to buy” : while “removed from buy” exhibits some post-recom m endation drift, one of its two subsets does not have continuation of significant abnorm al returns after the recom m endation The drift for “removed from buy” ap p aren tly is sensitive to both the old rating and th e new rating

Market Capitalization

Figures 3a, 3b, 4a and 4b are abnorm al returns for stocks of different sizes: in “added

to buy” , th e sm all stocks have significant abnorm al retu rn s during the first 10 days after the recom m endation Medium a n d large ones do no t have statistically significant post-event retu rn s; in “removed from b uy” , the small stocks have significantly negative abnorm al retu rn s until 60 days after th e event; th e m edium stocks have a significant abnorm al re tu rn during th e first 10 days after the recom m endation; large stocks do

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not have significantly negative abnorm al returns; in “added to u n a ttra c tiv e /s e ll” and

“rem oved from u n a ttra c tiv e /se ll” , none of them has significant post-event abnorm al returns

T h e differences am ong large, m edium and small stocks show th a t delayed stock- price responses are strongest for sm all firms This raises the possibility th a t th e post­recom m endation drift is sim ply a firm-size effect

Brokerage firms

Figure 5 presents stock abnorm al retu rn s for “added to buy” by different brokerage

firms D L J has no pre-event running up while other five firms have large running up before th e event D L J has positive abnorm al returns up to 60 days afte r th e event

while o th ers have no significantly positive post-event abnorm al re tu rn s In fact, the

abnorm al re tu rn tu rn s negative after 30 days for Morgan Stanley.

For “removed from buy” (Figure 6), Morgan Stanley, D L J and Paine Webber do

not have pre-event running up or running down and they do not have significantly

negative post-event abnorm al returns Prudential has pre-event ru n n in g up and has

no negative post-event abnorm al returns B oth Bear S tea m s and J P Morgan have

significantly negative abnorm al returns until 60 days after the recom m endation

T hus, on one hand, th e results show th a t stocks followed by individual brokerage firms have different pre-event and post-event returns, in term s of b o th m agnitude and trend I t is interesting to see th a t for different brokerage firms, th e pre-event and post-event retu rn s differ substantially, although they are all ranked in th e top 20 by

In stitutio n al Investor O n the o ther hand, w ith “added to buy” , th ere is no evidence of

post-recom m endation drift for any of the brokerage firms except D L J ; w ith “removed from b uy” , only B ear Stearns and J.P Morgan have post-recom m endation drifts of

about 60 tra d in g days

In sum m ary, th e continuation of significant post-event abnorm al re tu rn s does not exist in m ost of th e cases except “removed from buy” Furtherm ore, th e drift for

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‘^removed from b uy” is sensitive to th e m agnitude of th e ra tin g change, th e m arket cap italizatio n of th e su b ject com pany an d th e broker issuing th e recom m endation.

1.7 Robustness to Alternative Models

In this section, I exam ine robustness of th e results in Sections 5 & 6 to alternative models K othari & W arner (1997) point out the potential m isspecification problem in various models used for testin g long-horizon abnorm al securities retu rn s, including the

m arket-adjusted m odel, th e m arket model, CAPM , and the Fam a-French three-factor

model B arb er &c Lyon (1997) try to correct the misspecification problem by m atching

sam ple firms to control firms of sim ilar sizes and book-to-market ratios T h e b o o tstrap procedures, such as those used by Ikenberry, Lakonishok and Vermealen (1995), use

re tu rn d a ta for ran d o m sam ples o f m atch ed non-event firms to co n stru ct a b o otstrap

d istrib u tio n of long-horizon abnorm al retu rn s under the null hypothesis T h e work of Lyon, B arber, and T sai (1999) also a tte m p ts to establish m ethods which can yield well- specified te st statistic s for long-run abnorm al stock returns T hese papers do not find

th a t one m ethod is always preferred an d show th a t great caution is needed in analysis

of long-run abnorm al retu rn s

T h e two altern ativ e models I consider here are the restricted m arket model and non-

p aram etric local linear regression model I briefly described them in th e introduction

of the paper, and th e next two sub-sections provide more details

1.7.1 Pre-event Abnormal Returns and Restricted Market Model

T h e size-adjusted m odel takes benchm ark returns as a stock’s expected retu rn s It assum es th a t th e individual stock is not m ore or less risky th a n the cross-sectional benchm ark B y co n trast, th e m ark et model makes use of th e stocks’ specific param eters (Fam a, 1998)

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In th e maxket model, th e re tu rn of stock i a t day t is:

R i t 0^2 “f" P i R m t "t" S it,

where Rm t is re tu rn of value-weighted CRSP m arket index on day t.

Assum ing E ( £ i t \ R m t ) = 0, we have

E ( R i t \ R m t ) = OCi 4- P i R Tnt

period

T hus the abnorm al retu rn for stock i at day t, A R t, can be estim ated as:

A-Rit = Rit Oti

P^Rmt-However, as observed in th e last section, large pre-event abnorm al returns are com­

m on For example, “added to buy” has one-year pre-event running up and b o th “added

to u n a ttra ctiv e/se ll” an d “removed from un attractiv e/sell” have one-year pre-event

ru n n in g down T he existence of significant pre-event abnorm al returns poses a prob­lem for th e m arket model, since param eter estim ates made in the presence of abnorm al

re tu rn s are biased T h e size-adjusted model avoids this problem as it does not require

an estim ation period

I use a restricted m arket model to solve the problem of significant abnorm al returns

in th e estim ation period In the restricted m arket model, the expected re tu rn o f stock

i a t day t is:

A R n = R i t ~ P i R m t

where p i is th e coefficient on the benchm ark re tu rn obtained from th e estim ation period

using th e m arket model T he claim is th a t th e constant term estim ated by the m arket

m odel, aci, captures th e pre-event running up or running down To show this, we

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observe th a t, for th e m arket model, th e average abnorm al re tu rn a t t is:

For the m arket-adjusted m odel (using Rmt instead R size,t as th e benchm ark), since

it assumes th a t a — 0 and (3 = 1, the ACAR becomes

£ = £ 1 2 = 1 £ = £ 1 2 = 1

If we com pare th e two equations for A C A R ( t \ , t 2), it is clear th a t th e difference

betw een the two models depends on the values of a , (3i , t\ and £2 A n 5 sm all in itself

will make a big difference if the period is long enough, i.e., to — £1 is large enough It will not be significant if th e period is very short, i.e., several days

from buy” , “added to u n a ttra ctiv e/se ll” and “removed from u n a ttra c tiv e /se ll” In the case of “removed from u n a ttra ctiv e/se ll” , 5 is -0.00050 /?T- is ab o u t 0.94 on average and

is not significantly different from 1 A t 260 days after the event, th e difference between

ACAR caused by non-zero a will be ab ou t 13% The difference a t 260 days is indeed

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ab o u t 13% (Figure 7a) So, th e difference betw een the m arket-adjusted model and the

m arket m odel can be a ttrib u te d to a in th e existence of pre-event abnorm al returns

In th e case o f “added to u n a ttractiv e/sell” , a is -0.00040 At 260 days after the event,

th e num ber becomes significant, i.e about 10.4% T he actual difference is around 16% (Figure 7b) Here because it is on average significantly different from 1 (w ith mean

of 0.87 a n d s ta n d a rd error of 0.06), also contributes to the difference between the

significantly different from 1, a non-zero a can explain the gap betw een the m arket

m odel and th e m arket-adjusted model; if /3t- on average is significantly different from 1,

Pi also contributes to th e difference between th e two models Due to space lim itations,

these o th e r examples are not shown here21

stric te d m arket m odel as an alternative to th e m arket model

1.7.2 Nonparametric Model

T he previous models assume th a t stock re tu rn s are linearly related to Rmt or R Size,t- If

linearity is not satisfied, we would expect biased estim ates of abnorm al returns Close exam ination reveals the existence of nonlinearity between the stock retu rn and the

m arket re tu rn , for example, in about one th ird of the samples, th e qu ad ratic function form b e tte r fits th e d a ta 22 To allow for nonlinearity and also to reduce the influences

of outliers on estim ators, I next consider a nonparam etric model

In nonparam etric models23, we do no t im pose a fixed functional form, instead we

consider a general unknown function Let us s ta r t w ith the model of R it as:

Rit = Qi^Rmt) " b £it->

' l T h e y are availab le upon request.

" T h e coefficen t o f squared m arket return is sign ifican t, rejecting the linear relationship betw een the sto ck return and th e m arket return.

i:lFor references ab o u t n onparam etric m eth od s, se e H ardle(1989) and Fan & G ijbels (1996).

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w here gi is an unknow n function.

Assuming E (sit\R m t) = 0, we have,

E ( R i t \ R v n t ) — Q i ( R m t ) •

T h e question is how to e stim ate gi I use a Local Linear Regression (LLR) to

estim ate the expected re tu rn E ( R i t \ R m t ) , t is any day from th e pre-event period to the

m inim ization problem

T he estim ator of th e conditional m ean is a* K {.) is a kernel function and h r > 0

is a bandw idth which converges to zero as T —* oo If bi were constrained to equal zero, then a * would give the local con stan t regression estim ator, also called the kernel

regression estim ator Thus, kernel regression can be viewed as a special case of LLR.Fan (1992) shows th a t th e local linear estim ator has th e sam e variance as the kernel estim ator bu t has a lower order bias a t boundary points T h e sm aller bias associated

w ith the LLR estim ato r implies th a t it is m ore rate-efficient th a n th e kernel estim ator

A nother advantage o f LLR em phasized by Fan is th a t th e bias of th e LLR estim ator does not depend on th e design density of the d ata Because of these advantages, local linear m ethods are usually a b e tte r choice th a n sta n d a rd kernel m ethods for nonparam etric regression T he local linear estim ator is asym ptotically normal with a

ra te of convergence equal to \J T h r - M asry and Fan (1997) establish sim ilar properties

of local linear estim ators for tim e-series d ata

In th e process of im plem enting LLR, th e most im p o rtan t issue is to find the optim al

bandw idth, h r - I use th e least squares cross-validation (LSCV) m eth o d to find the

optim al bandw idth A lthough I also have to make a decision ab o ut th e kernel function, A'(-), the results from the lite ra tu re show th a t the choice o f kernel function is not likely

mm

a-iM T

w h ere T = len g th o f th e e stim a tio n w indow

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to be crucial I use the G aussian kernel function, K (t)= (\/2 T l)~ l ex p (—f2/2 ) Details

ab o u t th e choice of th e optim al bandw idth are described in th e Appendix

T h e event d a te is defined to be day 0 T h e estim atio n period covers day -261 to day -132 T h e event window is three days, day -1 to day -f-1 Therefore there is a gap

of 130 days between th e estim ation period and event window I choose to do so to reduce th e im pact of pre-event abnorm al returns, which is more severe in the 130-day gap th a n in th e estim ation window as we see in Section 1.6

1.7.3 Short-run Returns

Columns 2 and 3 of Table 6 are the ACARs o f th e three-day event window for all cate­gories from th e restricted m arket model and the nonparam etric local linear regression model These models give results sim ilar to those from th e size-adjusted model in terms

of the level of ACARs and significance tests in m ost cases

1.7.4 Longer-term Returns

In exam ining th e longer-term returns, th e nonparam etric LLR is used when there are

no significant abnorm al retu rn s in the estim ation period Otherwise, th e restricted

m arket model is used T h e results from these two altern ativ e models are generally consistent w ith those from th e size-adjusted model In some cases, they further reject the existence of “post-recom m endation d rift” T h e following are two examples

For “added to u n a ttra ctiv e/se ll” (Figure 8a), the restricted m arket model actually shows slightly positive abnorm al returns during th e first 30 days after the recommen­dation T h e ACAR tu rn s positive 120 days after th e recom m endation

For “added to buy” , D L J has significant abnorm al retu rn s until 60 days after the

event according to th e size-adjusted model, while th e post-event abnorm al retu rn is not statistically significant according to th e LLR (Figure 8b)

In sum m ary, these alternative models give results very close to the size-adjusted model in th e short period, i.e., three-day event window In th e longer-term , their

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results do not establish th e existence o f th e d rift either In some cases, th ey fu rth er reject th e continuation of post-event abnorm al returns.

1.8 Discussion

1.8.1 The Models

In any event study, th e use of an in ap p ro p riate model can result in system atic biases This problem is less serious for sh o rt periods, e.g., the th ree-d ay event window, since daily expected retu rn s are close to zero and so have little effect on estim ates o f abnor­mal retu rn s B u t the problem grows w ith the re tu rn horizon Over a long horizon, the variation in expected retu rn estim ates across different benchm ark models can be large

T hus, longer-term results are poten tially sensitive to the assum ed function forms for expected return s W hich model(s) should we choose to s tu d y longer-term abnorm al returns? As discussed by Fam a (1998), all asset pricing m odels are incomplete descrip­tions of th e system atic pattern s in average returns during any sam ple period T h is is the “bad-m odel” problem in the s tu d y of m arket efficiency

In this paper, I first employ th e size-adjusted model to derive the m ain results, then examine th e robustness of the results to different models T h e m arket model is a firm- specific model, lim iting the bad-m odel problem (Fam a, 1998) However, the existence of pre-event abnorm al returns makes using the m arket model problem atic In those cases

w ith significant pre-event running up or running down, I use the restricted m arket model, in which the constant term derived from th e estim atio n period by th e m arket model is set to be zero I believe th is is one way to elim inate th e impact of pre-event running up or running down on post-event returns To reduce potential bias caused by

th e assum ption of linearity and existence of outliers, I a d o p t th e nonparam etric local linear regression (LLR) m ethod T hese models have sim ilar results in the sh o rt-ru n

T hey also derive results consistent w ith those from the size-adjusted model over longer horizon

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