Citation
On estimating the growth term for use in the discounted flow model of determining the cost of equity

Material Information

Title:
On estimating the growth term for use in the discounted flow model of determining the cost of equity forecasts by historical methods versus security analysts' forecasts
Creator:
Vinson, Steve R., 1948-
Publication Date:
Language:
English
Physical Description:
xvi, 367 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Analytical forecasting ( jstor )
Dividends ( jstor )
Error rates ( jstor )
Financial securities ( jstor )
Forecasting techniques ( jstor )
Investors ( jstor )
Net income ( jstor )
Securities analysis ( jstor )
Securities markets ( jstor )
Statistics ( jstor )
Discounted cash flow ( lcsh )
Dissertations, Academic -- Finance, Insurance, and Real Estate -- UF
Finance, Insurance, and Real Estate thesis Ph.D
Public utilities -- Finance ( lcsh )
Public utilities -- Prices ( lcsh )
Public utilities -- Rate of return ( lcsh )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Steve R. Vinson.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
001102447 ( ALEPH )
19617664 ( OCLC )
AFJ8514 ( NOTIS )

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ON ESTIMATING THE GROWTH TERM FOR USE
IN THE DISCOUNTED CASH FLOW MODEL
OF DETERMINING THE COST OF EQUITY:
FORECASTS BY HISTORICAL METHODS VERSUS
SECURITY ANALYSTS' FORECASTS






By


STEVE


VINSON


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY


OF FLORIDA


1i Qa






















































Copyright


Steve


1988


Vinson




























For


Elizabeth


and Elizabeth


Claire














ACKNOWLEDGMENTS


This


research


been


conducted


over


rather


extended


period


of time,


through


many phases


of my


life


and


career.


There


are so many people who


have


contributed


large


small


ways


that


is doubtful


that


can


recall


thank them all.


would


and


like


ever-ready


thank Eugene


assistance


Brigham


throughout


his guidance


academic


professional


career.


Without


Gene's


encouragement


support


would never have had


the opportunity


pursue


interests


in corporate


finance.


From


first


time


read


one


textbooks,


long


before


met


him


personally,


during


period


when


were


actively


working


together,


I have gained


continuing through


from him a


distinct body


present day,


of knowledge and an


immeasurable


number of


insights.


also thank the members


of the


finance and


economics


faculty


the University


Florida,


especially Sanford


Berg,


Arnold


Heggestad,


and Robert Radcliffe who


serve


dissertation


committee.


I have


greatly


enjoyed and


benefited


from their teaching,


friendship,


and wisdom.


Over


course


of preparing


this study,


numerous







AT&T,


including


Eric


Lindenberg,


Mark


Stumpp,


Bill


Ford,


George


Lee,


and Sue


Perles-Goldberg.


have


benefitted


from


number


conversations


with


members


academic


community


who


also


practice


rate-of-return


consulting.


In addition


Gene Brigham,


these


include


Bill


Carleton,


Jim


Vanderwiede,


Irwin


Friend,


Dick Bower,


Fred


Pettway,


Weston,


and


Chuck Linke.


.tzenberger,

Several m


Bill


Avera,


members


Dick


security


analysts


community provided


valuable


information


on their


profession


and methods.


would


especially


like


thank


John


Bain,


Mark Luftig,


Charles


Benore,


Charles


McCabe,


Leonard Hyman.


This


assistance


study


of my


also


good


benefits


friends,


from


Dilip Shome,


advice


Lou Gapenski,


Pietra


Rivoli,


Brad Jordan,


who on


more


than


one


occasion buoyed my


failing


spirits.


Finally,


lovingly


and


gratefully acknowledge


continuing


moral,


financial,


and spiritual


support


Elizabeth


Vinson,


from whom all


the good


things


in my


life


flow.














TABLE


OF CONTENTS


Page
. iv


ACKNOWLEDGMENTS................. ...................


LIST


OF TABLES. ................... ... .x


ABSTRACT. ................ ......................... .xv

CHAPTERS


EARNINGS REGULATION,
CASH FLOW METHOD, AND
ESTIMATION...........


THE DISCOUNTED
METHODS OF GROWTH


..I ....... .. .1


Intr
The
The


Fina

The

Comm
1.6.

1.6.


oductio
Economi
Cost of
Common
Establ
ncial a
of Ret
Discoun
For Es
only Us


1

2


Grow

Secu


n.... ..
c Princ
Common
Regula
fishing
nd Lega


urn..
ted C
timat
ed Gr
th Es
Hist
rity


ing
owth
tima
oric
Anal


f Regul
and It
ocedure


ards


e Co
stim
s De
Acc
ts'


ethod
st of
ators.
rived
ountin
Growth


Fair


Equity


* 1


Rate
....1

S21


00.0......
from
g Data....
Forecasts


S .


THE THEORETICAL
FORECASTS IN THE


ROLE OF SECURITY ANALYSTS'
FORMATION OF INVESTOR


EXPECTATIONS............


.. .. .. .34


Introdu
A Model
In
The Rol
A Model
Op
Diverge
A Simul
In


rket
ion P
onsen
forma
and
Opin
Analy


Effi
rodu
sus
tion
Cons
ion
sis


Consensus


* ...... .


cie


ncy
on.
ect
qui
us
a R
the


ana


Expectat


ions.....
tion, Div
pectation
k Factor.
fighting
ion......


... .36
. .40


s...44
. ..55


* ....63


.......... .34








A REVIEW


OF THE


EMPIRICAL


LITERATURE............66


Int
The


1
s
i


Li
' S
eld
Car
and
Gr
Stu
Li


terature o


h

e

u
d
t


reduction
Empirica
Analyst
.1 Baref
.2 Basi,
.3 Brown
.4 Elton
.5 Other
Empirica
Analyst
.1 Cragg
.2 Malki
.3 Cragg


ort-Ter
and Com
y and T
Roseff
ber, an
ies....
erature
ng-Term
Malkiel
d Cragg
Malkiel


m
is
wa
(1
d


Securi
recast
y (197
(1976
8)....
Itekin


ty
s. .
5).
). .

(1c


curity


a;


.. .. 66


......7
...... 7


981)..8
......9


sts. ..... .93
..... ...... 93
......... ...99
. 105


AN INTRODUCTION


TO THE


DATA...... .....115


Overview..
Long Term
Histo
Comparison
Withi
Comparison
Metho
By Se
Comparison
Metho
Indus
Value Line


...........
Growth Fore
rical Accou
of Forecas
n Industry
of Forecas
ds with For
curity Anal
s of Foreca


nd


IBE
Clas


Forecasts


casts Deri
nting Data
ts by Hist
Classifica
ts by Hist
ecasts Mad
ysts......
sts by His
Forecasts
ifications
of Growth.


orical
tions.
orical
e


.... 115
Dm
S. ....120
Methods
S... 129


S. .137
torical
Within
S........ ..140
S. 147


AN EXAMINATION


OF FORECAST


ACCURACY............151


Introduct
Computati
Fore
Forecast
Forecast
Cate
Forecast
Decomposi
Diag
Industry
Error Dec
The Corre
The
Pric


ion.
on o
cast


f Actual Growth
Errors.........
racy............
racy Within Indu


Rate:


.........151
s and


trial


cy Within Utility
f Forecast Errors


actors
id Err


rror Decomposition.....
ion By Utility Sector..
of Forecast Methods to
ectional Structure of


earnings


Ratio


..1
..1


.168
.187
r


. .2
. 2


s..... ... .


s' Lo
and
el an
and


.


1


. .231








SUMMARY


AND


CONCLUSIONS........................ 238


Introduction..........
Findings..............
An Explanation For the
Performance of
Security Analysts


.......Superior

Superior


.. .. ....2
..........2


Forecasts.......... 257


BIBLIOGRAPHY.............. ... ................ .... 269


APPENDICES


SECURITY ANALY
ESTIMATES


CONTRIBUTING
THE IBES DATA


BASE ............280


INDUSTRY
SIC


CATEGORIES AND ASSOCIATED
CODES...... ...... ...... ........ ......282


FORECASTS BY
PEARSON


HISTORICAL
CORRELATION


METHODS:
COEFFICIENTS...........284


FORECASTS BY HISTORICAL METHODS AND IBES FORECASTS:
PAIRWISE COMPARISONS OF FORECAST AGREEMENT.
COMPUTED VALUES OF FRIEDMAN STATISTIC......299


FORECASTS BY
PAIRWISE


HISTORICAL
COMPARISON


METHODS AND
OF FORECAST


IBES FORECASTS:
AGREEMENT..314


DECOMPOSITION OF FORECAST ERROR:
DECOMPOSED BY BIAS, EFFICIENCY,
ERROR. FORECAST ERRORS ASSESSED
ACTUAL EARNINGS GROWTH..........


DECOMPOSITION OF FORECAST ERROR:
DECOMPOSED BY BIAS, EFFICIENCY,
ERROR. FORECAST ERRORS ASSESSED
ACTUAL DIVIDEND GROWTH..........


AND RANDOM
AGAINST


. .321


AND RANDOM
AGAINST


. ...331


ACCURACY OF FORECASTS
IBES FORECASTS.


BY HISTORICAL METHODS
WILCOXON SIGNED RANKS:
Tl -rnrTITm a nnrifT -r r.,1Tn ^T-rtrnn


VERSUS








ACCURACY OF FORECASTS
IBES FORECASTS.
ERRORS ASSESSED
GROWTH..........


BY HISTORICAL METHODS
WILCOXON SIGNED RANKS:
AGAINST ACTUAL EARNINGS


VERSUS


BIOGRAPHICAL


.......... .354


SKETCH. ...............................366















LIST


OF TABLES


.1 Average

.2 Average

.3 Analysis


Annual Forecast E

Industry Forecast

of Turning Point


rror....

Error..

Errors.


.


. .73


. .73

S. .. ..74


Theil'


U-Stati


stic


. .75


.5 Representative

.6 Specification


Forecast E

of Forecast


rrors.......

Horizons...


. .78


...... .... 80


T-Values


Associated


with


Forecast


Errors


. .83


Rank


Order


Average


Correlation


Cumulative


Coefficients.


Excess


Returns


. .88


.............. .88


Other


Studi


............. ....... .. .... .92


Theil'


U-Statistic.


.. .. .............. .. ... .98


Regress


Estimated


Asymptotic


Result


S .


Parameter


t-Statisti


................103


Values............


CS....


. .....104


. .111


.1 Forecasts


criptive
storical


storical


Statistics


Methods


Methods..


: Growth


. .123


Forecasts


....125


Agreement
Pearson


Among


Forecasts


Correlation


Historical


Coefficients


and


Methods


Number


Common


Observations...........


.130


Agreement
Pairwise


Among


Forecasts


Comparisons


Historical


of Forecast


Methods


Agreement...


.131







.6 Forecasts


Agreement


Historical


within


Methods:


Industrial


Forecast


ass


cations


. .135


.7 Descriptive


Stati


cs: IBES


Forecasts


(Full


Sample).....


criptive


Stati


stics


: IBES


Forecasts


(Reduced


Sample)


Agreement


Among


Forecasts


storical


Methods


and


IBES


Forecasts


Pearson


Correlation


Coefficients.


.139


Agreement


Among


Forecasts


Historical


Methods


and


IBES


Forecasts


Pairwise


Compari


son


Forecast


Agreement......


IBES


Forecasts


: Intraindustry


Summary


Statistics.


. 143


.12 Forecast
Forecast


ssifi


Historical


Agreement
cations...


Methods


Within


Indus


IBES


Forecasts


trial


...144


Descriptive


Stati


CS:


Value


Line


Forecast


.149


Value


Line


Forecasts


Agreement


with


Forecasts


storical


Methods


and


IBES


Forecasts


. .150


Accuracy


of Forecasts


storical


Methods


IBES


Foreca


sts:


Errors


Assessed


Against


Actual


Growth


Earnings


per


Share..


.157


Accuracy


of Forecasts


Historical


Methods


and


IBES


Forecasts


: Errors


Assessed


Against


Actual


Growth


Dividends


per


Share...


....158


Accuracy


of Forecasts


Historical


Methods


And


IBES


Forecasts


Mean


Square


Forecast


Error...


. .158


Accuracy


And


IBES


of Forecasts


Forec


asts


by
Thi


stori


Methods


U-Statistic..


. .161


5.5 Accuracy


of Forecasts


storical


Method


IBES Forecasts:
Errors Assessed
Growth.........


Wilcoxon
Against A


Signed


ctual


Ranks


Tests


Earnings


.164


. ..138


. ..138


S .141








5.6 Accuracy


Forecasts


Historical


Methods


IBES


Forecasts


coxon


Signed


Ranks


Tests


Errors


Assessed


Against


Actual


Dividend


Growth...


...167


Median A
Methods
Against


ctual
and


Errors
IBES F


Actual


Forecasts


forecasts


Earnings


: Errors


Historical
Assessed


Growth..


....174


5.8 Median


Absolute


Percentage


Errors


Forec


asts


Historical


Methods


and


IBES


Forecasts:


Errors


Asses


Against


Actual


Earnings


Growth.


....177


.9 Median Actual
Methods and


Against


Median


Errors


IBES


Actual


Absolute


Forecasts


Forecasts:


Dividend


Perce


Errors


storica


Assessed


Growth...


ntage


S. .180


Errors


Forecasts
Forecasts:


stori


Errors


Methods


Asses


and


Against


IBES


Actual


Dividend


Growth.


. 183


summary
Industry
Vs. IBES


of Wil


coxon


Forecasts
Forecasts:


Signed


Ranks


Histori


Errors


Assesse


Test


Methods


d


Against


Actual


Earnings


Growth..........


..188


Summary
Industry
Vs. IBES


Actual


Median

Median


of Wilcoxon
SForecasts
Forecasts:


Dividend


Actual

Absolut


Signed


Ranks


Histori


Errors


Assess


Growth


Forecast


Test


Methods
ed Against
.............189


Errors.....


Percentage


Errors


.15 Wil


coxon


Signed


Ranks


Tests


Telephone


Companies


coxon


Company


Signed


es.


Wilcoxon


Signed


Ranks
* ...

Ranks


Tests


Tests


Electric


Servi


. .197


Natural


Gas


Transmi


ssion


Companies


.....*198


Wilcoxon


Signed


Ranks


Tests


Natural


Gas


Distribution


ra4 1 n ^


Companies


C nn v rJ


Tr'1 anr^^ i r.


. ..199


I


. .191

. .192


. ..196


*D -a'M'b


rplaeC+-E-


r, c







Decomposition
Aggregation:


of Forecast
Errors Asse


Error


ssed


Level


Against


Actual


Earnings


Per


Share


. .206


5.21 Decompos


ition


Aggregation:


Dividends


Per


of Forecast


Errors
Share


Asses


Error
sed A


Level


against


Actual


. .206


5.22 Decomposition


Error.


Errors


y Bias,
Assessed


Efficiency,


Against


and


Actual


Random
Earnings


Growth. . .................


Decomposition


Error.


Errors


Bias


Assessed


, Efficiency,


Against


and


Actual


Random
Dividend


Growth..


.210


5.24 Evaluation


of Linear


Bias


and


Inefficiency


. ... 212


.25 Compari


son


of Sources


of Error:


Forecasts


Historical
Differences


Methods


Linear


. IBES


Bias


Forecasts


Tests


Contribution


MSFE.


...220


.26 Decomposition


of Forecast


Error


: Telephones


...223


Decomposition


of Forecast


Error


: Electric


Service


Companies


. ..224


Decompo


Gas


sition


Transmiss


of Forecast
on Companies


Error:


Natural


. .225


Decomposition


of Forecast


Error:


Natural


Gas


Distribution


Companies......


. .226


Decompo


sition


of Forecast


Error:


Electric


And


Gas


Evaluati


Combination

on of Linear


Compani


Bias


es.


and


.....227


Ineffi


ciency:


Forecasts
Telephone


Historical


Methods


and


IBES


Forecast


s. .


5.32


Evaluation


of Linear


Bias


and


Inefficiency


Forecasts
Electric


Historical


Service


Company


Methods
es.....


and


IBES


Forec


asts
.229


Evaluation
Forecasts


Natural


Gas


of Linear


Bia


Historical


Transmi


ssion


and


Methods


Compani


Inefficiency:


and
es.


IBES


Fore


casts.


Growth..........


Growth................ .







Evaluation
Forecasts


Natural


of Linear


Bias


Historical


Distribution


and


Methods


Company


Inefficiency:


and
es.


IBES


Foreca


Evaluation
Forecasts


of Linear


Bias


Historical


and


Methods


Inefficiency:


and


IBES


Forecas


Electric


and


Gas


Combination


Companies..


.. .2


5.36 Correlation


Between


Forecast


Methods


and


Earnings


Ratio


S....


.234


5.37


Correlation


Earnings


Between


Ratios


Forecast
Industry


Methods
Category


and


.235


Average
Return.


Earnings


Retention


and


Earned


Rates


.258


6.2 Compari


son


of Analysts'


Revi


sions


Pre-


and


Post


Rate


Author


zation.......................













Abstract


of Dissertation


Presented


the


Graduate


School


the University
Requirements f


of Florida


the


Degree


Partial
of Doctor


Fulfillment of
of Philosophy


ON ESTIMATING


IN THE


THE


DISCOUNTED


GROWTH


CASH


TERM
FLOW


FOR


USE


MODEL


OF DETERMINING


THE


COST


OF EQUITY:


FORECASTS


BY HISTORICAL


METHODS


VERSUS


SECURITY


ANALYSTS'


FORECASTS


STEVE


April


. VINSON

1 1988


Chairman:


Eugene


Brigham


Major


Department:


The


cost


Finance


of capital


, Insurance,


of critical


Real


Estate


importance


in almost


financial


economic


deci


sion


making.


Nowhere


that


importance


more


observable


than


the


process


setting


prices


regulated


public


utilities.


Over


the


twenty


years


the


counted


cash


flow


(DCF)


model


of estimating


cost


of equity


capital


has


become


the


most


popular


method


ascertaining


the


cost


capital


regulated


public


utilities


However,


implement


the


DCF


model


necessary


estimate


the


long-term


growth


rate


cas


flows.


this


study,


several


methods


of estimating


growth







accounting


data


with


estimators


taken


from


security


analyst


forecasts.

Institutional


Security

Brokers


analysts'

Estimate


forecasts

System (


are


IBES)


taken


data


from

ase


represent


the


consensus


view


a number


of professional


security


analysts.


addition


direct


examination


growth

also


estimators


examines


regulated


large


cross


utility

section


companies


non


the study


-regulat


industrial


firms.


Historically


based


and


security


analyst


forecasts

systematic


are


contrasted


biases,


and


measures


strength


of foreca


relationships


accuracy


to stock


price


earnings


ratios.


The


study'


findings


indicate


that


the


consensus


security


analysts


' foreca


most


reliable


estimator


long-term


growth


utility


company


es.


For


most


other


industrial


sectors


, the


consensus


security


analysts'


forecasts

properties


generally


storically


equivalent


based growth


desirable


estimator


estimators.


The


study


also


demonstrates


that


estimators


of growth


taken


from


security


analysts'


forecasts


are


more


informationally


efficient


than


growth


estimators


based


solely


on historic


time


series


data.













CHAPTER


ONE


EARNINGS


REGULATION,


THE


DISCOUNTED


CASH


FLOW


METHOD


AND


METHODS


OF GROWTH


ESTIMATION


Introduction


explicit


critical


knowledge


importance


the


many


cost


capital


economic


decisions.


Capital


budgeting


choices


require


estimates


Cos


capital


screening


hurdle


investment


rates


cut-off


opportunities.


The


points


valuation


closely


held


firms


with


untraded


stock,


valuation


of divisions


projects


within


firms


that


have


traded


stock


will


normally


call


estimate


cost


capital.


Nowhere,


however


, does


determination


the


cost


capital


receive


more


attention,


more


scrutiny,


and


more


debate


than


the


process


of regulating


prices


and


earnings


public


utility


companies.


The


reasons


such


close examination


are


straightforward.


1986,


example


, the


total


invested


capital


maj or


domestic


electric


, gas,


telephone


utilities


was


about


$593


billion.


A change


the


cost


of capital


that


averaged


only


one


percentage


point


across


this


total


investment


would


have


changed







annual


revenue


anticipated


requirements,


cost


the


that


aggregate


the


consumption


total


of these


regulated


goods


and


services


, by


almost


billion.


That


equivalent


wealth


annual


of about


per


capital


event


such


redistribution


immediate


immense


economic


impact


on society


must


obviously


examined


carefully


Yet


determination


the


cost


capital,


including


consideration


of how


and


when


does


change


not

are


an exact


used


science.

evaluate


The


methods


cost


and p

capital


Procedures


are


that


evolving


dynamically


point


time,


the


methods


are


neither


unanimou


accepted


nor


subj ect


to universally


consistent


application.


many


respects,


regulatory


proceedings


have


served


many


years


testing


development


a new


1iteratur

witness


laboratories


of cost


concept


financial


of capital


or theory


somewhere


appearing


there


before


economists


methods. Almost

introduced in th


will


a regulatory


an expert

body at


the


soon


academic


financial


tempting


introduce


that


concept


in estimating


the


utility'


cos


capital


And


because


the


stakes


are


high


and


the


regulatory


process


the


United


States


has


become


increasingly


adversarial,


these


innovations


rarely


unchallenged.


fact,


as Harrington


(1979)


, IS







process,


the


ensuing


debate


provides


valuable


feedback


the


academic


community


at large,


stimulating


vast


amounts


of empirical


and


theoretical


research.


within


this


regulatory


environment


that


questions


about


appropriate


estimate


of growth


use


determining


discounted


cash


flow


cost


equity


capital


have


received


significant


attention,


especially


within

producing


the


recent


growth


several


estimates


years


using


the


when


consensus


method


of security


analysts'


forecasts


emerged


as a direct


challenge


more


traditional


estimating


technique


that


relies


on the


extrapolation


of historical


time


series


data.


The


that


purpose


regulatory


this


environment,


chapter


discuss


is to briefly


the


describe


importance


cost


of capital


the


det


ermination


of regulated


ces


and


set


the


stage


the


specific


analy


ses


the later


chapters


Section


1.2,


introduction


underlying


economic


principles


price


and


earnings


regulation


is presented.


Thi


followed


Section


a simple


used


model


rate


that


setting


explains


how


procedures


cost


that


are


of capital


followed


almost


regulatory


jurisdictions.


Next,


Section


sets


the


economic


and


legal


standards


that


qualify


fair


rate


of return.


In Sections


1.5 and


the


basi


concepts


the


counted


cash


flow


model


are


reviewed







The


Economic


Principles


of Regulation


The


justification


regulatory


control


intervention


ses


out


alleged


inability


marketplace


to deal


with


particular


structural


problems.


Kaysen


and


Turner


(1959)


suggest


that


regulation


exemption


from


competition


may


appropriate


when


one


more


three


situations


are


found


within


industry:


Situations


cannot


exist


which


or survive


competition,


long,


an


as a practical
d in which, th


matter
erefore


an unregulated
results.


market


will


not


produce


competitive


Situations


which


active


competition


exists


, but


where
does


because


not


produce


of imperfections


one


or more


the


competitive


market,


competition


results


Situations


exist,


and


competitive


cons


iderations


has


which


produced


results,


but


compete itiv


competition


or may D
where in
e results


e exp
light
are


exists,
ected
of ot
unsatis


or could
to produce
her policy


;factory


one


or more


aspects.


a public


utility,


the


first


situation


the most


traditional


and


persistent


rationale


regulation


the


firm'


pri


ces


and


profits.


For


these


firms,


technology


the


industry


creates


the


existence


"natural


monopoly.


In other


words,


claimed


many


basic


types


services,


that


the


market


cannot


efficiently


support


more


than


one


firm.


For


example,


a point,


electricity


producers


find


progre


ssively


cheaper

1 nt's 1


to supply


a 1- 1 an1 ,1 -


extra


units


nnmn J i W a e


of electricity.


Ii stta


l at-rvn m nn l


Similarly,


nf Cen 1 o


S.','


*








one


telephone


company


attempted


to supply


service


in a


particular


area.


Thus,


traditional


rationale


has


been


that


more


efficient


grant


one


firm


monopoly


a service


territory.


And


, in


order


protect


the


consuming


public


from


abuses


that


monopoly,


the


firm'


prices


and


earnings


become


subject


government


regulation


This


market


traditional


failure


view


due


holds


existence


that


case


of economies


of scale


and


natural


monopoly,


the


aim


price


and


earnings


regulation

perfectly


emulate


competitive


the


results


market.


That


that

is,


exist


ere


perfectly


competitive


market,


firms


would


expand


output


the


point


where


price


equals


marginal


cost,


unregulated


monopolist,


the


other


hand


curtails


production


in order


to raise


prices.


While


higher


price


means


lower


demand,


the


monopolist


will


willingly


forego


quantity


sales


the


extent


that


lost


revenues


are


compensated


higher


revenues


on the


units


does


more


Panzar,
(1975),


recent


and
holds


sufficient


unless


production


may


engage


view,


Willig
that


ass


(1986)


the


produce


market
costs,
in "hit


ociated
, Bailey


potential f
competitive


is truly


the
and


primarily
(1971),


with
and F


competition


results.


characterized


possibility


run"


entry


that
and


a compe


exit


Baumol,
aulhaber


may


That


subadditive


ting


firm


is sufficient


cause


the


competitive


incumbent


manner.
*S


firm
that


* -


price


event,


exogenous


* S


goods


in a


regulatory


--Ti U-r -a -


q


I


X


q~ ~ X u X q m







sell


the


higher


price.


The


result


waste;


consumers


end


buying


more


cheaper


but


less


preferred


products


, even


though


costs


society


ess


in real


erms


produce


more


the


monopolized


product


Thus


, where


economic


scale


create


natural


monopoly,


regulator


will


attempt


to set


regulated


monopoly


pri


ces


(rates)


near


the


prices


that


would


obtain


a compe


titive


market,


and


thereby


induce


the


monopolist


to expand


output


the


socially


desired


level


and


to reduce


the


amount


ineffic


ient


consumption


substitution


buyers.


The


price


that


is set


the


regulator


, however,


generally

production


not eq

as would


uivalent


be required


marginal

standard


cos


model


perfect


competition.


Faulhaber


(1975)


more


recently,


Baumol


(1986)


have


pointed


out,


economic


scale


preclude


the


financial


viability


of a rule


requiring


equality


between


pri


ces


and


marginal


costs


Prices


which


cover


only


covering


marginal


any


the


costs

fixed


do not

costs


general


of production.


contribute


Thi


because


economies


scale


often


occur


the


presence


substantial


fixed


investment


stri


adherence


the


price-equal


s-marginal


-cost


standard


would


not


allow


the


owners


the


regulated


firm


recover


these


fixed


costs.


a consequence,


regulators


have


most


often


adopted


a policy


that


equates


price


with


the


average







the


fixed


plant


investment)


plus


return


investment.


that


process


and


procedures


how


regulated


prices


1.3.


are


And


determined


as will


that


be shown,


are

one


subjects


primary


Section

elements


setting


pri


ces


the


determination


the


return


allowed


equity


investors


the


firm.


concept,


regulator


can


achieve


at 1


eas


one


outcomes


perfect


competition


of eliminating


monopoly


profits


that


allowing


equivalent


a fair


the


return

marginal


on the

cost


equity i

of equity


investment

capital.


The


Cost of Common


Requlatorv


Eauitv


Procedure


and


Use


Establishing


In A Common


Prices


The


most


common


system


establishing


ces


regulated


ratemaking.


monopolies


It is currently


known


being


cos


used


t-of


to set


-service


ces


electricity


generation,


transmiss


ion,


stribution


companies,


gas


local


distribution


and


and


interexchange


transmiss


telephone


companies


companies


, water


sewage


companies


and


until


recently


was


used


price


-setting


mechanism


such


industries


airline


transportation,


bus


and


livery


transportation,


and


trucking


and


cartage.


Cost-of


-service


ratemaking


essentially


a two


step







operating


costs


include,


where


appropriate,


direct


costs


production


such


fuel,


labor


salary


and


fringes,


supervi


sion,


and


indirect


cos


such


maintenance,


general


administration,


marketing,


finance


and


accounting,


and


other


overheads,


as well


as taxes.


Added


the


basic


operating


costs


of production


are


the


capital


cos


depreciation


fixed


which


investment,


represents


and


the


a reasonable


periodic


level


recovery


earnings


that


allows


firm


pay


debt


interest


expense


and


afford


return


equity


putting


their


investors


money


a compensatory


at risk


rate


productive


endeavors


firm.


The


total


of operating


costs


service


and


capital


costs


of servi


call


the


revenue


requirement


(RR),


RR = OC + D


which


equivalent


amount


money


the


firm


needs


collect


production,


from


customers


recover


fixed


pay


investment


and


expen


ses


provide


investors


with


a fair


rate


return.


The


second


step


in cost-of


-servlice


ratemaking


establish


unit


price


the


firm'


goods


servi


ces


dividing


the


total


revenue


requirement


anticipated


number


of output


units


that


will


be sold,


=RR /


+ E







Thi


has


effect


of setting


unit


price


equal


average


total


unit


cost


of production.


Through


service,


through

that


certain


the


investigation


investment,


setting


societal


and


prices,


the


management,


regulators


objectives


are


utility'


and


seek


achieved.


cost


ultimate


ensure

Breyer


(1982)


has


noted


that


while


the


precise


objectives


cost


-of-service


ratemaking


vary


from


jurisdiction


jurisdiction,


regulators


would


generally


agree


that


such


system


should


ordinarily


seek


prevent


excess


profits


hold


prices


down


to costs,


avoid


economic


allocative


waste


minimizing


shortages


surpl


uses


eliminate


ineffi


cient


production


methods,


assure


admini


strative


ease.


The


first


four


objectives


are


generally


believed


occur


a competitive


marketplace,


thus


often


stated


that


the


ultimate


goal


earnings


regulation


through


the


mechanism


cost


-service


ratemaking


is to replicate


a competitive


market.


Although


cost-of


simple


-service


in concept


ratemaking


the


can


actual


become


application


burdensomely


description


difficulties
multiproduct


offering
whose t


stinct


abstracts


encountered


multi


several


otal


-cus


different


output


demand


tomer


intentionally
establishing


class


regulated


taken


characteristic


firms.


goods or
customers


, it


from
prices
For


service


with


the
for


firms
s. or


highly


necessary


allocate
r.WI aI A.rA nr.


the


costs


at. aI -YA a


servi


a1.


ces


- a a F


among
ml.. 4.4


those
-.n


goods


^ 1 a .4 4~ a


3Thi







complex.


Prices


are


generally


being


set


for


consumption


that


will


occur


the


next


and


several


immediate


future


periods


Thus,


the


measurement


underlying


costs


production


should,


theory,


reflect


the


costs


that


are


expected


incurred


during


those


future


periods.


Similarly,


the


output


quantities


that


are


anticipated


sold


must


also


forecast.


Regulators


seek


establish


a base


time


period,


called


the


test


year,


from


which


reasonable


forecasts


costs


and


output


can


made.


The


test


year


may


an actual


historical


period


time,


perhaps


the


most


recent


twelve


months


preceding


the


filing


of a request


a rate


change.


When


storical


test


years


are


used,


pro


forma


adjustments


to reported


accounting


data


are


often


made


to make


the


test


year


results


representative


as possible


the


expected


economic


environment


that


will


apply


when


the


new


rates


into


effect.


the


general


economy


has


become


more


volatile,


and


with


dramatic


rapidly


impacts


changing


inflationary


of uncertain


fuel


expectations


capital


costs,


both


nature


and


magnitude


these


adjustments


have


become


more


important


and


contentious


issues


during


rate


case


proceedings.


In other


regulatory


jurisdictions,


the


test


year


may


a hypothetical


future


twelve-month


period.


In that


case,


the


costs


of service


are


based


budgets


projections.


When


a future


test


year


is used,







Other


areas


debate


include


accounting


conventions


that


are


used


to record


expenses


revenues.


many


instances,


there


are


legitimate,


prof


ess


ional


disagreements


periods


over


deferring


or recognizing


them


certain

as costs


expenses u

of service


ntil


future


during


the


test


year.


some


extreme


circumstances,


costs


may


deemed


disallowed


imprudent


from


or unnecessary,


inclusion


and


totally


cost


or partially


service.


For


example,


management


salaries


may


deemed


excess


there fore


only


an amount


of salaries


acceptable


regulator


would


be allowed


the


cost


service.


the


regulator


may


feel


inappropriate


firm


advertise


goods


because


monopoly,


therefore


disallow


entirely


marketing


expenses.


Concurrently


with


estimation


operating


costs


service,


the


amount


of assets


required


to produce


the


expected


output


must


ascertained.


These


assets,


termed


the


rate


base


(RB) ,


represent


the


dollar


investment


land,


fixed


plant


equipment


material


supply


inventories


, fuel


stock,


and


other


productive


assets.


In addition,


an allowance


working


capital


used


to provide


timing


difference


between


the


rece


and


disbursement


of cash


often


included


the


rate


base.


discussion,


assumed


that


rate


base


financed


total


the


capital


supplies








Thi


investment


must


generate


enough


earnings


pay


interest


debt,


provide


dividends


preferred


stock,


their


and


money


compensate


at risk.


the


The


equity


return


investors


that


putting


is required


called


the


cost


of capital.


Within


the


framework


of cost-


-service


regulation,


the


cost


of capital,


or the overall


rate


of return


(ROR)


, is measured


as the


weighted


sum


the


cost


existing


debt


(Kd)


the


cos


sting


preferred


stock


(Kp),


and


fair


rate


of return


common


equity


capital


(ROE).


The


weights


are


det


ermined


the


relative


proportions


the


sources


of capital


used


to finance


rate


base,


ROR


The


= Kd


actual


(D/RB)


dollar


(PS/RB)


earnings


+ ROE


(CE/RB)


requirement


then


computed


multiplying


rate


of return


time


rate


base


= ROR


x RB


4There


are


other


sources


of capital


that


can


finance


rate


base including


deferred


income


accumulated


taxes


cus


cash
tomer


inflows


depos


provided
ts, and


investment


tax


credits.


With


minor


modification,


current


SCUSS


can


extended


to accommodate


ose


types


of capital.


5It
rate


may
base


the


case
ess


that
than


the
or


total
great


dollar value
r than the


of
sum


investor
implicit


-supplied
in rate


capital.


case


However,


proceedings


treat


generally


rate


base


i c rit i nfl


orma 1


.rn


t- nti- 1


r i 4 11


I ciiltA or^


tnr ~aiiitC+tmfc


+ Kp


I


1







and


the


dollar


revenue


requirement


equivalent


sum


individual


cost


components,


RR = OC + D


x ROR),


and


finally


after


substituting


the


complete


cost


capital


expression,


revenue


requirement


can


be stated


as a function


cost


of capital


through


RR = OC + D


+ RB


(D/RB)


(PS/RB)


+ ROE


(CE/RB)]..


In assessing


the


importance


the


cost


of capital


ultimate


revenue


requirement,


should


be noted


that


many


regulated


utilities


use


highly


capital


-int


ensive


produce


tion


technologies


These


firms


often


invest


dollars


in rate


base


assets


in order


to produce


output


that


can


be sold


revenue.


at all


unusual


to find


that


that


the


required


earnings


investment


these


capital


intensive


regulated


firms


can


constitute


percent


the


total


revenue


requirement.


a fair


Thus,


rate


the


of return


linkage


and


between


revenue


the


determination


requirements


and


ultimately


prices


paid


consumers


quite


direct


when


cost-of


-service


ratemaking


employed.


Financial


Leaal


Standards


Fair


Rate


of Return


Generally,


the


costs


debt


(Kd)


of preferred


stock


(Kp)


are


measured


embedded


or average


costs


+ Kp







contractual


agreements


that


exist


between


company


debt


and


preferred


stock


holders.


The


fair


rate


return


(ROE)


on common


equity


capital


not


formally


contracted.


Rather,


with


common


equity


investments,


the


return


common


equity


represents


residual


only


claim


after


on the


prior


earnings


claims


the


have


firm


been


that


met.


paid


However,


inves


tors


will


not


make


an equity


investment


unless


they


anticipate


that


this


residual


return


will,


over


time,


offer


them


fair


compensation


the


risks


they


bear.


the


province


cos


of capital


experts


determine


the


minimum


level


return


required


investors


that


will


induce


them


to make


a common


equity


investment


in the


regulated


firm.


To offer


more


than


the


minimum


level


would


generate


excess


profits


the


shareholders


and


unduly


burden


ratepayers.


offer


ess


than


minimum


required


level


would


penalize


existing


investors


have


the


effect


of confiscating


their


investment.


Gordon


(1974)


has


demonstrated


that


under


certain


assumptions


the


about


economic


the


reactions


environment,


regulators


fair


rate


to changes


of return


equity


capital


will


cause


the


market


value


the


firm'


common


the


equity


equity


to just


portion


equal

its


the

rate


accounting


base


book


investment


value of

In other


words,


regulators


allow


the


firm


earn


a fair


rate







corresponding


risk,


the


opportunity


excess


or monopoly


profits


will


be eliminated.


In turn,


the


market


value


the


firm'


common


equity


will


equal


regulatory-determined


value


earnings


base


, that


the


equity


portion


ratebase.


see


, let


the


accounting


book


value


equity


portion


the


ratebase


be defined


= RB


(CE/RB) ,


then e

equity


expected


annual


(ignoring


the


pool


impact


earnings available

of dividend policy


for

and


common

future


investment)


given


ROE


x B.


Gordon'


standard


determining


fair


rate


return


follows


from


assuming


that


the


equity


investors


are


purchasing


future


stream


earnings


with


expected


will


annual


be willing


value


pay


(ROE


x B).


an amount


The


just


marginal


equal


the


investor

present


value


this


stream


earnings


where


the


present


value


determined


discounting


the


earnings


stream


the


appropriate


risk-adjusted


cost


of equity


capital,


For


the


sake


of simplicity


but


without


loss of generality,


the


stream


definition


assumed


fair


rate


to be


a perpetuity


of return


can


, Gordon'


expressed


algebraically


(ROE


x B)


/ Ke.







ROE


=- Ke,


then


= B,


and


monopoly


profits


will


have


been


eliminated.


Thus,


the


goal


of regulators


setting


utility


pri


ces


should


be to determine


the


marginal,


market


required

as a fair


cost

rate


of equity

of return


capital,

on the


and

book


to utili


value


that


the


value

common


equity


portion


of the


rate


base


investment.


Gordon's work


provided


direct


opportunity


cost


linkage


and


between


the


the


economic


estimation


concepts


fair


rate


return


ratemaking


common

purposes


equity


that


As such,


his


was


appropriate


approach


was


largely


responsible


shifting


the


focus


of regulatory


attention


away


from


book


accounting


results


and


toward


the


capital


markets


for


determining


the


cost


of equity.


Although


Gordon'


conceptualization


the


regulatory


problem

estimatin


provided

a the


economic


cost


guidance


of equity


measuring


capital,


the


controlling


regulatory


principles


standards


fair


established


two


rate


of return


Supreme


Court


are


deci


legal


sions,


Bluefield


Water


Works


Improvement


Company


Public


Service


Commission


West


Viraina


(262


U.S.


679,


1923)


and


Federal


Power


Commission


Hope


Natural


Gas


Company


(320


U.S.


391,


1944).


In Bluefield,


the


court


determined


the


standard


against


which


just


and


reasonable


rates


(prices)


are


measured:


A public
t-ri l n a v


utility


-m 4-


entitled


a a ~ Y.n


rn~lrrr


o such
ank


rates
tr~ 1 ii


n r


l r-







undertakings


risks and
be reason
in the fi
should b
economical
its cred
necessary
duties. (


U
ab
na
e


it
fo
Pa


which


are


uncertainties
le, sufficie
ncial soundn
adequate,
management,
and enable
r the proper
ge 116)


attended


*. *
nt
ess
u
to
e
di


The
to ass
of th
under e
maintain
it to
charge


corresponding
return should
ure confidence
e utility, and
efficient and
n and support
raise money
of its public


In Hope,


the


court


expanded


guidelines


to be used


assessing


reasonableness


the


allowed


rate


return.


The


court


again


reemphasized


comparable


risk


nature


the


return


made


special


note


that


costs


of service


include


a fair


amount


earnings,


rate-making


fixing
a bal
intere
Pipeli
insure


re
co
a
in
re
of
re
fo
in
st
eq
on
co
sh
fi
ma
25


of "
ancing
sts.
ne Co


t


venues.
nsidera
legit
tegrity
gulated
view
venue n
r the
clude s
ock....
uity ow
inves
rrespon
would be
nancial
intain
)


ust
of
Thus
ca


hat th
" 315
tions
imate
of th
. Fro
it is
ot only
capital


process


and
the
we
se


e


as
c
e
m
im
f
c


i

C


under


the


act,


.e.y


reasonable" rates, inv
investor and the con
stated in the Natural
that "regulation does


busi
U.S.
de,
ncer
ompa


the
por
or
ost


service on t
By that
ner should
tments in
ding risks
sufficient
integrity
its credit


ness sh
p. 5
the inve
n with
ny whose


nvest
nt th
erati
of t
debt
ndard


n

b


C


oth

to
of
and


or
at
ng
he
an


all p
90.
stor i
the
rate


or c
there
expen
busin
d divi
the re


reduce
But
nteres
fina
s are


ompan
be
ses b
ess.
dends
turn


y
e
ut


t


commensurate with r
er enterprises
That return, mor
assure confidence
the enterprise, so
attract capital.


on
o
et
ha
eo
in
a
(


the
lives
umer
Gas
not
net
such
has
cial
eing
oint
ough
also
hese
the
the
urns
ving
ver,
the
s to
Page


Morin


(1984)


has


termed


both


the


economic


and


legal


standards


fair


rate


return


transparent


and


stated


that


the


real


difficulty


determining


a fair


The








precepts


of Hope


and


the


financial


concept


the


cost


capital,

or presc


public

ription


utility

for


statutes


what


give


no detailed


constitutes


formula


"just


reasonable"


rate


return


equity.


The


applicable


legal


standards


permit


public


utility


commissions


choose


among


variety


analytical


techniques


procedures


setting


allowed


rate


return


equity.


Kolbe,


Read


and


Hall


(1984)


reviewed


the


hearing


transcripts


and


testimony


of a number


of rate


cases


found


that


five


general


cost


of capital


methods


have


been


commonly


used


to implement


concept


determining


fair


rate


of return


on common


equity


capital6


They


are


order


the


quency


their


total


storical


use


Comparable


Earnings,


Discounted


Cash


Flow


(DCF)


Capital


Asset


cing


Model


(CAPM),


Risk


Premium


Risk


Positioning),


and


Market-to


-Book


Ratio.


comparable


earnings


method


was


the


mos


t prevalent


method


establishing


rate


return


until


the mid


1970s.


According


Kolbe,


Read


and


Hall,


the


time


publication


their


study,


the


Discounted


Cash


Flow


6Morin


(APT) a
capital.
indicates


use.


identify


method


However,


that


Other


to date
methods


the


Arbitrage


estimating


review


the


Pricing


cos


regulatory


has received


that


have


extremely


received


t of


Tneory
equity


testimonies


limit


limit


use


S,,


a a a- A.- Z -- .3-,'a; A. -he -- -


,,,,,,,~,:


C1


U


A


I







method


had


become


the


predominant


methodology


in terms


current


usage.


Although


the


choice


of method


extremely


important,


should


standard


not


a fair


forgotten


rate


that


of return


the


is the


ultimate


so-called


legal


"end


result"


test


In effect,


while


the


rate


of return


that


used


set


rates


mus


compensatory


and


must


confiscate


the


wealth


investors


must


equitable


consumers.


Striking


a balance


between


competing


interests


investors


consumers


political


not


an economic


decision.


However


financial


economic


cost


may


may


of capital,


be predicated


be able


so that


upon


improve


ultimate


stronger


the


estimation


judgements


evidentiary


fairness


support


The


counted


Estimating


the


Cash


Flow


Cost


Method
Equity


The


cla


ssical


value


theory


of Irving


Fisher


(1907)


and


J.B.


Williams


(1938/1956)


holds


that


value


asset


determined


earnings


power


ability


generate


future


cash


flows.


That


theory


states


the


fundamental


value


an asset


is the


discounted


sum


of all


future


cash


flows


that


are


expected


to be received


the


owner


of that


asset.


The


Discounted


Cash


Flow


(DCF)


model


C_ -L *
A-k~~^ ffT nf i-a-^ nr^aae


r~~11 da


nabnarriC


an~


, 4 4


(rl~i vf nx


nara


r J







security


valuation


has


emerged


the


direct


application


that


classical


theory.


The


most


general


form


the


DCF


model


developed


first


expected


noting


cash


that


flows


the


come


holder


the


common


form


stock,


of dividends


the


and


changes


the


the


dividend


price


the


the


stockholder


stock.

expects


Letting


represent


to receive


Year


represent


price


the


stock


the


end


of Year


and


required


rate


of return


the


stock.


the


shareholder


anticipates


receiving


dividends


periods


and


then


selling


the


stock


the


period


the


pres


value


the


stock


can


determined


from


+ Pn)


. +


(1+K


(1l+Ke)2


(1+Ke)3


(1+Ke)n


this


equation,


the


pattern


dividends


unspecified


through


time.


That


, dividends


may


increase,


decrease,


become


zero


or quite


large


and


model


may


still


used


assess


value


stock.


imposing


structural


assumptions


upon


the


time


path


dividends


and


earnings


changes,


simplified,


eas


solved


version


of the


model


may


developed.


Gordon


(1962)


has


shown


that


dividends


are


expected


grow


at a constant


rate


over


an infinite


number


periods,


ess


than


and


the


firm


either


(3a)


, g,







loss


when


new


shares


are


issued,


the


model


reduces


This


known


as the


Gordon


or constant


growth


version


the


DCF


method.


rearranging


the


terms


the


equation,


the


constant


growth


model


may


be solved


the


required


rate


of return


on the


stock,


While


more


complex


and


less


restrictive


versions


the


DCF


are


sometimes


employed,


the


above


equation


forms


the


basis


the


most


commonly


used


DCF


technique


estimating


the


cost


of equity


capital.


further


assumed


that


the


observed


market


price


the


stock


equilibrium


and


that


reasonable


estimates


anticipated


next


period


dividend


and


long-term


growth


rate


can


be made,


then


is a straightforward


computation


arrive


an estimate


the


required


rate


return


common


equity


the


firm


question.


The


commonsense


logic


the


model


that


equilibrium,


sum


required


expected


rate


dividend


of return

yield


on the


and


expected


the


capital


appreciation


possess


growth


algebraic


simplicity


Moreover,


the


easily


model


explained.


Most


likely,


these


properties


that


have


made







constant


growth


model


the


currently


most


often


used


method


of determining


cost


of equity


capital


1.6 Commonly


Used


Growth


Estimators


While


simple


form,


DCF


model


does


have


a maj or


implementation


problem:


order


use


DCF


procedures


estimate


an independent


estimate


must


first


made


and


then


used


as an input


the


equation.


That


actual


application


while


not


always


generally


agreed


upon,


the


measurement


the


stock


price


and


anti


cipated


dividend


pose


less


problems


than


the


estimation


long


run


growth


rate.


According


to Morin


(1984),


The


princ


required


ipal
return


ascertaining


the


difficulty


DC


growth


rate


calculating


F approach
which inves


tors


in
are


currently
infallible


rate
its


the


expecting.


method


is precisely,


magnitude


growth


While


in assessing
an explicit


cannot


component


there


what


the


assumption


avoided.


the


most


growth
about


Estimate
difficult


controversial


inve


step


a quantity wh
stores. (Page


ich


in implementing
lies buried in


DCF
the


since
minds


123)


their


review


of rate


case


testimonies


, Kolbe,


Read,


and


Hall


(1984)


found


that


the


popular


methods


growth


estimation


may


placed


three


general


categories


th


Energy


recently com
e industries


pleted
that


Regulatory


generic


they


rate


regulate,


Commission


of return


both


and


the


the


dockets
Federal
Federal


Communications


Commission


specifically


adopted


rcnnne* m


rirnr.r+ 1


nTrlnl


4 r n


* ,m m r rt


mn^-hnA


n~F


Trnr]T







Use


over so
Sometime
per sha
growth,
in disc
growth r
starting


of historical


me past
s past
re is
because
rete j
ate can


and


period
growth
used
e divid
umps,
change


ending


gr,
, o


in
S
nd
no
no


points


owth
ften f
earni
a pr
s are
that
ticeab


rate
ive
ngs
oxy
chan
the
ly w


of the


of dividends


data


ten y
book
r div
by
esti
the
seri


ars.
alue
dend
irms
ated
xact
s.


Use
inve


of forecasts of
stment services.


growth
These


rates public
forecasts


shed
are


sumed to be
investors.


representative


of the


expectations


3. Use
"retenti
as the
times
retained
paid ou
growth i
recognize
its cos
for exis
overall
instead


the


on"
ra
the
w
t a
s e


es


t o
tin
re
of


or
te o
pr
ithi
s di
qual
tha
f ca
g eq
turn
bein


"sustainable"


"plowback")
f return


oport
n the
viden
to (
t if
pital
uity
to
g pai


ion of
firm,
ds. Tha
b x BRO
the firm
, future
can only
invest
d out.


growth
on book


(also


called


rate, measured
equity, BROE,


earnings
b, instead
t is, an
E). Thi
is earn
growth i
come if
rs is p
(Page 55)


tha


d of
estim
s ap
ing e
n div
part
lowed


a


is
eing
e of
coach
ctly
ends
the
back


the


discussion


below,


some


characteristics


each


the


first


two


these


growth


estimator


methods


are


described.


First,


standards


however,


assessing


useful


the


to list


quality


some


reasonable


growth


rate


estimators.


These


standards


allow,


essentially,


third


computati


appr
fore
sepa
peri
the


coach
cast
rate
od r
sust


trending
fn ra ror" e c +a


onal
may
data
and
tent
inab
of
nf


approach
method
be imp


an
di
ion
le


d will
stinct
ratio
growth
history


is less
ology.
lemente
not be
foreca
s and b
method
ical d
Ii-r/


a competing method
The sustainable


d u
tr
sti
ook
is
ata
ntrn


sing e
eated i
ng meth
rates
simply
If
P rav 1


either his
n this st
odology.
of return
a variat
security
caF *t1,


tor
udy
I
ar
ion
a


1-h


than a
growth


o
na
v


prior
used,
n the
lysts
Rnnn


9The


I


(
(







formulation

empirically


testable

later c


hypotheses


which


hapters.


this


will


be examined


stage


the


study


the


standards


provide


basis


for


logical


prioril


reasoning


about


the


relative


strengths


weaknesses


the


competing


estimator


methods.


evaluate


the


Brigham,


appropriateness


Vinson,


Shome


of growth


(1983)


estimating


methods,


identified


four


desirable


properties


of a growth


rate


estimator,


Estimates


should


unbiased


Valid


procedures


that
than
inter
techn
tend
techn


are
the
est.
ique
to
ique


should,


either
"true"
Thus,
can be
be too
fails a


on ave


system
value
if a
shown t
high
critic


0

a


rage, produce
ically higher
of the var
growth rate
produce esti
r too low,
1 test.


estim
nor 1
able
estima
mates
then


ates
ower
of
ting
that
that


2.
est
inf
dis
est
exi
aff


Es
imati
ormat
regar
imati
sts
ect g


ti
ng
io
d
ng
an
ro


mates should
method sho
in; that is,
information
growth fai
,d which can
wth, then the


be
uld
tho


efficient.
utilize al
actimate


If a
Is to utiliz
logically be
method fails


m
e
ex
t


A
1 rel
should
ethod
data
pecte
his t


val
eva
d n


which
d t
est.


3. Estimates
should produce
highly sensiti
particular samp
value. Thus,
different estim
given company
seemingly slight
method fails the


should be consis
growth estimate
ve to the s
le of data used
if a method pr
ates of the gr
in a given tim
changes in inpu
consistency tes


tent.
es that
electric
to est
oduces
owth r
e peric
t data,
t.


)n
:i
r
*a
>d


A method
are not
of a
mate the
adically
te for a
due to
then the


4.
opi
cri
bec
opi
and


Est
ons
cal
se
on
ts c


inmates should
of market parti
in a DCF cost
it is the rep
that determines
ost of capital.


be reflect
cipants.
of capi
resentativ
a company'
(Page 2)


tive
This
tal
e i
s st


0
po
ana
nve
ock


f th
int i
lysis
stor'
price


1 .







.6.1 Growth


Estimates


Derived


From


storical


Accounting


Data


Cost


capital


analysts


have


often


bas


their


historical


computations


on earnings


per


share


, dividends


per


share


and


book


value


per


share.


While


theory


states

in the


clearly


form


that


the


of dividends


that


expected future

constitute value,


cash


flows


a case


can


be made


using


other


quantities


as well.


First,


the


ability


pay


dividends


stems


from


company'


ability


generate


earnings,


therefore


growth


earnings


per


share


can


expected


influence


the


market'


dividend


growth


expectations


major


disadvantage


using


directly


dividend


growth


the


discretionary


nature


the


firm'


dividend


policy.


That


historical


dividend


growth


may


be biased


because


short


run


changes


in the


payout


rate


the


firm.


Over


the

pace


longer

for


run,

future


growth


dividend


earnings


growth


per


and


share


thus,


may


the


expec


station


earnings


dividend


growth


growth.


may


more


A drawback


representative


to using


historic


future

1 time


series


earnings


per


share


to derive


expected


growth


the


relative


volatility


earnings


When


earnings


per


share


become


negative


very


small,


historically


based


growth


estimates


may


become


highly


started


computationally


infeasible.


In addition,


firms


are


known


r' ar'r-nniiT i nfl


*rtI II in/I n h /*


rt"l II


~h~ra


th rrnninh


6oma vn ^nr


nar







reflective


the


expected


the


ongoing


level


earnings.


The


use


of historical


growth


book


value


per


share


as a proxy


the


expected


dividend


growth


of a regulated


utility


may


be justified


under


certain


conditions


Book


value


a principal


determinant


of earnings


utiliti


original


cost


rate


base


jurisdictions.


Because


earnings


return


per


and


share


book


are


value


the


per


product


share,


the


the


earned


storical


rate


growth


book


value


per


share


may


provide


indication


the


growth


growth


of earnings


per


earnings


share.


per


share


turn


may


, as noted


pace


above


growth


dividends


the


per


share.


usefulness


of b


However,

ook value


two

per


assumptions


share


are


crucial


growth,


the


future


earned


rate


of return


must


be expected


remain


stable,

stable


and


about


the


unity.


market


The


to book


later


ratio


must


assumption


remain

ecially


important


because


book


value


per


share


will


increase


decrease


with


the


issuance


new


shares


when


the


market


to book


ratio


different


from


one.


The


type


growth


that


attributable


to book


value


accretion


dilution


generally


transient


and


serves


produce


biased


proxies


long-term


expected


growth.


After


selecting


historical


seri


of data,


time


period


over


which


growth


to be measured


must







current


economic


conditions.


the


same


time


the


data


period


should


long


enough


avoid


short


-term


influences.


Selection


of a time


period


depends


largely


judgement,


but


customarily


historical


based


estimates


rely


the


most


recent


five


ten


years


of data,


although


some

series


analysts

, and o


have


others


used


as short


long


a period


a twenty

as the


-year

most


time

recent


single


year


rate


of growth.


The


analyst


must


also


choose


a computational


form


extracting


Numerous


the


methods


growth


have


rate


been


from


employed


raw


accounting


including


the


data.


root


the


ratios


(geometric

averages,


averaging

weighted


the


least


averages,


beginning


squares

centered


and


trend


ending


fitting,


averages


values


moving

simple


averages.


These


computational


methods


are


more


or 1


ess


highly


sensitive


the


choice


of beginning


ending


values


are


not


generally


cons


istent


when


the


data


period


changed


slightly.


More


sophis


ticated


computational


methods


such


as Box


-Jenkins


or extrapolation


with


intervention


are


not


generally


used


due


the


large


10it
among
For
would


an understatement


those
example
apple


seeking
, in fo
v to


to compute
rmulating


1400


that


historical


cost


firms


confus
rates


of capital


that


provide


exists


of growth.


rules


that


interstate


telecommunications


Commi


ssion


coefficient


recently
derived


services


the


proposed


from


Federal


the


simple


Communic


use


linear


the


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data


input


requirements


that


are


necessary


establish


the


base


model.


The


choices


of data


seri


, computational


form,


data


period


are


examined


more


detail


Chapter


However,


general,


can


be said


that


historical


data


reflect


the


economic


conditions


that


prevailed


prior


periods.


economic


structure


has


changed


there


is an anticipation


that


may


change,


the


use


historically


based


growth


rates


can


not


reasonably


expected


produce


quality


estimates


the


current


growth


expectations


investors


It has


been


said


that


the


naive


extrapolation


of historical


data


determining


expected


growth


very


much


like


driving


a car


only


looking


rear


view


mirror


While


criti


cism


certainly

historical


valid,


data


the


seri


use


are


growth

popular


rates

because


derived


the


from


ease


data


acquis


ition


and


the


presumed


factual


character


data


themselves.


1.6.2


Security


Analysts'


Growth


Forecasts


alternative


to the


use


of historical


data


base


growth


estimates


on security


analysts'


forecasts.


Most


large


investment


banking


firms,


some


large


institutional


investors,


and


many


investment


research


firms


employ


security


analysts


who


produce


forecasts


1^ 1+.fa a1 ne AI rAa e f


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dividends,


or the


implicit


growth


rate


may


be extracted


from


the


underlying


earnings


and


dividend


forecasts


The


analysts


who


make


these


forecasts


often


special


particular


financial


industry


analysis


and


profession


they


with


often


come


substantial


experience


from


previous


employment


in the


particular


industry


which


they


analy


ze.


any


given


time,


several


different


analysts


may


making


forecasts


about


the


same


company.


Because


has


been


recognized


market


participants


that


the


composite


consensus


of these


forecasts


might


more


informative


than


any


single


analyst


forecast,


information


service


companies


that


collect


forecasts


and


publish


them


summary


form


have


come


into


operation.


The


oldest


such


service


the


Standard


and


Poor'


Earnings


Forecaster


which


provides


information


on the


one


year


ahead


and


two


year


ahead


earnings


per


share


forecasts


many


security


analysts.


different


inadvertently,


1968.


type

Burton


service


Malkiel,


began,


then


almost


of Princeton


University


and


John


Cragg


of the


University


British


Columbia,


cooperation


with


the


Institute


Quantitative


Research


Finance,


collected


both


short


run


earnings


per


share


forecasts


and


the


long-term


earnings


growth


forecasts


of several


investment


firms


order


to conduct


research


nature


and


accuracy







purposes


over


for

the


several

Wall


years


Street


until


firm


maintenance


Lynch,


Jones


was

and


taken

Ryan.


Lynch,


Jones


and


Ryan


began


marketing


the


consensus


(mean)


one


year


ahead


and


two


year


ahead


earnings


per


share


forecasts


the


mid


1970s


under


the


name


Institutional


Brokers


Estimate


System


(IBES).


They


expanded


the


number


companies


covered


to include


almost


New


York


Stock


Exchange


listed


firms


and


a number


of firms


the


American


and


over-the-counter


exchanges.


They


also


increased


the


number


analysts


that


contributed


forecasts


the


consensus


value.


In late


1981,


Lynch,


Jones


and


Ryan


began


systematically


collecting


long-term


earnings


(five


or more


years


ahead)


growth


forecasts


January


of 1982,


first


ongoing


, well


maintained


data


base


security


analysts'


long-term


growth


forecasts


became


publicly


available.


Lynch,


Jones


and


Ryan


intended


the


data


base


provide


used


subscribers


valuing


with


security


growth


es.


estimates


That


that


could


subscribers


were


generally


known


to be using


growth


estimates


inputs


the


model


received


future


computing


periods,


the


and


expected


then


dividends


discounting


to be


that


stream


of dividends


the


cost


of capital


they


felt


to be


appropriate


the


security'


sk in


order


to determine


their


intrinsic


value


the


stock.


That


intrinsic


value







Although


cos


capital


analysts


had


been


using


individual


security


analyst'


forecasts


growth


several


years,


mos


t notably


the


foreca


Value


Line


many


cost


of capital


analysts


were


quick


recogni


improvements


to be gained


through


the


use


of a broad


based


consensus


forecast.


Not


only


was


there


immediate


improvement


the


representation


of differing


opinions


embedded


the


consensus,


but


there


was


also


a gain


from


using


standardized


consensus


forecasts


from


an independent


source.


That


, the


availability


the


IBES


consensus


forecasts


removed


an element


of judgement


and


potential


selection


bias


that


had


plagued


the


evidentiary


quality


the


use


of analysts


forecasts


that


point


While


the


use


IBES


long


-term


growth


fore


cast


data


has


spread


quickly


since


their


introduction,


questions


remain


about


the


appropriateness


use


the


reported


consensus


measure.


Morin


(1984)


has


suggested


most


that


reliable


"one


could


forecasts


decide


and


then


which a

confine


analysts


the


make


analy


S1S


those


forecasts"


(page


, although


goes


on to


note


that


approach


securing


the


may b

track


e impractical


records


due

the


the


difficulty


individual


forecast


agents.


Litzenberger


(1985)


suggested


that


only


analysts


who


have


been


recognized


their


investment


clients


providing


superior


information,


such


as those


analyst


who







suggested


that


the


median


the


individual


forecasts


use


the


consensus


measure


as opposed


using


the


mean


forecast


because


the


median


ess


influenced


outlying


and,


presumably


, 1


ess


influential


opinions


about


the


growth


prospects


the


stock.


Those


opposition


the


use


of security


analyst


or the


analysts'

investment


forecasts

houses t


have


hey


argued


represent


that

are


the

often


friendly


the


firms


whose


earnings


are


being


regulate


and

if


would,


they


therefore,


felt


they


bias


could


their


growth


influence


forecasts

outcome


upwards


author


zation


rate


of return


level


Still


others


relying


upon


anecdotal


evidence,


dismi


the usefulness


the


foreca


because


their


poor


forecast


accuracy


More


complaint


than


criticism


observation


analysts


that


are


the


not


precise


generally


forecasting

known.


methods

Because


used


proprietary


nature


the


analysts'


services


they


rarely


acknowledge


how


they


actually


about


making


forecasts.


reasonable


assume,


however,


that


they


often


begin


with


historically


based


extrapolation


and


then


supplement


the


that


industry


information


or the


with


company


their

under


private


analysis.


knowledge


This


consi


stent


with


some


results


Chapter


where


the


correlations


historically


based


growth


rates


analysts'


forecasts


are


shown


to be generally


positive


but







Finally


, during


the


initial


period


introduction


the


IBES


forecasts


into


regulatory


arena,


the


IBES


values


have


tended


to be greater


than


the


growth


estimate


values


derived


from


storical


time


seri


es.


This


condition


created


a clientele


of cost


of capital


witnesses


who


opposed


the


use


of IBES


values


apparently


because


the


security


analysts'


forecasts


generated


cost


of capital


estimates


that


were


higher


than


the


cost


of capital


estimates


produced


historical


growth


estimates














CHAPTER


TWO


THE


THEORETICAL


THE


ROLE


FORMATION


OF SECURITY
OF INVESTOR


ANALYSTS


' FORECASTS


EXPECTATIONS


.1 Introduction


Most


existing


research


that


important


the


study


security


analysts'


forecasts


empirical


nature.


This


apparently


so because


existence


security


analysts


their


long-run


equilibrium


employment


and


obvious


demand


their


costly


servi


ces


provide


sufficient


economic


justification


scientific


observation


and


analyst


without


the


necessity


establishing


formal


theoretical


basi


noted


Stanley,


Lewellen,


and


Schlarbaum


(1981),


The question
payoff from


whether


devoting


there


resources


truly a
producing


those
been


[security
addressed


analysts']
n a number


outputs


occas


, however,


ions


has
the


literature


date


are


of finance


decidedly


. [and]


the


reviews


mixed.


Clearly,
large q
directly


individual


quantitiess
through


investors
this
>scriptior


are


paying


research,
is to i]


either


investment


sory


commissions


though
private


services
charged.
product


enterprise


characteristic


economy,


thought


indirectly
. Thus, it


the


appears


demand--which,


IS
be


not


generally


possessed


item


having


no value.


(Page


Thi


observation,


however,


inconsistent


with


advi







reflect


perfectly


instantaneously


available


information.


firms,


This


implies


industries,


the


that a

economy


analysis

cannot


individual


contribute


returns,


and


therefore


such


analysis,


while


having


a cost,


has


payoff.


Further,


rational


markets


characterized


strong-form


efficiency,


security


analysis


would


cease


exist.


When


taken


logical


extreme,


strong-form


efficiency


implies


that


prices


are


fully


revealing


information,


and


therefore,


investor


expectations


are


endogenously


determined,


conditional


only


upon


the


pri


ces


themselves.


other


words,


information


like


security


analysts'


forecasts


which


comes


from


an exogenous


source


other


that


security


prices


would


play


no theoretical


role


the


formation


investor


expectations.


This


support


chapter


the


is concerned


function


with


of security


developing


analysts


theoretical


as producers


useful


information


within


efficient


market


context.


Section


2.2,


the


notion


market


efficiency


expanded


allow


exogenous


information


such


security


analysts'


formation


models


forecasts


investor


growth


potentially


expectations.


incorporating


diversity


impact


Sections


and


opinion


and


information

specification


production


the


are


consensus


derived

expectation


that


allows


way


that


specifically


demonstrates


why


the


expectations


of wealthy,







basis


the


analysts'


observation


forecasts


may


that


diversity


positively


security


related


the


riskiness


securities.


Section


2.6,


simulation


analysis


using


empirical


estimates


the


relevant


parameters


reported


attempt


quantify


weight


classes


market


participants


formation


the


consensus


expectation.


A Model


of Market


and Information


Efficiency


Production


Fortunately,


the


working


security


analyst


concerned


about


the


long-term


viability


of her


job


and


the


empirical


researcher


with


significant


data


to analyze,


the


strongest


form


the


efficient


markets


hypothesis


been


generally


rejected.


For


example,


Grossman


and


Stiglitz


(1980)


, have


demonstrated


under


plausible


conditions


that


even


theory


when


prices


that


cannot


reflect


information


perfectly


costly


information


obtain.


keeping


with


Akerloff


(1970),


they


show


that


price


system


were


fully


informative,


there


would


differences


expectations


(that


expectations


would


determined


endogenously


from


prices


which


are


freely


observable


market


participants),


and


there


were


differences


expectations


then


there


would


trade,


and


markets


would


collapse.







trading


their


endowments,


no trading would


take


place.


alternative,


Grossman


and


Stiglitz


have


constructed


an alternative notion of market efficiency that allows


some


private


information


production


and


some


endogeny


information


prices.


Competitive


market


efficiency


viewed


process


instead


fixed


equilibrium,


where


the


force


driving


prices


toward


their


efficient


level


the

their


prices


production


model


only


of

an


private

equilibrium


partially


information.


degree


reflect


the


sense,


disequilibrium:


information


investors


who


choose


become


informed,


there


may


always


incremental


gains


acquiring


private


information.


The


following


presents


stylized


version


the Grossman-Stiglitz model.


There


are


two


assets,


one


safe


and


one


risky.


risky


asset


has


uncertain


return,


which


depends


random


variable,


which


can


observed


cost,


and


another,


unobservable


random variable,


so that K


Both


and


are


independent


and normally


distributed.


Knowing


reduces


but


does


eliminate


the


risk


associated


with


the


asset.


Some


investors


choose


become


informed


about


therefore


their


per


capital


demand,


will


depend


both


the


price


asset and u,


Di=Di (P,u).







Demand


assumed


increasing


decreasing


The


per


capital


demand


the


uninformed,


, depends


only


on P,


Dj=Dj (P).


Equilibrium


each


period


requires


that


supply,


equal


demand


f[Di(P,u) ]


f) [Dj (P)],


where


the


fraction


the


individuals


who


are


informed.


Given


these


basic


conditions


it


follows


immediately


that


the


uninformed


can


infer


there


are


other


sources


uncertainty


the


model


fixed


supply


and


deterministic


demand).


That


since


the


informed


will


exhibit


higher


demand


associated


with


higher


values


corresponding


there


any


price.


will


precisely


This


price


one


system


fully


revealing,


conveying


information


from


informed


the


distribution


uninformed,


given


the


since


same


the


the


conditional


conditional


distribution


of K


given


However,


additional


sources


uncertainty


are


admitted


(e.g.


stochastic


demand


and


uncertain


supply),


prices


will


convey


some


but


not


information.


That


may


when


also


high


may


be due


be because


supply


the


high,


risky


but


ass







possible


values


The


price


system


conveys


some


information,


because


average,


when


high,


return


high


are


correlated),


but


the


price


signal


noisy


that


and


not


convey


same


information


about


This


outcome


leads


demand


information


production


about


Note


that


when


one


informed,


price


system


does


not


convey


any


information,


and


value


incremental


information


about


high.


other


hand,


when


almost


everyone


informed,


the


price


system


with


very


precision


informative,


small.


the


The


result


value


knowing


equilibrium


which


the


price


conveys


some


information


but


does


fully


reveal


information.


The


fraction


investors


who


opt


become


informed


contrasted


with


those


who


infer


something


about


the


information


from


prices)


determines


how


fully


the


information


reveal


Further,


equilibrium


would


predicted


that


the


marginal


informed


investor


equal


finds


the


expected


expected


utility


utility


being


remaining


uninformed.


These


results


provide


form


market


efficiency

efficiency,


that

where


weaker


expectations


than

are d


pure


determined


strong-form

completely


endogenously.


Strong-form


efficiency


not


appealing








information.


other


hand,


these


results


provide


escape


from


complete


exogeneously


formation


expectations,


which


would


not


be rational


pri


ces


reveal


some


useful


information.


other


words


market


characterized


prices


that


are


only


partially


revealing


, an individual


will


utilize


endogenous


variables


such


pri


ces


forming


expectations,


because


benefits


from


the


bits


impounded


information


that


have


been


collected


others.


the


same


time,


because


prices


are


not


totally


revealing


there


remains


incentive


This


function

formation


otherwi


to collect


argument


private

investor


efficient.


question


private


creates


whether


information.


theoretical


information

expectations


then

security


production


market


becomes

analysts


that


empirical


outputs


the


information


outputs


other


agents


methods


better


explain


the


actual


structure


prices.


The


Role


of Consensus


Expectations


Although


theoretical


justification


the


for


security


analysts


producers


private


information)


the


formation


investor


beliefs


expectations


has


been


established,


still


necessary


show


that


security


prices


might


actually


imbed


r.,-%a nen el


'mn ellrnr r


nrtr


l a 1 4a-

1 19- 4- 1,


a -n


1 airal


, in


CkV 1I h







Although


individual


investors


independently


in
holc


arriving


i


deci


sons


their
the


individual


observed


buy


market


sell,


price


stock


reflects


the


consensus


view


investors


regarding


future


growth.


Therefore, 1
is embodied


argument
investors


consensus


market


depends
do actually


analysts'


pric


es.


the


use


fore


Or course,
assumption


analysts


forecasts


casts


that


and


market


However,
majority
forecast
numbers c
adequate
forecasts
until its
valuation
analysts.


The


prices
is not


are


based


required


investors


information:


,f large
financial
, then t


market


and,
(Page


purpose


on these


that


utilize


there


institutional


backing,


hey


price


hence


thi


will


who


are


forecasts


or even
analyst


suffi


investors


use


trade


reflects


, the


their


the


cient


, with


analysts'
security


intrin


sic


foreca


section


develop


theoretical


underpinning


seemingly


plausible


argument.


begin


thi


analysis,


assume,


addition


the


conditions


the


Grossman-Stiglitz


model


the


prior


section,


that


there


only


one


source


information


about


thi


case,


would


highly


redundant


inefficient


any


investor,


other


that


the


first,


become


informed


because


they


would


receive


the


same


piece


information.


With


only


one


source


information,


the


Grossman-Stiglitz


model


reduces


polar


example


asymmetric


information,


investors


are


either


informed


uninformed,


but


there


are


degrees


informational


accuracy


diversity


beliefs.


the


Grossman-Stiglitz


model


prices


can


not


aggregate


diversity


beliefs


expectations,


simply


because


that








order


obtain


role


consensus


beliefs,


first


necessary


construct


richer


model


prices


and


the


formation


expectations


that


incorporates


both


asymmetric


information


and


diversity


of opinion,


and


yet,


still


retains


the


notion


of market


efficiency.


imposing


structure


of preference


functions


over


the


marketplace


and


allowing


investors


engage


process


acquiring


private


information


beyond


that


contained


stock


prices,


possible


derive


analytic


expression


the


consensus


expectation


and


determine


the


necessary


conditions


that


would


embed


that


consensus


into


the


market


clearing


price.


Before


beginning


development


such


model


simple


example


will


used


establish


where


the


analysis


should


lead.


First


, assume


that


market


composed


two


investors


who


are


identical


respects


except


the


following.


One


investor


has


formed


expectation


say,


growth


dividends,


over


a highly


optimi


stic


information


set,


The


other


investor


formed


her


expectations


over


highly


pessimis


1This


The


analysis


analysis


is
cas


similar
t in t


erms


that
of


of
the


Verrecchia
expected


(1980)
rate c


return


risky


expectation.
uncertainty


growth


expected


rate


those


then


rate


security
; assumed


and
that


expectations


would


return


a -.


with


the
the
is


variance
primary
the ar


appropriate t
rn expression


0


that


source


iticipated


replace


expected
OYT- a n


LL


,,,'1


E LLI


~L ~L ~ 1L ~L


1


L


A







information


set,


Assume


further,


that


trading


between


the


two


investors


results


price


that


reflects


"average"


expectation.


The


average


information


the


union


of 0 and


Next,


allow


entry


third


investor


who


knows


information


The


third


investor


clearly


better


informed


than


the


other


two


since


his


information


the


contains


the


relevant


bits


information


each


others.


same


time


, there


way


can


earn-an


excess


the


return


equilibrium


from


this


price


informational


been


determined


advantage


on the


because


basis


consensus


belief.


this


notion


pursued.


informational


Rubenstein


(1975)


efficiency


has


that


suggested,


necessary


and


sufficient


condition


informational


efficiency


information


that


fully


individual


reflected


perceive


prices.


that


In other


of his


words,


even


investor


possesses


additional


information


compared


the


information


possessed


other


individual


market


participants


there


will


not


possibilities


gains


his


informational


advantage,


his


additional


information


reflective


the


consensus


expectation.


However,


also


possible


that


the


optimistic


investor


held


a vastly


superior


expectation,


the


sense


that


had


devoted


significant


time


and


expense


, A,








process


between


those


two


investors


would


take


place.


Instead,


driven


superior


knowledge,


optimistic


investor


could


buy


the


security


from


the


pessimist


bargain


price


and


earn


excess


returns.


Therefore,


critical


condition


the


market


clearing


price


reflect


consensus


expectation


that


inve


stor


have


"better"


consensus.


information


That


ex


than


that


ante,


contained


informational


the


effi


ciency


obtain,


the


consensus


expectation


must


least


accurate


any


individual'


personal


expectation,


will


possible


that


investor


capture


excess


returns


from


private


information.


A Model


Diverse


Opinion


of Information


and


Consensus


Acouis


Expe


ition


stations


The


analytic


following


framework


notation


examining


used


the


role


develop


the


consensus


expectations


determining


equilibrium


pri


ces:


the


periodic


rate


return


risk


free


security.


.s the e:
security
is the p


expected
before


rnor


periodic
private


expected


rate


return


information


value


held


the


obtained


risky
1. It


investor


the


risky
obtained


variance


security


the


expected


before


rate


private


of return


on the


information


the


security
aL 1.. .6. -a


expected


periodic


indicated


-n


- a .8 a -


rate


the
*a


trh


return
private


J-1~ a


-I aI -


the


sky


information


s4c A


~ nl -


k


L







obtained
sample o


investor


the


variance


f information.


investor


return


s posterior


on the


information.
expectation


risky


It
with


is
the


belief


security
formed
private


about
after


comn


expected
obtaining ]
binina the


-- -J


rate


private
prior


information.


investor


the


expected
s formed


private


s posterior


rate


belief


return


combining


the


about
i the
prior


the


risky
belief


variance


security.
with the


information.


Ui (W)


investor


s utility


function


of wealth,


investor


risk


aversion


Pratt-Arrow


It is


coefficient


absolute


defined


-U" (Wi)

U' (Wi)


where


' and


" denote


first


and


second


derivatives


the


utility


function


with


respect


wealth,


respectively.


the


number


in acquirir


of sample
ig private


observations
information.


taken


investor


P is


the


equilibrium


price


the


risky


security.


C(n)


the


function


cost
of


of
the


obtaining
number o


private


information


observations


taken


cost


function


assumed


common


investors.


the


(unlimited)


supply


the


risk


free


security.


the


fixed


supply


the


risky


security.


investor'


DiR

DiK


investor


demand


the


s demand


risk


the


free


risky


security.


security.


the


true


but


unknown


mean


the


distribution


random


rate


of return


on the


risky


security.


the
the


true
random


and u
rate


known


variance


of return


on the


the
risky


distribution
security.








Investors


enter


the


market


with


unequal


endowments


wealth,


They


are


offered


the


opportunity


purchase


either


the


risk


free


security,


or a


risky


security,


The


the


risk


free


end


security


some


offers


future


certain


period.


Before


return


trading


information


acquisition


activities


begin,


the


random


return


the


risky


security


believed


investor


normally


distributed


with


mean


return,


' and


with


variance,


Before


opportunity


engaging


acquire


trading,


additional,


investors


private


have


information


about


the


risky


security.


The


information


acquisition


process


will


described


sampling


process,


with


samples


drawn


from


normal


probability


distribution.


This


additional


information


characterized


sample


predetermined


size


observations,


Xil,


*.,in


, which


are


known


independently


and


identically


normally


distributed


with


mean,


and


variance,


Under


the


conditions


described


above


Raiffa


Schlaifer


(1961)


have


shown


that


investor


i will


have


posterior


(after


obtaining


private


information)


beli


that


the


rate


of return


on K


distributed


normally


with


3In
acquire


more


descriptive


information


from


terms,


the


security


investor


analyst


A at


might
some


-- -- -- -


first
dollar


S- -3 -3*L* -- -


1


~II


_I ^_


__ __1-- -- __ --






mean


variance,


where


following


definitions


apply:


nik"


where


t =1


(ii.)


and


(iii


The


posterior


expectation


weighted


average


the


prior


mean


the


sample


mean,


with


the


weights


being


the


reciprocals


distributions.


variances


The


weight


received


the


the


the


sample


two

mean


also


depends


size


the


sample.


Thus,


amount


more


of sample

influence


information


the


increases,


sample


the


results.


posterior


The


mean


reciprocal


the


posterior


variance


the


sum


the


reciprocals


the


variance


the


prior


and


sampling


distributions.


This


implies


that


the


posterior


variance


smaller


than


either


the


prior


sample


variance.


other


words,


there


ess


uncertainty


posterior


distribution


than


either


the


other


two.


Investor


i wishes


to maximize


her


expected


utility


future


the


wealth


posterior


choosing


expectation


holdings

ns forme


of R and

d over


K based


her


upon


private







sample


observations


she


takes,


the


more


strongly


held


will


be her


beliefs


about


the


expected


rate


of return.


statistical


sense,


the


smaller


will


her


posterior


expectation


information


the


costly


return


variance.


obtain.


However,


assumed


that


that


the


cost


acquiring


information


can


be described


the


function,


where


increasing


twice


differentiable


Thus,


formal


problem


facing


investor


1 is


Maximize
(ni,DiR, DiK)


U(Wi)


dF (kis2i)dF(k,s2)


m K


subject


to Wi


= DiR


+PDiK+C(ni)


assumed


that


investors


have


exponential


utility


functions


form


-ai(W)Wi


U(Wi)


= -ai(W)e


tractable


closed


form


solution


the


maximization


can


problem


explicit


because


determined


formulation


well


the


known


which


turn


consensus

economic


results


belief


This


property


4The as
primarily
permits.


;sumption


due
When


of
the


investors


exponential


ease


have


utility


algebraic m
heterogeneous


function


manipulation it
expectations,


I* A n f


a -


-A s an e tIC


1Al t a e


Al aT a r1w i n n a 5


nT


C(n),







exponential


utility


function


constant


absolute


risk


aversion,


a3je


ai(W)


-ai(W)Wi


ajie


or that


the


coefficient


of ri


sk aversion


independent


wealth.


Substitution


into


allows


explicit


formulation


of the


maximize


ation


problem


-ai(RfDiR


+ mDiK)


Maximize
(ni,DiRDiK)


-aie


dF(ki,s2i)dF(k,s2),


m K


subject


= DiR


+ DiKP


+C(ni)


The


price


the


risk


free


security


taken


numeraire.


That


price


normalized


one.


Conditional


upon


value


say


n*i,


optimal


holdings


the


risk


free


and


the


risky


security


can


determined


from


the


solution


the


following


LaGrangian


equation:


-ai(RfDiR


L(DiR


,DiK


aie


+ mDiK)


dF(ki,


[DiR


+ DiKP


+ C(n*i)]}.


Taking


derivatives


with


respect


DiR


n.K


*a *


4-1--A


#4 --4-


-ai(W)Wi


= ai


,li)


EI~n/ 3 *: '


AY~3AY


A A A A 9lIl *Y1







expression


determined


the


investor


price


optimal


the


risky


demands


security


then


given


-ai(RfDiR


/me


-ai(Rf DiR


dF(ki,


+ mDiK)


dF(ki,


Integrating


and


simplifying


results


- (s2iaiDiK)


And


rearranging


terms


results


determination


individual


investor'


demand


for


the


sky


security


- RfP)


DiK


Summing


over


investors


yields


the


total


demand


the


risky


security


- RfP)


DKTOTAL


Then


equating


total


demand


with


supply,


DKTOTAL


allows


specification


the


equilibrium


price


function


the


aggregate


expectations


of all


investors


the


form


Vgki


+ mDiK)


SKVo







The


term, E(VOki


can


thought


type


geometric


weighted


average


individual


investor


expectations


the


risky


security'


rate


of return,


where


the


weights


are


the


product


individual


preferences


risk


and


the


posterior


variance


estimate


each


investor


brings


the


marketplace.


Note


that


constant,


and


that (Vo


thus


confirming


that


those


terms


are


weights


and


their


sum


can


can


be normalized


unity.


Next,


multiply


both


numerator


and


denominator


1/V0,


and


define


ais2i


(10)


Then


the


consensus


expectation


can


be written


Voki


(11)


Inspection


(11)


indicates


that


the


expectations


investors


with


smaller


coefficients


risk


aversion


(more


risk


tolerant)


will


have


greater


impact


the


consensus


expectation.


Similarly


the


expectations


investors


with


beliefs


a smaller


variance


of returns


will


also


receive


greater


weight


consensus.


5Note


that


Pratt-Arrow


risk


1 ntxWctnrM


sai is
premium


nrnnnr* a 4


equivalent
[v2/2] [-U"/U


functionally


and


r'nn~r4 huI+ 4 n


i r


repres


*ho Tn


the
ents


'Tarofc


1 '


C:







the


same


sense


that


the


union


the


information


sets


the


optimistic


and


pessimistic


investors


represented


the


consensus


expectation


the


simple


example


presented


above,


the


term


Voki


also


a consensus


expectation.


demonstrate


that


this


also


the


consensus


expectation


that


informationally


contained


efficient


a price


market,


determined


sufficient


to show


that


that


individual


investor


has


expectations


that


are


more


accurate


than


the


consensus.


Under


Rubenstein'


definition


market


efficiency,


sufficient


demonstrate


that,


ex ante,


the


consensus


expectation


least


accurate


any


individual


expectation.


This


equivalent


showing


that


no one


can


earn


excess


returns


from


their


private


information.


the


statistical


framework


this


model,


determination


the


relative


accuracy


respective


information


variances


equivalent


individual'


comparing


posterior


distributic

consensus


the


expectation.


variance


The


the


formal


distribution


condition


the


stated


more


formal


justification


using


the


variance


as a


measure
(1948)


ths


nnti nr


informational


Thiel
f nf


(1971)


accuracy


. For


i n fnrmnart i nnAl


can


non-symmetric


sntrnnv


1SC5


found


Shannon


distributions,


mnre


general -


I







follows:


Var


s2i,
Si'


to I.


(12)


Noting


that


the


variance


of ki


simply


and


assuming


that


each


investor'


expectation


independent


other


investors'


expectations,


the variance


the


consensus


expectation


given


Var


(13)


Which


must


less


than


equal


the


variance


individual


investor'


sterior


distribution


expected


returns


for


market


efficiency


obtain.


Inspection


(13)


indicates


that


the


variance


the


consensus


expectation


will


tilted


favor


variances


investors


with


small


coefficients


risk


aversion.


This


because


the


investors


the


variance


with


weight


the


large


given


their


summation


coefficients


will


risk


posterior


estimate


greater


aversion.


than


And


general,

investors


better


the


with


(more


condition


less


precise,


aversion

lower v


stated


risk


variance)


(12)

must


assessmei


hold,


contribute

nts toward


determining


the


market


clearing


price


than


those


investors


with


greater


risk


aversion.


basic


i nriiui iuinal


assumption


the


analysis


that


Sn o ncr ~n i


any
r-i


1 *nty~car h1


avhi ki1- +


ah r-rll11"








among


investors,


those


with


more


wealth


will


ess


risk


averse


than


those


with


lower


wealth.


Thus,


smaller


coefficients


aversion


should,


general,


associated


with


investors


with


greater


wealth


. These


ess


risk


averse


investors


will,


most


likely,


allocate


proportionately


more


their


wealth


investments


the


risky


security,


which


turn


implies


they


will


hold


larger


absolute


amounts


the


risky


security.


this


indeed


reasonable


depiction


the


characteristic


market


participants,


investors


with


greater


risk


tolerance


(lower


risk


aversion)


may


expected


safeguard


their


greater


investments


risky


assets


demanding


more


information


about


those


assets.


The


implications


thi


analysis


are


ear,


there


increasing


cost


obtaining


information,


then


degree


of risk


aversion


will


determine


how


much


additional


information


investor


acquires.


situation,


most


risk


tolerant


investor


will


acquire


the


most


7Following


thi


economic


logic,


Verrecchia


(1980)


shown
the


that


under


development


condition


the


the


demand


information)


risk


aversion.


assumptions


this


weak


equivalent


model,


inequality


information
I decreasing


But


this


(the


the


size,


function


condition


the


coe


simply


those


formal


made


suffic


to hold


ient
that


sample


ffi
the


cient
same


saying


that


investors


act


their


own


best


interests


protecting


seeking
j .


their
acquire
S,


investments
private


the


risky


information


security


beyond


that


- 0 f


[


'


k


-I A







additional


information.


Thi


further


implies


that


most


risk


tolerant


investor


will,


in general


, be


best


informed


the


sense


that


holds


the


smallest


expectation


the


variance


expected


returns


the


risky


security.


Finally,


thi


implies


that


the


market


clearing


price


and


the


consensus


expectation


that


impounded


will


weighted


favor


individual


expectations


the


more


informed


inves


tors


with


greater


risk


tolerance,


presumably


the


large


institutional


investors


with


large


wealth


endowments.


And


from


thi


theoretical


perspective,


the


bases


the


intuitive


arguments


Brigham,


Vinson,


Shome


(1983)


appear


to be justified.


.5 Divergence


of ODinion


as a Risk


Factor


Several


authors,


including


Miller


(1977),


Cragg


Malkiel


(1985)


(1982),


have


Peterson


noted


that


and


Peterson


market


(1982)


where


, and


Varian


diverse


and


heterogeneous


opinions


aggregate


determine


prices,


measure


the


amount


diversity


may


important


determinant


security'


riskiness.


this


observation


correct,


and


accepting


the


theme


this


thesi


that


security


analysts'


forecasts


are


important


determinants


investor


expectations,


then


follows


that


measure


that


might


highly


correlated


with


SA.. .


1 ~ i _* -* I^


L


m


__~~___


*







the


review


the


empirical


literature


that


follows


Chapter


Three,


this


topic


examined.


this


point,

Section


however,


the


model


goal


was


somewhat


developed


more

that


abstract. I

demonstrates


under


plausible


stock


prices


conditions,


that


equilibrium


reflective


determination


consensus


individual


expectations.


That


model


is now


to be


extended


way


that


permits


prediction


how


stock


prices


will


respond


the


diversity


the


consensus


expectation


increases.


More


specifically,


can


shown


comparative


static


analysis


that


the


equilibrium


stock


price


declines


when


the


diversity


the


consensus


Increases,


then


increasing


diversity


can


theoretically


associated


with


increasing


risk.


The


first


consideration


this


analysis


determine


how


change


the


individual


posterior


variance estimates

expectation and u


impacts


Itimately


the

the


diversity


equilibrium


the


consensus


stock


price.


Note


that


equilibrium,


the


price


given


supply


the


risky


asset


and


known


value


the


risk


free


rate


interest,


largely


function


variables,


and


where


a function


and


s2i,


VOSK


(14)







Recalling


that


and


are


the


parameters


the


posterior


distributions


of expectations


and


are


determined


under


the


definitions


given


[iii.]


allows


a writing


as follows:


i + ni(


Clearly


increase


information


the


, leads


variance


increase


sample


the


posterior


variance


as shown


ds2i

ds2"


i(ni)


i(ni))


similar


fashion,


increase


the


prior


variance


for


a given


sample


variance


and


sample


size


would


lead


Increase


the


posterior


variance


Thus,


general,


any


increase


the


uncertainty


the


prior


beliefs


diminution


the


quality


private


information


will


lead


increased


uncertainty


about


the


posterior


expectation.


This


would


turn


lead


increase


given


dqi


aiV0


-ai2s


(V0)2


because


Because

expectations


terms


the

are


are


weights

the rec.


positive


applied


iprocals


and


the

the


aiVo


> ai


individual


return


an increase


leads


decrease


the


weighting


. For


xed


ds2i







expectation


Thus


, in


aversion


will


lead


almost


and


reduced


trivial


increase


sense,


the


equilibrium


constant


individual


price.


risk


posterior


variances


that


does


not


alter


the


individual


beliefs


about


the


posterior


mean,


the


stock


price


will


unambiguously


decline.


examination


(13)


indicates


that


increase


will


also


lead


increase


the


variance


the


consensus


distribution.


Thi


because


the


consensus


variance


will


directly


increase


with


increases


in s


but


will


only


indirectly


decrease


through


proportionately


smaller


decreases


the


weights


Under


the


assumed


structure


preferences


and


distributions


expectations,


beliefs .

consensus.


increase


eads


Therefore,


the


increase

either


dispersion


the


event,


individual


dispersion


increased


individual


uncertainty


increased


consensus


uncertainty


leads


lower


equilibrium


stock


price.


The


analysis


becomes


ess


clear


when


the


assumption


constant


case


explicitly


absolute


longer


and


risk

possibW


therefore


aversion


to evaluate


a closed


dropped.

e the in


form


that


Itegral


expression


the


consensus


expectation


and


the


variance


the


consensus


can


not


derived.


Heuristically,


the


coefficient


becomes


function


expected


terminal







distribution.


Thus,


the


assumption


constant


absolute


risk


aversion


dropped


and


no restrictions


are


placed


the


manner


in which


posterior


distributions


can


change,


analytical


prediction


the


risk


effects


increasing d

If changes


diversity


the


of opinion

posterior


can


be made.


distributions


returns-


are


restricted


changes


that


alter


the


posterior


variance


but


leave


the


posterior


mean


unchanged,


some


additional


assumption


implications


of constant


can


absolute


obtained


risk


relaxing


aversion.


begin,


redefine


=(ai(wi)


i)/V0


, where


now


Zai(wi)


Note


that


now


assumed


function


terminal


wealth


and


will


more


generally,


constant


value


assumed


previously.


obtain


decrease


find


his


posterior


necessa


variance,


acquire


more


investor


sample


will


observations.


However,


with


increasing


marginal


cost


obtaining


that


information,


expected


terminal


wealth


will


decrease


with


each


additional


unit


information


obtained.


coefficient


risk


aversion


increases


"too


fast"


with


8At


this


consensus


under


point it it
expectation


conditions


assumed


that


equivalent


constant


risk


the
to


basic
the


aversion.


I


form


form
That


derived


the


consensus
weighted
generally


at least


average
true


determination


the


analysis


of
can


can
the
also


a positive


individual


derived


consensus


beain


from


function


expectations.


from


the g
That


Litner'


expectation.


the


Pratt


This


(1964)


geometricc
this is


(1967)
part of
or Arrow







decreases


terminal


wealth,


possible


that


reductions

aversion.


the

other


variance

words 4


will

even


not

though


offset

h the


increased


returns


risk

the


security


become


more


certain,


the


investor


becomes


proportionately


risk


averse.


this


the


case,


stock


prices


will


decline


with


reductions


the


consensus


variance


instead


rising.


that


event,


change


the


the


diversity


the


consensus


expectation


cannot


be directly


associated


with


Algebraically,


ai(wi)s2i


and


letting


= ai(wi)


i + YO,


where


Eaj (wj)s2j,


then


ai(wi)


ai(wi)


i + Yo


And


letting


indicates


ai(wi)


i + YO


(15)


ai(wi)


Defining


this


way


allows


a more


direct


inspection


the


the


changes


that


occur


when


a variable


takes


new


value.


effect


the


weight


each


investor


brings


the


consensus


expectation.


The


goal


to determine


how


changes


s2i


that


are


brought


about


increased


acquisition


information


=1/qi







previous


analysis,


ai(wi)


will


also


change


with


but generally


in an


opposite direction


from


s2 i


Utilizing


(ri)ki.


given


(15),


The


re-write


total


change


the


consensus


differential


the


number


the


sample


expectation


expectation


observations


acquired


d(ri)


ds2mi


ds2 \

dni/


d(ri)

dai(wi)


dai(wi)


dwi


dwi


dC(n)


dki
nidni
{dni


dC(n)
dni
dni/


(16)


Manipulation


(16)


indicates


that


order


a change


brought


about


change


offset


the


countervailing


effect


change


ai(wi),


that


the


consensus


expectation


increases,


the


following


must


hold


as a necessary


condition,


ds2i


(17)


ai (wi)


where


the


first


derivative


the


coefficient


risk


aversion


with


respect


wealth,


the


first


derivative


the


information


cost


function


with


respect


and


dni


has


been


normalized


unity.


From


Pratt


(1964)


Arrow


(1971)


well


known


that


ai(wi)


positive.


Further,


positive


economically


acceptable,


and


the


left


hand


side


(17)


negative.


Therefore,


(17)


will


always


hold


positive.


The


a'i


a'1







quadratic


utility


function


exhibits


this


property


The


negative


exponential


utility


function


has


will


fulfill


such


as the


the


requirement


logarithmic


and


. For


power


functions


functions,


with


certain


additional


restrictions


must


be imposed


ensure


that


the


consensus


expectation


will


increase


with


increased


sampling


that


brings


about


decreased


variance


the


expense


decreasing


wealth.


These


restrictions


are


relative


and


somewhat


interdependent,


and


may,


hold


either


singularly


some


combination:


the


incremental


cost


of additional


information


small


the


large.


sample


Note


data


that


informative


a'i/ai (wi)


that


reduces


logarithmic


and


power


functions


, which


turn


will


very


close


zero


most


investors


with


ese


types


utility


functions


general,


finance


most


literature


utility


supported


functions


empirical


assumed


studi


the


will


9See,


example,


Alexander


and


Franci


(1986)


page


SCUSS


functional


forms


assumed


the p:
utility


properties
functions


various


10The
ai(wi)
The g
ai(wi)


=1/


generic
w4. and


eneric


- -1/wi.


log
a'i=


positive


The g


and
*


eneric


function,


-l/wi2 ,
power


a'i=-(l


U=ln(wi),


therefore
function,


-c)/wi2


negative


power


indicates


wi)=


a'i/ai(
U=wic,


therefore


function


-1/wi


indicates
a'i/ai (w)
, U=-wi ,


-- n -


, so


therefore,


-1/wi


=(l-c)/wi,


( I





I







exhibit


the


properties


of risk


aversion


a manner


which


will


cause


(17)


hold.


summary,


from


theoretical


perspective,


increase


the


diversity


the


expectations


individual


investors


may


increase


decrease


equilibrium


value


the


security


utility


prices


function.


depending


However


upon


, the


the


most


likely


effect


to decrease


security


pri


ces


A Simulation


Analysis


the


Weichtina


in the


Consensus


Expectation


Utiliz


equation


(11) ,


the


algebraic


expression


consensus


expectation


that


was


developed


Section


values


and


risk


taking


aversion


point


from


estimates


the


studi


the


relevant


Blume


Friend


(1975),


Grossman


and


Schiller


(1971)


, and


Litzenberger


and


Ronn


(1986),


and


point


estimates


security


Ibbotson


returns


and


and


Sinquefield


associated


(1982)


variances


studi


from


, simulation


analy

the m


ses


the


market


individual


clearing


consensus


investor'


expectation


contribution


were


toward


performed.


Investor


expectation


the


return


hypothetical


risky


security


was


generated


taking


the


simple


mean


twenty


random


observations


drawn


with


replacement


from


11The


empirical


res


each


Blume


and


Friend


(197


Gro


ssman


I, nnrt


and


Schiller


(1971)


and


Lit


zenberger


and


Ronn


-- *1 .1 -- r e!1 -- -.u 2- -- -I


,I


i, I


4m


. Ir


_







normal distribution

reference to Ibbotson


with


and


parameters


Sinquefi


established


eld,


ki=


Sxin/20


Investor


coefficient


risk


aversion


was


obtained


coefficients


the


random


based


above


draw


from


references


studies.


distribution


the


Several


empirical


different


such


results


types


distributions


the


risk


simulations,


aversion

including


coefficients


were


distributions


utilized


that


were


symmetric


about


mean


coefficient


and


those


that


were


skewed


toward


lower


and


higher


values.


Next,


estimated


posterior


variance


was


calculated

variances


for

were


each


expectation.


ranked


from


this


point,


smallest


however,


largest


and


disassociated


from


any


particular


expectation.


The


smallest

greatest


variance


risk


was


tolerance


assigned


coefficient,


the

and


investor


with

until


investor


with


the


lowest


risk


tolerance


coefficient


was


assigned


the


greatest


measure


variance.


This


keeping


with


the


inference


the


self


interest


nature


the


model.


Using

aversion

consisting


different


coefficients


types


with


10,000


distributions

hypothetical

investors,


risk


markets

numerous


simulations


were


performed.


The


consensus


expectation







weights,


shown


(11)


are


the


product


individual


variance

aversion


estimates

coefficients


multiplied

Normalized


by

to


the

their


individual


total


risk


weighted


sum.


The


remarkably


impact


market


results


stable,


the


participants


the


indicating


choi


simulations


little


stributions


For


example,


were


differential


number


representative


simulation


indicated


that


the


individual


expectations


the


40 percent


investors


with


the


highest


risk


aversion


contribute


slightly


ess


than


percent


the


weight


towards


the


consensus


expectation.


Whereas


, the


individual


expectations


the


percent


investors


with


the


least


risk


aversion


contribute


almost


percent


the


weight


the


consensus


expectation.


Noting


that


the


simulation


results


not


account


poss


differences


wealth


and


the


trades


the


market


participants,


conservative


the


terms


results


the


true


are


impact


most

large,


likely


ris


tolerant


investors


actually


have


consensus


expectations


. As


crude


rule


thumb,


gen


erally


stated


that


percent


stock


market


activity


attributable


institutional


investors.


that


ratio


mapped


into


the


simulation


results,


would


indicate


that


more


than


percent


the


weight


the


consensus












CHAPTER


THREE


A REVIEW


OF THE


EMPIRICAL


LITERATURE


Introduction


The


existing


empirical


literature


and


research


that


important


study


security


analysts'


forecasts


generally


fall


into


two


categories.


The


first


topic,


which


literature

of short-1


covered


that


term


examines


values.


Thi


Section


security

research


the


analysts'


can


empirical


forecast


decomposed


into


three


distinct


types


comparative


studi


, (1)


evaluations


short-term


forecasts


against


naive


extrapolations


historical


time


series


evaluations


security


analysts'


forecasts


against


forecasts


made


management,


and


evaluations


short-term


forecasts


among


security


analysts.


Often


, thi


research


accuracy


characterized


security


tests


analysts


the


other


forecast


foreca


agents


or methods,


the


diagnosis


forecast


error


or the


influence


of unexpected


changes


short-term


forecasts


share


prices.


literature


There


thi


extremely


area;


therefore,


large


this


body


review


concentrates


on the


more


recent,


representative


article


es.


-a-vi







study,


includes


the


examinations


security


anal


forecasts


long-term


growth.


contrast


studi


about

resear


short-term fc

ch attention,


recasts,


fact


thi

most


area


likely


has

due


received


the


little

limited


types


and


small


amount


data


that


have


been


available


analysis


The


focus


section


literature


review


will


the


work


Cragg


and


Malkiel


who


have


provided


the


seminal


(1968)


and


most


comprehensive


(198


examinations


long


-term


forecasts


and


the


recent


extensions


to Cragg


and


Malkiel.


Chapter


security

individual

consensus


Two,


analysts' fc

investor E

expectation


theory


recasts


was


might


expectations


developed


how


incorporated


and


embedded


the


ultimately


market


into


into


clearing


price.


This


chapter


explores


the


question


security


analysts'


forecasts


might


important


formation


keep


investor


mind


expectations.


reviewing


general


literature


point


security


analysts'


forecasts,


that


either


one


two


distinct


theori


the


can


actual


be invoked


formation


as a basis


their


expectations


The


importance


older


theoretical


views


can


traced


the


celebrated


beauty


contest


profe


John M

ssional


newspaper


:aynard


Keynes


investment


competitions


(1935/1964),


may ne
.n which


likened
the cc


where


those


mmpetitors


have


pick


out


the


prettiest


faces


from


----- -. -_. -


why


I _


1


JtL.-


- A I- A --


., I


l_ .. ... -- _1 _







finds pr
likeliest


ettiest,


but


catch


competitors,


from


the


same


point


those


the f
whom ar
of view.


which


"ancy


e


he
the


looking at
(Page 132)


thinks
other
problem


The


theory


emanating


from


this


view


indicates


that


more


important


know


what


the


market


thinks


expects,


say,


earnings


per


share


earnings


growth


will


than


know


precisely


what


actual


earnings


growth


are


realized.


Under


this


theoretical


specification,


security


analysts'


forecasts


are


tested


against


forecasts


from


other


sources


determine


which


type


forecast


methodology


best


explains


the


cross-sectional


structure


share


prices


the


cross-sectional


structure


price/earnings


ratios.


The


forecast


that


provides


best


explanation


the


structure


then


inferred


representative


the


market


expectation.


This


view


holds


that


not


the


ultimate


accuracy


forecast


methods


that


important


but


rather


how


strongly


particular


type


forecast


influences


the


formation


investor


expectations


The


more


recent


theoretical


view


a product


rational


expectations


literature.


Brown


and


Rozeff


(1978)


claim


that


rational


investors


incorporate


into


their


expectations


only


the


most


most


useful


information


which,


extension


from


the


definition


rationality,


the


most


accurate


information.
-A I


This


theoretical


perspective


_ -- L_ -- _- J -- -


-- _


--IL







errors


produced


security


analysts'


forecasts


with


errors


produced


alternative


forecast


methods


date,


the


empirical


results


from


the


tests


security

distinguish


analysts'

between


forecasts


the


cannot


existence


used


marketplace


dominated


investors


forming


expectations


about


what


they


believe


the


best


forecasts


future


values


(rational


expectations)


investors


forming


expectations


over


what


they


believe


other


market


participants


forecasting


(Keynesian


beauty


contest).


Empirical


results


tend


indicate


that


the


structure


security


pri


ces


best


explained


security


analyst


forecasts


and


that


security


analysts


forecasts


tend


have


the


small


est


forecast


error.


Note,


however,


that


under


theory


rational


expectations,


forecasted


values


that


are


derived


from


best


forecasting


method


should


also


expected


offer


the


best


explanation


cross


-sectional


variation


price


structure,


that


method


used


formation


expectations.


the


other


hand,


theory


the


formation


investor


expectations


keeping


with


the


Keynesian


beauty


contest


does


not


rule


out


security


analysts


forecasts


being


the


best


predictors


future


necessary


values.


nor


That


, forecast


sufficient


accuracy


support


neither


that


theory







from


implications


hypotheses


formed


under


the


other


theory.


knowledge


investor e

determining


the


expectations


the


correct


would


usefulness


model


be

of


the


valuable


security


formation


asset


analysts'


long-term


forecasts


the


discounted


cash


flow


model


estimating


that


the


model


cost


would


capital.


allow


That


, a


prediction


knowledge


benchmark


measure

security


neither


long-term


analysts'


growth


forecasts


observations


expectations


could


actual


against


measured.


expectations


which


However,


nor


sound


theoretical


predictions


are


possible,


thus


thi


study


will


necessity


rely


statistical


inference


coupled


with


reasoned


economic


logic.


such,


the


literature


review


focuses


equally


logical


assumptions,


data


sources,


application


statistical

empirical


methods,


studies .


and

For


resulting


the


conclusions


dual


of exi


purposes


sting

this


study


identify


and


offer


correction


methodological


infirmities


existing


studies


well


extend


the


lone


Malkiel
forecast
accuracy


scriminating


(1982).


They


methodology


and


consistently
necessary a]


explains


over


Although


an I
not


test


has


claim
both


been


that t
produces


suggested


:he


cross-sectional


extended


period


sufficient


for


Cragg


showing


superior
price


of
the


time


and


that


forecast
structures
would be


existence


l .


* q


A


* f


'I


1~ L


* I t







body


knowledge


regarding


security


analysts'


forecasts


of long-term


growth.


The


Emoirical


Literature


Security


Analysts'


Short-term


Forecasts


3.2.1


Barefield


and


Comi


skev


(1975)


This


article


reports


study


analyst


forecasts


one-year-ahead


earnings


per


share


(EPS)


company


sample


New


York


Stock


Exchange


firms.


Barefield


and


Comiskey


(BC)


analyze


forecasting


performance


relation

addition


investigate


year

naive


and


industry


mechanical


the examination

analysts' ability


classification


forecasting


forecast


predict


error,


"turning


points"


in a company'


earning


series.


source


analyst


forecasts,


used


Standard


and


Poor'


Earnin.s.


Forecaster


The


forecasts


are


provided


Standard


and


Poor'


brokerage


houses,


and


other


Wall


Street


researchers


and


analysts


reported


two


three


forecasts


per


company


was


the


norm


, although


the


number


forecasts


varied


positively


with


the


size


the


firm


and


the


volume


trading


activity


. Barefield


and


Comi


sky


drew


company


sample


that


satisfied


December


three


fiscal


constraints:


year-end;


the


the


company


company


was


had


sted


the


New


York


Stock


Exchange;


and


the


company


was







consisted


observations,


forecasts


the


next


year'


EPS


companies


each


of 6


years.


Each


average


forecasts


year

the

were


I


forecast


individual

measured a


was


analyst


defined


forecasts


approximately


ten


the


provide


months


simple

d. The


prior


the


end


the


respective


fi-sal


year


Barefield


and


Comiskey

absolute


defined


value


annual


the


forecast


percentage


error


difference


(FE)

between


actual


and


forecasted


EPS,


FEt =


Ft-At


/Ft,


where


forecast


EPSt


year


and


actual


EPSt


for


year


They


also


defined


average


forecast


error


(AFE)


over


the


six


year


period


AFE


(1/6)


FEt.


In addition


to computation


forecast


error,


BC al


investigated


analysts


' abilities


to predict


turning


points


company'


earnings


stream


over


the


six


year


period.


For


example,


suppose


that


analysts


are


predicting


year-


over-year


positive


changes


three


years,


symbolically


the


predicted


series


would


+++.


actual


earnings


changes


turn


out


two


years


positive


changes


follow


a decrease


EPS,


which







pattern


given


then


the


analysts


have


failed


predict


one


turning


point.


reported


the-


cross-sectionally


following


year


over


forecast


their


errors


firm


averaged


sample


Table


Average
As Reported


Annual


Forecast


Barefield


and


Error
Comiskey


Average


Year


Forecast


Error


Average


1967
1968
1969
1970
1971
1972
1967


14.14%
13.92
13.31


14.22
16.07%


They


also


reported


average


forecast


errors


industry


over


the


same


period:


Tabl


Average
As Reported


Industry


Barefi


Forecast


eld


and


Error


Comiskey


Average


Industry


Forecast


Error


Utiliti


Banking
Drugs
Food/Beverage/Tobacco
Other


Chemical


.49%


6.05
7.71


15.29


Oil


Manufacturing
Transportation


The


examination


turning


point


predictions


produced


the


following


results







Table


Analysis
As Reported


of Turning
by Barefi


e


Point
Id and


Errors
Comiskey


Predicted


Turning
Point


No Turning
Point


Turning a. c.
Point 132 67

No Turning b. d.
Point 37 164


Cells


and


represent


the


two


types


turning


point


errors:

actually


(b),


materialize


turning

s, and


point


(c) ,


predicted

turning |


but


point


none

does


occur


but


was


not


forecast.


The


number


correct


forecasts


the


sum


and


or a


total


out


400.


Finally,


BC compared


the


forecasts


of analysts


the


prediction


naive,


mechanical


forecast.


The


naive


forecast


change"


prediction,


that


EPSt+I


EPSt


Utilizing


Theil'


U-statistic,


where


the


difference


- Ai)2


{Ai2} 1/2

of predicted


year


actual


EPS


year


for


company


and


the


difference


actual


year


t-1


and


year


company


Coefficient


approaches


zero


lower


boundary


when


predictions


are


correct,


and


takes


S(Pi







And


greater


than


unity


when


the


predictions


are


ess


accurate


naive


than


model


the


, BC


naive,


report


no change


the


benchmark.


following


Against


distribution


computed


U-values:


Table


Theil'


U-Statistic


As Reported


Barefield


and


Comiskey


U-Value


Number


of Companies


0
.26
.51
.76
1.00
1.26


1.25
1.50


>1.50


Total


Barefield


and


Comiskey


conclude


that


fore


cas


errors


forecast


security


errors


analysts


management


compare


favorably


reported


other


with


studi


They


find


the


average


forecast


error


about


percent


reported


their


study


about


the


same


the


average


the


percent


Financial


forecast


Analysts


error


Federation


managers


1973


reported

study.


also


note


that


security


analysts


are


very


successful


forecasting


earnings


turning


points,


having


accurate


ely


predicted


the


direction


of change


almost


75 percent


time.


comparisons


against


naive,


change"


predictions


, security


analysts


forecasts


were


more


nn '*/*i' v- +-A aiIm


Eamrn% nA


mha7r


t,,+-


rrhmn~~~ dE


kY


- -,- ^-^ I I I I







comparison


decline


and


that


more


analyst


sophis


forecasting


ticated,


performance


mechanical


model


might


were


employed


as a benchmark.


.2.2


Bas


Carev


. and


Twark


(1976)


Basi


, Carey,


and


Twark


(BCT)


consider


two


questions


forecast


accuracy:


How


well


does


management


forecast


EPS?


What


the


relative


accuracy


security


analysts'


forecasts


as compared


the


forecasts


of managers?


From


the


Wall


Street


Journal,


BCT


gathered


annual


earnings


forecasts


made


managers


over


the


period


1970


to 1971.


ese


forecasts


were


of four


general


types:


. Point

. Range


estimates

estimates


of EPS


EPS.


Point


from


the


estimates


previous


year'


percentage
s earnings.


Increases


decreases


Range


from


the


estimates


previous


year'


percentage
Earnings.


increases


decreases


the


forecast


was


made


the


form


of a percentage


change,


the


BCT


computed


percentage


the


the


dollar


prior


EPS


year'


forecast


EPS.


the


applying


forecasts


were


the


form


a range,


used


the


midpoint


the


range


the


point


comparative


estimate.


accuracy


order


managers


construct


and


analysts


test


, it


was


also


required


that


analysts


forecasts


-
nan .1. 'tw -C~ a | lfcI k


*


___ __ ~ A *L ;


r CkA


<-'---/- an rl w rr


LnA







were


able


construct


sample


firms


having


necessary


data.


The


tests


designed


BCT


actually


address


four


hypotheses


regarding


forecast


accuracy:


Forecasts


for


utilities


are


more


accurate


than


those


non-utilities.


Forecasts


firms


are


Exchange


more


listed


accurate
firms.3


New


than


York


Stock


those


Exchange
American


listed
Stock


Company


than


those


(manager's)
of security


forecasts
analysts.


of EPS


are


more


accurate


4. Forecast
approaches


accuracy


the


end


improves
of the


the


date


accounting


the


period


fore
when


cast
the


actual


results


are


computed.


order


following


test


measures


these


hypotheses


computed


both


, BCT


the


utilize


managerial


forecast


and


the


analyst


forecasts


(Forecast


- Actual)


Mean


Percentage


Error


Actual


Forecast


Actual


Mean


Absolute


Percentage


Error


Actual


(Forecast


Mean


Square


Percentage


- Actual)


Error


Actual


considering


the


simple


mean


percentage


error,


BCT


are


able


determine


the


average


direction


forecast


error


and


considering


the


mean


square


error,


*







outliers


are


given


proportionately


more


weight


the


final


analysis.


Average


representative


results


the


BCT


study


are


shown


in the


table


below:


Table


Representative


Forecast


Errors


As Reported


Basi


, Carey


, and


Twark


Mean


Mean


Absolute


Mean


Squared


Percentage
Error


Percentage
Error


Percentage
Error


Utilities
Non-Utiliti


NYSE
AMEX


Firms


Values
errors


columns
security


-.005


.095


.018
.211


.060


under


.003
.134

.029
.303


.088


columns


r company
labeled S
analysts'


.045
.131

.065
.231


.101


labeled


forecasts


are


the


.052
.185

.088
.321


.138


are


and


average


-.009
.072

.016
.172


.050


the


values


.009
.123

.025
.293


.083


average


under


errors


forecasts.


After


computing


the


error


values,


BCT


rank


ordered


the


errors,


and


created


cumulative


distributions


error


values


Using


the


method


stochastic


dominance,


forecast


method


was


claimed


dominate


more


accurate)


cumulative


distribution


function


was


never


ess


than


that


of another,


competing


forecast


method


and


was


greater


than


the


other


method


least


one


point.


order


dominance


determine


statistically


the


significant


distributional


, BCT


employ


Kolmogorov-Smirnov


two


sample


test.


general,


BCT


find


a-- ,.- -a-4.a- anae anf -- 4-a -t -- p1rI ~


Ckrn


Ckh*n1./.


CklrC


~~I~~~~LI~CA


~ AIIIYI ~ YLII


~yA 'III~LYA







security


analysts


but


the


difference


not


significant.


Finally


, to


test


Hypothesis


BCT


correlat


mean


percentage


errors


with


the


length


time


between


publication


the


forecast


and


the


reporting


actual


results.


They


found


that


both


company


and


security


analysts


forecasts


showed


significantly


smaller


errors


the


nearer


the


actual


reporting


date


the


fore


cas


was


made.


For


example


, the


average


correlation


coefficient


between


the


mean


percentage


error


company


forecasts


and


the


length


time


until


actual


results


were


known


was


.275,


which


stati


stically


significant


.001


level


Bas

company


analyst

errors


Carey,


forecasts

Forecasts


and


and

were


both


stochastic


Twark


conclude


slightly


on the


dominance


better


basi


criteria.


that


than

size


Furth


average

security

average

ler they


find


that


both


companies


and


security


analysts


forecasted


for


utility


better


than


non-utiliti


, and


NYSE


listed


firms


better


than


AMEX


listed


firms.


Brown


and


Roz


eff


(1978)


Arguably


the


best


and


most


to date


the


studies


security


analysts'


short-term


forecasts


, Brown


Rozeff


(BR)


examine


relative


forecast


accuracy


i,







proxy


for


the


average


forecast


security


analysts,


use


primarily


the


published


forecasts


the


Value


Line


Investment Service.


The


study


examines


several


forecast


horizons


Their


choice


horizons


reflected


considerations


micro-level


information


obtained


security


analysts


often


impacts


earnings


projections


one


five


quarters


ahead,


the effects on corporate earnings of


changes


fiscal


and


monetary


policy


often


take


eighteen


months


wind


through


the


economy


and


the


available


published


forecasts are mainly for short horizons.


They


chose


investigate


point


estimates


quarterly


EPS


for


forecast


horizons


one


five


quarters


advance,


over


the


period


1972


1975.


Specifically,


they


took


forecasts


several


points


time


that


were


conditional


the


knowledge


different


sets


past


results.


For


example,


the


the


year


1973,


they


investigated


the


following quarterly


forecasts:


Table


Specification of Forecast Horizons


As Employed by


Brown and Rozeff


1 Quarter


Ahead


Quarters Ahead


Quarters Ahead


F(73Q1
F(73Q2
F(73Q3
F(73Q4


72Q4)
73Q1)
73Q2)
73Q3)


F(73Q1
F(73Q2
F(73Q3
F(73Q4


72Q3)
72Q4)
73Q1)
73Q2)


F(73Q2
F(73Q3
F(73Q4


72Q3)
72Q4)
73Q1)


Quarters Ahead


5 Quarters Ahead


F(73Q3
F(73Q4


72Q3)
72Q4)


F(73Q4


72Q3)







that


had


the


necessary


earnings


forecast


data


published


Value


Line.


addition


those


constraints,


was


also


necess


ary


include


only


firms


that


had


available,


public


shed


source


quarterly


the


period


1951


through


1972.


This


time


series


historical


data


was


necessary


implement


the


Box-Jenkins


technique.


insufficient


earnings


data


utility


were


excluded


from


the


sample


population.


In addition


the


evaluation


of quarterly


forecasts


also


annual


investigated


forecasts


annual


were


forecasts


obtained


EPS,


summing


where

the


the

four


quarterly


forecasts


that


were


conditional


on knowledge


the


prior


year'


For


example,


the


annual


forecast


1973


the


sum


F(73Q1


72Q4),


F(73Q2


72Q4),


F(73Q3


72Q4),


and


F(73Q4


72Q4).


The


Box-Jenkins


technique


makes


very


effici


use


the


available


data.


Under


the


Box-Jenkins


procedures


, BR


estimated


different


forecasting


model


each


the


fifty


firms


their


sample


. In


implementing


Box-Jenkins,


the


analyst


chooses


model


structure


from


among


numerous


alternatives


that


satisfies


one


more


pre-determined


diagnostic


conditions


such


the


structural


form


with


highest


R-square,


most


significant


t-statisti


and


forth.


making


priori


assumptions


about


the


process


that


generates


EPS,


the


Box-Jenkins


approach







researchers.


effect,


the


Box-Jenkins


technique


selects


the


best


forecasting


model


available


given


the


historical


data


utilized,


other


words,


Box-Jenkins


lets


data


speak


itself.


noted


earlier,


the


source


security


analysts'


forecasts


were


the


quarterly


EPS


forecasts


Value


Line.


The


measurements


these


forecasts


were


taken


way


that


made


the


historical


information


available


the


security


analyst


approximately


coincident


with


the


data


available


the


Box-Jenkins


forecast


method.


test


the


relative


accuracy


the


two


forecast


methods,


employ


the


Wilcoxon


Signed


Ranks


test.


For


each


forecast


period,


forecast


errors


from


each


method


are


paired


company.


The


members


each


pair


are


reduced


to a single


observation


taking


the


absolute


differences


the


assigned


paired


ranks


errors.


from


Next,


these


to n according


differences


the


relative


are


size


the


actual


difference.

difference


Then,


the


dependent

errors,


upon


the


the


rank


sign


given


the

the


same


sign.


Finally,


a test


statistic


computed


] Rank

SRank


where


the


ranks


and


the


squared


ranks


are


summed


over


companies


for


forecast


horizon







thus


the


critical


region


can


be read


directly


from


a table


areas


the


normal


distribution.


reject


the


hypothesis


that


the


Box-Jenkins


forecasts


are


more


accurate


than


Value


Line'


forecasts


requires


T-value


greater


than


2.326


the


percent


significance


level


and


T-value


greater


than


1.644


the


percent


significance


level.


Brown


and


Rozeff


report


the


following


T-values


the


quarterly


forecasts:


Table


T-Values


Associated


As Reported


with
Brown


Forecast


and


Errors


Rozeff


Forecast


Hori


zon


(Number


of Quarters


Ahead)


Year
1972
1973
1974
1975


1.75
2.48
1.16


4.09
3.34


-1.45


1.62


-1.04
-0.22


3.93


-0.92


0.08


0.45


, the


Value


Line


forecasts


were


more


accurate


comparisons,


and


stati


stical


significance


occurred


11 of


those


For


the


annual


forecasts,


report


Wilcoxon


Signed


Rank


T-values


3.45,


2.17,


0.61,


and


1.28


years


1972,


1973,


1974,


and


1975,


respectively.


Thus,


based


the


BR analysis


Value


Line'


forecasts


were


more


accurate


than


the


Box-Jenkins


forecasts


each


the


four


years,


and


were


significantly


in 2


the


four


years


Brown


and


Rozeff


provide


strong


conclusions


based


their


analyses.


The


following


tend


to capture


the


essence







significantly


seri


model


better


The


predictions
statistically


than


time


significant


experiments


the


remainir


Wilcoxon t
additional


overwhelmingly
ig experiments


:ests


favor


support


the


favor
the m
Value


Value


Line.


majority


Line


hypothesis


In
the


, providing
of analyst


superiority.


If market


earnings


follows tha
forecasts sh
earnings exp
expectations,


t


the


expectations


best


used


lould


,ectations.
our


are


available


measure
rational
of


Given
evidence


rational,


earnings
market
market
analyst


superiority


analysts


firm
(Page


over


time


Forecasts


valuation


[anc


series


should
d] cost


model


be use
: of


means
studi


that


capital


.2.4


Elton.


Gruber


, and


Gultekin


(1981)


Whil


Brown


and


Rozeff


construct


explicit


hypothe


ses


about


forecast


accuracy


under


the


theory


rational


expectations,


Elton,


Gruber,


and


Gultekin


(EGG)


examine


the


importance


expectations


determination


share


price.


Implicitly,


the


study


EGG


more


keeping


with


the


Keynesian


beauty


contest


than


rational


expectations.


That


, irrespective


forecast


accuracy


itself,


EGG


are


concerned


with


determining


the


type


expectational


data


that


has


the


greatest


influence


share


price.


their


tests


, the


type


expectational


data


that


known


individual


could


produce


excess


returns.


acknowledged


EGG,


the


testing


expectations


the


determination


share


price


was


poss


ible


before


the


development


large,


consistent


data




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

PAGE 192

7DEOH +( $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( f§FRQWLQXHG +% +% +% +% +, +

PAGE 193

7DEOH /2,%(6 $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( FRQWLQXHG +,,%(6 01,%(6 0',%(6

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PAGE 195

7DEOH $*5,&8/785( t 0,1,1* +( %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' L &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( FRQWLQXHG +% +% +% +% +, +

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$*5,&8/785( t 0,1,1* 7DEOH /2,%(6 %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' L &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( f§FRQWLQXHG +,,%(6 01,%(6 0',%(6

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7DEOH 0HGLDQ $FWXDO (UURUV IRU )RUHFDVWV E\ +LVWRULFDO 0HWKRGV DQG ,%(6 )RUHFDVWV (UURUV $UH $VVHVVHG $JDLQVW $FWXDO 'LYLGHQG *URZWK +' +' +' +' +( +( +( $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'(

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7DEOH +( $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( f§FRQWLQXHG +% +% +% +% +, +

PAGE 199

7DEOH /2,%(6 $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( f§FRQWLQXHG +,,%(6 01,%(6 0',%(6

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7DEOH +( +% $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( FRQWLQXHG +% +% +% +, +

PAGE 202

7DEOH /2,%(6 +,,%(6 $*5,&8/785( $1' 0,1,1* %$1.,1* &+(0,&$/6 $1' '58*6 &21680(5 *22'6 (/(&7521,&6 )22' $1' %(9(5$*( )25(67 352'8&76 0$&+,1(5< 0(7$/6 121%$1. ),1$1&( 3(752/(80 5(),1,1* 38%/,6+,1* $1' 35,17 5($/ (67$7( 5(67$85$176 $1' 63(& 75$'( 5(7$,/ 75$'( 58%%(5 3/$67,& $1' /($7+(5 6(59,&( 62&,$/ 6(59,&(6 6721(&/$<*/$66 $1' &21&5(7( 7(;7,/(6 75$163257$7,21 75$163257$7,21 (48,3 87,/,7,(6 :+2/(6$/( 75$'( FRQWLQXHG 01,%(6 0',%(6

PAGE 203

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