FULLTEXT01

ISBN 978-91-7258-883-7
Licentiate Dissertation
in Business Administration
Stockholm School of Economics
Sweden, 2013
OntheRelationshipBetweenAccountingEarningsandStockReturnsHansHällefors•2013
Hans Hällefors
On the Relationship Between
Accounting Earnings and Stock
Returns
Model Development and Empirical Tests Based on Swedish Data

On the Relationship Between Accounting
Earnings and Stock Returns
Model Development and Empirical Tests Based
on Swedish Data

On the Relationship Between
Accounting Earnings and Stock Returns
Model Development and Empirical Tests Based
on Swedish Data
Hans Hällefors

ii
Dissertation for the Degree of Licentiate of Philosophy, in
Business Administration
Stockholm School of Economics, 2013
On the Relationship Between Accounting Earnings and Stock Returns:
Model Development and Empirical Tests Based on Swedish Data
© SSE and the author, 2013
ISBN 978-91-7258-883-7 (printed)
ISBN 978-91-7258-884-4 (pdf)
Front cover illustration:
© Valentina Kouchnarenko Hällefors, 2011
Printed by:
Ineko, Göteborg, 2013
Keywords:
Current returns, current earnings, future earnings, ERC,
earnings response coefficient, earnings surprise

Foreword
This report is the result of a research project that has been carried out at
the Department of Accounting at Stockholm School of Economics (SSE).
The report is submitted as a licentiate’s thesis at SSE. In keeping with
the policies of SSE, the author has been entirely free to conduct and pre-
sent his research in a manner of his choosing as an expression of his own
ideas.
SSE is grateful for financial support provided by Bohlins stipendie-
fond, Torsten och Ragnar Söderbergs Stiftelser, and KPMG which has
made it possible to carry out the project.
Göran Lindqvist Johnny Lind
Director of Research Professor and Head of the
Stockholm School of Economics Department of Accounting

Acknowledgements
Eventually this research project has reached its end – by being completed
in the form of a licentiate thesis. The first steps as a Ph.D. student were
taken in days when songs from Nirvana’s Nevermind album and Metalli-
ca’s black album were running high on the charts, when Depeche was
about to release Songs of Faith and Devotion, and when Vetlanda won a
second consecutive gold. It has been a long time period and memories
from the B-sektionen (Department of Accounting) days are numerous;
such as the escapades of the B-sektionen ‘innebandy’ team and at EAA
conferences.
Apart from all memories that come to mind at this moment, I feel re-
lief and gratefulness – relief that the final step of this path is about to be
taken and gratefulness for all support and patience of former SSE col-
leagues and, now in the final stage, also persons at KPMG.
First of all, I would like to thank Professor Kenth Skogsvik, my tutor.
He has supported and guided me from the very beginning to this very
day – in the idea phase, in modeling, in statistical issues, in structuring, in
language, and now in completing the work after some hibernated years
for the project. His competence in this area and type of research and his
support has been invaluable for me.
Several other colleagues have also helped me to improve upon this
piece of research. There was especially a group of colleagues at B-
sektionen doing more quantitative research that used to discuss each oth-
er’s work that I am grateful to: Katerina Hellström, Tomas Hjelström,
Hanna Setterberg, Stina Skogsvik, and Håkan Thorsell. Beside this
group, I am grateful for helpful contributions by Professor Peter Jenner-
gren, Mikael Runsten, and Catharina Pramhäll. I also want to take the
opportunity to thank Professor Stephen Penman for taking me on a cou-
ple of months during his stay at the London Business School.

viii ON THE RELATION BETWEEN EARNINGS AND RETURNS
I very much enjoyed the collegial atmosphere at B-sektionen during
my somewhat more than a decade there. The memories are positive –
teaching and solving life puzzles with Catharina Pramhäll; teaching, es-
presso and bandy with Magnus Bild; teaching, farfetched associations
and floorball with Mikael Runsten; progressive rock and malts with
Göran Nilsson; teaching and food with Tomas Hjelström; teaching and
Eastern adventures with Jörgen Nilsson to just name a few fond memo-
ries. The list of B-moments and B-people could be made long – thank
you all.
Above, I mentioned gratitude for the patience shown by people. Pro-
fessor Kenth Skogsvik’s patience is, of course, central. The support from
Professors Lars Östman and Johnny Lind, by allowing me to take the
time, is also crucial for the completion of this study.
Kenth and Lars have also played an important role in helping to ar-
range with financial support for my research. I am especially grateful to
the Stockholm School of Economics, Bohlins stipendiefond, and Torsten
och Ragnar Söderbergs Stiftelser for financial support during my time at
B-sektionen, and to KPMG for supporting me to now complete this
work.
Since the first steps in the earlier parts of the 90s much has changed.
Tina came in, grew up and is partly on the way away; Alice was born
and amazingly keep on changing to a more wonderful person; Depeche
and Metallica changed to the worse; bandy changed to the better with
Edsbyn grabbing some golds instead of e.g. Vetlanda – but the existence
of the research project was constant. I very much look forward to taking
the last step, with the upcoming dissertation, and to learning how life
then changes.
Spånga, April 25, 2013
Hans Hällefors

Contents
1. Introduction & Previous Research........................................................1
1.1 Introduction..................................................................................1
1.2 Research Background...................................................................2
1.3 Purpose, Discussion of Purpose, Limitations and Assumptions ...4
1.4 Disposition ....................................................................................5
1.5 Previous Research.........................................................................5
1.5.1 Introduction ........................................................................5
1.5.2 Valuation Models and the Relation between Returns and
Earnings ........................................................................................7
1.5.3 Empirical Studies of the Univariate Relation between
Returns and Earnings .................................................................10
1.5.4 Empirical Studies of the Relation between Returns and
Current and Future Earnings .....................................................13
1.5.5 Empirical Studies of Permanent and Transitory Earnings
Surprises and the Returns-Earnings Relation ............................19
1.5.6 The Present Study in Relation to Previous Research.......22
2. Valuation Framework .........................................................................25
2.1 The Generic Valuation Model...................................................25
2.2 Returns and Earnings.................................................................26
2.2.1 The First Case: Constant Expected Future Earnings .......30
2.2.2 The Second Case: Constant Expected Future Earnings
Growth Rate ...............................................................................36
2.2.3 The Third Case: Variations in Expected Future Earnings
44
2.2.4 Conservative Accounting and Growth .............................57
2.2.5 Truncated Modeling .........................................................65
3. From Valuation Framework to Statistical Regressions.......................73
3.1 The Regressions..........................................................................74
3.2 The Full Sample – No Partitions................................................76
3.2.1 The Univariate Regression ...............................................76

x ON THE RELATION BETWEEN EARNINGS AND RETURNS
3.2.2 The Multivariate Regression.............................................78
3.2.3 Summary of Expectations for Full Sample Tests..............82
3.3 Constant Future Earnings and Earnings Surprises .................... 82
3.4 The Full Sample and Earnings Surprises................................... 86
3.5 The Full Sample and Solitary Truncation ................................. 88
4. Operationalizations and Sample Characteristics................................ 91
4.1 Sample Selection......................................................................... 91
4.2 Operationalizations and Variable Definitions ........................... 92
4.2.1 Returns..............................................................................93
4.2.2 Earnings ............................................................................93
4.2.3 Earnings Growth...............................................................94
4.2.4 Earnings Surprises.............................................................95
4.2.5 Truncation Variables........................................................99
4.3 Descriptive Statistics ................................................................. 103
4.3.1 The Full Sample – General Descriptives ........................103
4.3.2 Earnings Surprise Partitions – Descriptives....................105
4.3.3 Industry Distribution.......................................................107
4.4 Econometric Aspects ................................................................ 108
4.5 Characteristics of the Accounting Regime............................... 110
5. Results ............................................................................................... 113
5.1 The Full Sample ....................................................................... 113
5.2 Constant Future Earnings ........................................................ 119
5.3 The Full Sample and Earnings Surprises................................. 122
5.3.1 Univariate Model............................................................123
5.3.2 Multivariate Model .........................................................127
5.4 A Truncated Model.................................................................. 130
5.5 Tests of Sample Characteristics and Model Robustness.......... 133
5.5.1 Different Periods .............................................................133
5.5.2 Different Company Sizes ................................................138
5.5.3 Different Industries .........................................................142
6. Summary and Concluding Remarks ................................................ 147
6.1 Theoretical Modeling............................................................... 147
6.2 Empirical Results and Suggestions for Future Research ......... 149

xi
6.2.1 General Samples .............................................................150
6.2.2 Different Periods, Company Sizes, and Industries .........151
6.2.3 No Growth, Earnings Surprise Samples, Truncated Model,
and Future Research.................................................................153
7. Appendices ........................................................................................157
8. References .........................................................................................177

Chapter 1
1. Introduction & Previous Research
1.1 Introduction
A core objective of financial accounting as presented in published finan-
cial statements is to provide information that is useful for investors and
creditors in making resource allocation decisions. Investors are interested
in making judgments about the value of equity of companies and about
potential returns from investing in stocks. Different accounting based
measures can be of interest for such tasks.
Book value of equity constitutes the accounting based value for own-
ers and might be useful in judging on the “true” value of equity. Net
earnings (profit or loss) constitute the accounting based core measure of
value creation for owners during a period and use of earnings infor-
mation might be useful for judgments on stock returns, the market value
1
based value creation for owners. Net earnings might also be useful for
prediction of future earnings and dividends, and as a consequence in
judging on the “true” value of equity.
The concept of ‘economic earnings’ is often used for earnings’ value
creation role. In a hypothetical world where the net value of assets and
liabilities recognized in the balance sheet (statement of financial position)
always equals the market value of equity, earnings will always equal stock
returns. In such a world there would be a one-to-one relationship be-
1
No distinction between market and “true” (intrinsic) value of equity is intended here.

2 ON THE RELATION BETWEEN EARNINGS AND RETURNS
tween book and market value of equity, and between current net earn-
ings (‘economic earnings’) and stock returns.
The concept of ‘permanent earnings’ is often used for earnings’ role
as an indicator of future value creation. In this role the “true” value of
equity can be derived by capitalizing current earnings.
The role of current earnings as illustrated by the ideal concepts of
economic and permanent earnings is, however, in practical equity valua-
tion not as complete. Often additional information is sought in explicit
forecasting of future earnings.
In this study the relationship between earnings and stock returns will
be explored. Returns-earnings relations have been and are commonly
used in market based accounting research, with different purposes. Re-
turns-earnings regressions of different forms are often estimated (especial-
ly with US data). Structured development of expectations of returns-
earnings relations under different conditions have, however, been less
common.
Below, a structure for different types of returns-earnings relations will
be derived and tested empirically (with Swedish data). Aspects as perma-
nence of earnings over time and as earnings surprises will be explored. In
the empirical tests aspects relating to company sizes, different time peri-
ods, and different industries will also be studied.
1.2 Research Background
In the 1960s there were doubts about whether accounting conventions
such as verifiability and prudent measurement of assets and liabilities
provide an earnings measure that is at all related to stock market returns.
After two studies in 1968 by Ball & Brown (1968) and Beaver (1968), the
doubts decreased and further exploration of the associations followed.
During subsequent years research focused on how unexpected earnings
could influence abnormal returns, based on a perspective that unex-
pected earnings sent signals about the current and future performance of
the company.

CHAPTER 1 3
From the early 1990s measurement and fundamental valuation per-
spectives have received more attention in the studies of the association
between stock returns and accounting earnings.
2
In the formulation of
theoretical connections, one starting point has been that returns and
earnings ultimately include the same economic events and that the asso-
ciation should be strong over long periods. Another starting point has
been fundamental valuation models such as the “present-value-of-
expected-dividends” (PVED) and “residual income valuation” models.
Within the measurement perspective the relation between returns
and earnings has moved away from unexpected earnings and abnormal
returns. Instead, the level of returns is often related to the level of earn-
ings. Although many empirical investigations of this relation have been
conducted there has not been a clear consensus on a theoretical bench-
mark level of returns relative to current earnings. Often a one-to-one re-
lationship has been used as a benchmark. But at the same time it is
sometimes mentioned that the earnings coefficient should be larger than
one if certain covariances exist in the data. It is sometimes also claimed
that the earnings coefficient should be equal to the inverse of the re-
quired rate of return.
Since fundamental valuation models are based on expected future
pay-offs from the company, it could be interesting to investigate how a
fundamental valuation model such as PVED can be used to structure the
theoretical relations between returns and current and future earnings. It
is then natural to empirically test these theoretical structures. Apart from
testing the theoretical modeling in itself, empirical tests based on Swedish
data can add to the large amount of returns-earnings associations that
previously have been estimated only to a limited extent with other than
US and UK data.
2
See e.g. Ohlson (1995) and Penman (1992).

1.3 Purpose, Discussion of Purpose, Limitations and
Assumptions
With the above background in mind, the purpose of the study is formu-
lated in the following way.
The purpose of the study includes a theoretical and an empirical part.
In the theoretical part relationships between stock returns and current
and future earnings will be established, based on the “present-value-of-
expected-dividends” model. In the empirical part the empirical rela-
tion between returns and current and future earnings will be investi-
gated, with special attention to the theoretically developed
relationships.
Swedish data for almost all companies listed on the Stockholm stock ex-
change during the period 1967 to 1998 will be used to empirically test
the theoretical models. The empirical results will consequently describe
relations between stock prices and earnings as recognized in accordance
with the Swedish accounting convention(s) during this period.
Annual returns and annual current and future earnings will be stud-
ied. Annual data will be used since previous research indicate that quar-
terly and semi-annual accounting earnings have little explanatory power
for returns – see e.g. Warfield & Wild (1992) – and since the availability
of Swedish interim report data is quite limited. In order to limit the scope
of the study, longer periods than one year are also excluded. Also, with a
base in fundamental valuation and the idea that stock prices and returns
depend on the discounted value of the dividend-part of current and fu-
ture annual earnings, the use of an annual window is natural.
In analyzing and interpreting the empirical results the reasoning will
often connect to the theoretical valuation framework. It should be re-
membered that the relevance of the reasoning hinges on the validity of
the generic valuation model that is used – which defines stock prices as
the present value of expected future dividends. Also, the study does not
empirically investigate questions related to market efficiency.

CHAPTER 1 5
1.4 Disposition
Modeling and empirical tests of the returns-earnings relation in previous
research is described in the following section, section 1.5. In chapter 2,
“Valuation Framework”, the PVED-model is used as a basis for model-
ing different returns-earnings relations under different conditions. Condi-
tions when current earnings are sufficient in explaining returns are
derived and multipliers that relate earning to returns are specified in sub-
sections 2.2.1, 2.2.2, and 2.2.4. Multipliers for cases when future earn-
ings are included in the relation are derived in sub-sections 2.2.3 and
2.2.5. All five sub-sections contain separate derivations for periods with
no, transitory, and permanent earnings surprises, respectively.
Chapter 3 and 5 follow a similar structure based on the univariate
and multivariate modeling, and with separation on different types of
earnings surprises. Empirical tests to be performed are described in chap-
ter 3, and regression coefficient and R
2
expectations based on the valua-
tion framework are developed. In chapter 5, the estimated regressions
are reported and discussed.
The sample selection is described in chapter 4, which also covers
specifications of how different variables are calculated, descriptive statis-
tics, and an overview of prevailing accounting conventions in Sweden
during the studied time period. The study’s summary and concluding
remarks follow in chapter 0. A number of appendices are reported in
chapter 7.
1.5 Previous Research
1.5.1 Introduction
Ball & Brown (1968) and Beaver (1968) are often viewed as the start of
an extensive empirical research on the association between stock market
data and accounting information. The articles studied stock price reac-

tions in relation to earnings announcements. Ball & Brown (1968)
showed that stock returns above (below) the general stock market return
were positively correlated with the presentation of good (bad) earnings
news. Beaver (1968) showed that residual volume and residual returns
were abnormal around the earnings announcement date. A conclusion
was that accounting earnings contain useful information for stock market
participants.
These are two examples of information content studies
3
, which focus
“on the relation between new accounting information and short-term
changes in stock prices”
4
and on whether accounting information pro-
vides useful signals about future performance. Within this perspective,
residual returns are typically regressed on unexpected earnings (often
operationalized as the change in earnings) without articulation of any
formal relationship between earnings and returns. During the two dec-
ades following Ball & Brown (1968) and Beaver (1968) the information-
al/signaling perspective dominated the empirical market based
accounting research.
Towards the end of the 1980s many researchers turned their interest
towards accounting based fundamental valuation. At this time e.g. Lev
(1989) noted – in a review of the empirical research of the 1980s – that
reported results on the relationship between returns and earnings had
neither been particularly strong nor stable. Bernard (1989) also found
that recent research could be developed and both Lev (1989) and Ber-
nard (1989) suggested deepening the understanding of the relationship
between accounting variables and equity values.
The roots of fundamental valuation, relating economic values to ac-
counting data, are quite old. Early contributions were made in the 1930s
[e.g. Preinreich (1938), Williams (1938) and Hicks (1939)]. Important
theoretical contributions during the revival of valuation studies in the
early 1990s were made by e.g. Ohlson (e.g. 1990, 1991 and 1995). In this
period, there was an increased focus within empirical research on the
3
Examples of other labels/descriptions of this research approach are ”market reaction
studies” and ”studies with a signaling perspective”.
4
Brennan (1991), p. 67.

CHAPTER 1 7
ability of earnings and earnings changes to explain raw returns. The ex-
planatory power of earnings and earnings changes were compared, dif-
ferent return and earnings windows were used, accounting recognition
criteria were examined etc. [e.g. Easton & Harris (1991), Easton, Harris
& Ohlson (1992), Warfield & Wild (1992)]. These studies are further de-
scribed below.
In the following, different parts of previous research will be de-
scribed. Sub-section 1.5.2 brings up previous theoretical modeling of the
relationship between returns and earnings. This is followed by sections
about empirical studies of the association between returns and current
earnings, future earnings, and effects of permanent and transitory earn-
ings surprises. Finally, in sub-section 1.5.6, the position of the present
study is briefly related to previous research.
1.5.2 Valuation Models and the Relation between Returns
and Earnings
Most modeling of how earnings can explain stock returns focus on earn-
ings and returns from the same period. Usually, the modeling is based on
a linear model where current earnings are multiplied with a multiple in
order to explain returns. Below, some theoretical modeling in previous
research regarding the size of this earnings multiple is reviewed.
Research that deals with the relation between stock returns and cur-
rent earnings often refers to the idea of Hicksian income theory [Hicks
(1946)] and views earnings as a measure of value change; Easton et al.
(1992) is one example. They note that earnings and returns are equal
when the difference between the market value and the book value of eq-
uity is the same in the beginning and the end of the period.
5
Under this
assumption earnings should be multiplied with one in order to explain
returns. The authors also note that if the change in the difference be-
5
Modeling of this relation is presented in appendix F.

tween market and book value is positively correlated with earnings, the
coefficient should be larger than one.
6
Runsten (1998) models a relation where the change in price (capital
gain) is explained by the change in the book value of equity. This relation
is similar, but not identical, to the relation where earnings explain re-
turns. He models that the coefficient is expected to be equal to the per-
manent market-to-book ratio in a steady-state; i.e. somewhat higher than
1 if accounting is conservative.
Earnings response coefficient (ERC) benchmarks that are considera-
bly larger than 1 are sometimes seen in research articles. With a required
return of e.g. 10 % such ERC benchmarks are 10-11.
7
These ERC levels
are usually connected to earnings explaining prices or unexpected earn-
ings explaining returns. In e.g. Ohlson (1991) it is modeled that cum-
dividend price is equal to current earnings times 1 + 1/required return.
He used the term “returns” for cum-dividend price scaled by beginning-
of-period price and consequently models that these “returns” are equal
to scaled earnings times 1 + 1/required return. Being a price-earnings
ratio, it is natural that this earnings response coefficient is higher than a
coefficient that explains raw returns (price change + dividends) in a re-
turns-earnings relation. When raw returns are explained with unex-
pected earnings, e.g. Watts & Zimmerman (1986) note that the ERC
should be equal to 1 + 1/required return if earnings follow a random
walk (i.e. if unexpected earnings are permanent).
To conclude, regarding the relation between raw returns and con-
temporaneous earnings, previous research indicates that returns as a
benchmark should be equal to earnings multiplied by one or a number
somewhat above one. Regarding the relation between returns and future
earnings, previous research does not seem to offer any formalized guid-
ance.
6
Easton et al (2000) model the expected coefficient to be 1 + covariance (deflated earnings,
deflated change in value difference) · variance (deflated earnings).
7
These ERC levels are typically written as 1/required return or 1 + 1/required return
[= (1+required return)/required return], respectively.

CHAPTER 1 9
Changes in market expectations about companies’ future pay-offs are
important for the sign and size of returns and any changes in expecta-
tions may alter the size of the earnings multiplier. When expectations
about future pay-offs change in a positive (negative) direction, fundamen-
tal values increase (decrease). Therefore, the relation between observed
earnings (surprises) and revisions of expected future pay-offs is vital for
the relation between returns and current earnings.
Miller & Rock (1985) show how the magnitude of a return reaction
to an “earnings innovation” depends on the persistence of the innova-
tion, i.e. to what extent a current earnings surprise affects the expected
levels of future earnings. Based on an extension of Miller & Rock’s (1985)
modeling, Kormendi & Lipe (1987) model how returns are influenced by
a current earnings innovation and its effect on revisions of expectations
of future earnings. They use the following model:
Returnt = Expected returnt + Return effect from current earnings in-
novationt + Other return effectst
Assuming that the present value of the revision of expected future equity
cash flows equals the present value of the revisions of expected future earn-
ings, the return effect from a current earnings innovation is modeled as a
multiple times the current earnings innovation. If the earnings innova-
tion is purely transitory – i.e. the current innovation does not incur any
revisions of expected future earnings – the multiple equals 1. If the earn-
ings innovation is purely permanent – i.e. all expected future earnings
are revised with the current innovation amount – the multiple equals 1 +
1/required return.
Based on similar modeling, Easton, Shroff & Taylor (2000) model
raw returns on the current earnings level when unexpected economic
events are either permanently or transitorily incorporated in the current
year’s earnings. As a first step Easton et al. (2000) assume that “account-
ing earnings may be viewed as a perfect summary of the events that have
affected returns inasmuch as recorded earnings and returns are related

via an identity”
8
. This may be interpreted as current earnings being as-
sumed to be equal to the expected return plus full or partial recognition
of the future cash flows of the unexpected returns. Earnings are defined
as transitory when current unexpected returns are fully recorded in cur-
rent earnings, and as permanent when “only the permanent shift in ex-
pected future cash flows is recorded”
9
. In this first step Easton et al.
(2000) conclude that the earnings multiple that explains returns is 1 when
earnings are transitory and 1 + 1/required return when earnings are ful-
ly permanent and unexpected returns very large (relative to expected re-
turns)
10
. Hence, if e.g. the required return is equal to 10 % and the
earnings surprise positive, the earnings coefficient would be between 1
and 11.
As a second step Easton et al. (2000) add an accounting recording lag
that models the effect of current earnings not being a perfect summary of
the events that have affected current returns. Easton et al. (2000) con-
clude that “accounting recording lag will reduce the value relevance of
earnings. The effect of this lag is to draw the estimate of the earnings co-
efficient toward zero.”
11
1.5.3 Empirical Studies of the Univariate Relation between
Returns and Earnings
One of the earliest empirical studies of the relation between raw returns
and the level of earnings with the new focus on fundamental valuation
was Easton & Harris (1991). They compare earnings change and earn-
ings level as explanatory variables for returns and find that earnings level
is better than earnings change, which used to be a typical independent
variable. Results in this and a selection of other studies of the relation
8
Easton et al (2000) page 285.
9
10
Very large unexpected returns relative to expected returns, implies that earnings in prin-
ciple only consist of the earnings effect from the unexpected economic events – i.e. that
earnings are equal to unexpected earnings, as in Kormendi & Lipe’s (1987) modeling.
11

CHAPTER 1 11
between returns and current earnings level are summarized below in ta-
ble 1.
In a following study Easton et al. (1992) note that the share of eco-
nomic events that affect returns and earnings in the same period should
be larger for longer periods. As hypothesized, the explanatory power of
regressions for 10-year periods proves to be considerably higher than for
1-year periods (R
2
of 63 % vs. 6 %). The authors also note that the aver-
age earnings coefficient gradually increases from 0.533 for the 1-year pe-
riods up to 1.659 for the 10-year periods. Warfield & Wild (1992) also
relate to the fact that accounting recognition of economic events tends to
lag that of the stock market. In order to investigate the recognition lag
they study the effect from adding future earnings as independent varia-
bles (see the next sub-section about returns and current and future earn-
ings).
Several studies have since then explored different aspects of the re-
turns-earnings relation. Many of the articles reported in table 1 receive
base regression R
2
s in the area 6 % to 11 % and earnings coefficients
around 0.7 to 0.95. Warfield & Wild (1992) cover a more limited period
(1983-86) and report the lowest values on both R
2
and earnings coeffi-
cient. Dechow (1994) and O’Hanlon & Pope (1999) report the highest
values in both respects.

Table 1: Empirical results of the relation between returns and current earnings
level; ttt EarningsCoeffConstantReturns ε+⋅+= 12
Author(s) Adj R 2
Const Coeff n Period
Dechow (1994) 1 year, p 16.2% -0.084 1.297 27308 60-89 US
4 years, p 40.3% -0.510 1.686 5175
Easton & Harris (1991) 1 year, p 7.5% 0.11 0.82 19996 68-86 US
Easton, Harris & 1 year, a 6% 0.126 0.533 1292 68-86 US
Ohlson (1992) 5 years, a 33% 0.128 1.450 1291
Easton, Shroff & 1 year, p 9% - 0.72 132940 59-97 US
Taylor (2000) Intangibles 3.20
1-time items 2.47
Loss years 0.08
All other 2.77
Hayn (1995) 1 year, p 9.3% - 0.95 75878 62-90 US
Profit years 16.9% - 2.62 61366
Loss years 0.0% - 0.01 14512
O'Hanlon & Pope 1 year, p 14% 0.00 1.89 3086 72-92 UK
(1999) 5 years, p 42% -0.39 2.54 614
Ohlson & Penman 1 year, a 11% 0.077 0.872 1610 70-87 US
(1992) 5 years, a 29% 0.354 1.183 1827
Runsten (1998)* 1 year, p 7.4% 0.11 0.77 2363 68-93 Sw
1 year, a 8.7% 0.12 0.56 91
5 years, a 26.6% 0.52 1.03 67
Shroff (1995) 1 year, p 6% 0.126 0.737 7096 75-87 US
H P/E & ROE 20% -0.240 4.969 885
Strong (1993) 1 year, a 8.8% 0.05 0.73 159 69-89 UK
1 year, p 6% 0.09 0.61 3058
Warfield & Wild (1992) 1 year, p 5.6% 0.18 0.38 5714 83-86 US
4 years, p 39.8% 0.62 1.30 1135
Periods in second column refer to window size. Other characteristics are described below.
a: Average values of regressions for individual window sizes
p: Pooled regressions
*: Dependent variable = change in stock market capitalization (i.e. capital gain); independent variable =
change in book value of owners’ equity
12
In all studies the dependent and independent variable are deflated with stock market capi-
talization in the beginning of the period. Annual returns are either measured over the 12
months of the financial year, or 12 months periods ending 2 or 3 months after the finan-
cial year end.

CHAPTER 1 13
Hayn (1995) means that the returns-earnings relation should be stronger
for profit years than loss years and that this could be an explanation to
low explanatory powers in previous studies. Her empirical results are
consistent with this hypothesis – the R
2
increases from 9.3 % to 16.9 %
when loss years are eliminated.
Shroff (1995) and Easton et al. (2000) touch on aspects that can be
related to the effect of conservative accounting and growth and/or per-
manent earnings surprises, which are important factors in the valuation
framework below. Shroff (1995) studies several partitions for different
price-earnings and ROE levels. The partition with high price-earnings
ratio and high ROE show the most remarkable results – both the R
2
(20 %) and the earnings coefficient are high (4.969). Companies with
high price-earnings ratios are expected to have high earnings growth and
with a high ROE the expected earnings growth does not come from a
temporarily low level. According to modeling below and depending on
the nature of the observations in this partition, the large coefficient can
depend on a large proportion of positive permanent earnings surprises
and/or high earnings growth and high stable ROE (= high degree of
conservative accounting).
Easton et al. (2000) investigate how intangible asset intensity, one-
time items, and losses influence the earnings coefficient. The results of
Easton et al. (2000) will be further discussed below, when effects of transi-
tory and permanent earnings are treated. It can here be noted that the
relatively large earnings coefficient for intangible intensive industries,
which Easton et al. (2000) explain with high permanence, also touches
on issues related to effects of conservative accounting and growth.
1.5.4 Empirical Studies of the Relation between Returns
and Current and Future Earnings
Studies of the relation between returns and future earnings are less
common. Warfield & Wild (1992) is an exception. In the same spirit as
Easton et al. (1992), they mean that due to the lag in the accounting

recognition of economic events, future earnings should contain events
that influence stock returns in the current period. They also hypothesize
that future earnings should add more information about current returns
for industries with a longer expected recognition lag and for shorter re-
turn windows. Their results are consistent with these hypotheses. For the
one year window and for the two industry groups with high and low ex-
pected sensitivity to accounting recognition criteria Warfield & Wild re-
ceive the following pooled results (for the period 1983-86).
Table 2: Returns-earnings regression results of Warfield & Wild (1992)
Alternative Combinations of Explanatory Variables
Current
Year’s
Earnings
Current and
Next Year’s
Earnings
Current and
Next Two
Years’ Earnings
Current and Next
Three Years’
Earnings
All industries (n=2650)
Adjusted R2
5.41 % 15.71 % 16.20 % 17.00 %
Percentage increase ⎯ 190 3 5
High sensitivityH
(n=1588)
Adjusted R2
3.78 % 16.40 % 16.92 % 18.11 %
Percentage increase ⎯ 334 3 7
Low sensitivityL
(n=415)
Adjusted R2
21.63 % 25.99 % 25.82 % 25.87 %
Percentage increase ⎯ 20 -1 0
H: Industries in the “high” group: mining, construction, and manufacturing (SIC code industries 1, 2 and 3)
L: Industries in the “low” group: wholesale-retail trade, and services (SIC code industries 5, 7 and 8)
The study’s heterogeneous middle group is not reported here. Returns are measured over 12 months ending
with the current period’s earnings announcement. All variables are deflated with price at the beginning of the
return period (Pt-1).
A general result is that adding next year’s earnings adds much to the ex-
planation of returns – R
2
increases from 5.4 % to 15.7 %. In terms of R
2
little is gained from adding two- and three-years-ahead earnings. Earn-
ings coefficient values are, unfortunately, not reported in the article. The
industry tests show that industries that are predicted to be less sensitive to
accounting criteria have a stronger returns-earnings relation in the uni-
variate regression. Also as predicted, the more sensitive industries gain
relatively more explanatory power when future earnings are added.

CHAPTER 1 15
In studying the effect of firm disclosure activity on the returns-
earnings relation, Lundholm & Myers (2002) estimate a regression which
explains returns with current and three future years’ earnings. The inde-
pendent variables, however, also include the previous year’s earnings and
the three following years’ stock returns. A main purpose with the article
is to study if more informative disclosures are positively correlated with
current returns incorporating more information related to future earn-
ings news.
The coefficient values in the benchmark regression, for future earn-
ings levels and the other independent variables reported in the article –
for a pooled regression with data for the period 1980 to 1994 – are re-
ported in table 3.
Table 3: Returns-earnings regression results in Lundholm & Myers (2002)
Independent variables
Const Earnt-1 Earnt Earnt+1 Earnt+2 Earnt+3 Rett+1 Rett+2 Rett+3
Coeff .0986 -.4281 .4006 .7250 .4538 .3643 -.2094 -.0908 -.0030
P-value .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .8298
Adjusted R2
: 22.88 %. t = current period. Returns are buy-and-hold returns for the 12-month period starting
three months after the fiscal year end. All variables are deflated with price at the beginning of the return peri-
od (Pt-1). Realized future earnings proxy for expected future earnings. Future returns are included in order to
control for measurement errors due to unexpected future earnings. Past year’s earnings allow “the regression to
find the best representation of the prior expectation for current earnings” (p. 813).
The coefficients for current and future earnings are significant and follow
a pattern that resembles that of the present study. Next year’s earnings
has the largest coefficient and following years’ earnings coefficients de-
crease with increased remoteness; the decay is more rapid in the present
study, though.
13
It is, however, not clear how the earnings coefficients are
affected by the inclusion of future returns and past earnings.
13
Regarding the effect of including future returns Lundholm & Myers refer to Collins, Ko-
thari, Shanken & Sloan (1994), who write that “future returns should be positively related
to (unexpected future earnings) and coefficients on (future returns) are expected to be
negative. A negative sign ensures that irrelevant components positively related to future
returns are removed from (future earnings), leaving a better approximation to the changes
in expectations of future earnings … that occurred in period t” (p. 299). Collins et al. also
estimate a multivariate regression that explains returns with future earnings. They, how-

Regarding the effect of disclosure activity, Lundholm & Myers’ re-
sults are consistent with better disclosures being positively correlated with
the amount of future earnings news being incorporated in current re-
turns. In a regression where dummy variables for each independent vari-
able represent the level of disclosure activity, the coefficient for one-year-
ahead earnings is considerably larger for firms with high disclosure in-
formativeness than for firms with low informativeness. In a regression
were future earnings are represented by the sum of the earnings for the
coming three years, the coefficient for that variable is also higher for
firms with more disclosure activity. The results are summarized below in
table 4, where the dummy variable coefficients have been added to the
basic coefficients to show the earnings coefficients for each characteristic.
The mentioned effect on one-year-ahead earnings in Lundholm &
Myers’ study can be seen in that the coefficient for one-year-ahead earn-
ings is 1.151 when disclosure activity is at its best, while it is 0.444 when
disclosure activity is at its worst. The corresponding coefficient in the
benchmark regression is 0.725. In the regression where the three coming
years’ earnings have been aggregated, the coefficient for these future
earnings is 0.542 and 0.364 for the best and worst end of the disclosures
scale.
The same method to study the level of anticipation in current returns
of future earnings in relation to different characteristics has, after
Lundholm & Myers, been used in several studies.
14
In Tucker & Zarowin
(2006) firms with more income smoothing receive a higher coefficient for
both future and current earnings. In Oswald & Zarowin (2007) firms that
have chosen to capitalize costs for R&D receive a higher future earnings
coefficient than firms having chosen to expense. In Orpurt & Zang
(2009) firms presenting a direct method cash flow statement receive a
ever, deflate the independent variables with lagged earnings, which means that percent-
age returns are regressed on current and future earnings growth.
14
References are in many of these studies made to Collins et al. (1994). The independent
earnings variables in that study consist of the change in earnings during the period (earn-
ings growth). Since the present study is focused on earnings coefficients and deals only
with absolute earnings, not change in earnings, the results of Collins et al. (1994) and oth-
er studies using change in earnings are not reported.

CHAPTER 1 17
higher future earnings coefficient than firms using the indirect method
cash flow statement. In Dargenidou, McLeay & Raonic (2011) results
regarding disclosure activities for European data are similar to those of
Lundholm & Myers (2002). In Kim & Li (2011) the effect of “firm infor-
mational market efficiency” is tested. Higher (lower) speed in the re-
sponse of a firm’s stock price to market-wide information proxy for high
(low) market efficiency. Firms with higher market efficiency receive a
higher coefficient for both future and current earnings. See table 4 be-
low.

Table 4: Studies of anticipation in returns of future earnings; effects of different
characteristics
Earnt Earnt+1 Earnt+2 Earnt+3 Adj. R2
L&M (2002) Benchmark 0.401 0.725 0.454 0.364 22.9%
US Worst disclosures 0.448 0.444 0.534 0.253 23.5%
1980-94 Best disclosures 0.383† 1.151 0.335† 0.488† 23.5%
L&M (2002) Benchmark 0.566 0.443 20.5%
US Worst disclosures 0.599 0.364 20.8%
1980-94 Best disclosures 0.555† 0.542 20.8%
T&Z (2006) Benchmark 1.074 0.146 6.8%
US More inc. smooth. 0.856 -0.002 7.2%
1993-2000 Less inc. smooth. 1.537 0.306 7.2%
O&Z (2007) Expense R&D 1.10 0.35 -
UK Capitalize R&D 1.37† 0.60 -
1990-1999
O&Z (2009) Indirect CF 0.773 0.102 6.1%
US Direct CF 0.999† 0.334 6.1%
1989-2002
DMR (2011) Worst disclosures 1.348 0.208 32%
Europe Best disclosures 1.220 0.285 32%
2000-2002
K&L (2011) Benchmark 0.873 0.109 7.3%
US Market eff., best 1.139 0.210 7.6%
1988-2006 Market eff., worst 0.721 0.065 7.6%

=τ
τ+
3
1
tEarn
†: Dummy variable not significant at 5 %.
t = current period
The above studies also include additional independent variables, as described above regarding Lundholm &
Myers (2002).

CHAPTER 1 19
1.5.5 Empirical Studies of Permanent and Transitory
Earnings Surprises and the Returns-Earnings Relation
According to theory, the size of the multiple that relates current earnings
to returns depends on the degree and type of earnings surprises in the
current period. Especially, large permanent surprises have large effects
on the multiple. Empirical studies related to the issue of permanent and
transitory earnings have mainly been concerned with the relation be-
tween unexpected earnings and returns / unexpected returns (e.g. Ali &
Zarowin (1992), Freeman & Tse (1992), and Burgstahler & Chuk (2010)).
Studies of the effect on the same relation from changes in analysts’ ex-
pectations about future earnings are closely related (e.g. Liu & Thomas
(2000) and Copeland, Dolgoff & Moel (2004)). These studies show, in
different ways, that permanence, transitoriness, and expectation changes
matter for R
2
and earnings coefficient values.
Like the present study, Easton et al. (2000) study the relation between
raw returns and earnings level. They use different partitions to study
earnings coefficient values when unexpected returns have either perma-
nent or transitory earnings effects. The authors hypothesize that one-
time items and losses are both likely to be treated as transitory and to re-
flect accounting recording lags. As expected the estimated earnings coef-
ficients prove to be lower in these cases. They also mean that shocks to
returns of intangible-intensive industries are more likely to be perma-
nent; but at the same time they expect the earnings coefficient to be re-
duced by a longer accounting recording lag.
15
Easton et al. (2000) find
that the earnings coefficient is larger for intangible-intensive industries
than others, which they mean is due to effects of the accounting record-
ing lag being swamped by the effect of the permanence of earnings.
These results are summarized in table 5a.
15
“…due to, say, the discovery of a new effective drug, or faster computer processors…” (p.
282).

Table 5a: Returns-current earnings regression results in Easton et al. (2000)
Earnings coefficient
Intang.-
intens.
industry
Earn.
incl. one-
time item
Negative
earnings All other Period
Regression with three
dummy variables
3.20 2.47 0.08 2.77 1959-97
Average values of regressions estimated per year are reported above. All variables are deflated with price at
the beginning of the return period (Pt-1). Note that the earnings coefficient values, and not the dummy variable
values (which are all significant at 1 %), are reported here. Intangible-intensive industries: SIC-codes 48 (elec-
tronic components and accessories), 73 (business services), 87 (engineering, accounting, R&D, and man-
agement related services), 282 (plastics and synthetic materials), 283 (drugs), and 357 (computer and office
equipment).
Finally, Easton et al. (2000) use price-earnings ratios to separate perma-
nent from transitory earnings effects. They mean that a high price-
earnings ratio suggests that unexpected returns have a permanent earn-
ings effect, and they find empirical evidence that is consistent with this
(i.e. a larger earnings coefficient). The results are summarized in table
5b.
Table 5b: Returns-current earnings regression results in Easton et al. (2000)
Earnings coefficient
Pos.
perm.
surp.
A
Pos.
trans.
surp.
B C D
Neg.
trans.
surp.
E
All
other Period
Regression with five
dummy variables
3.52 1.90 2.93 0.80 0.11 0.35 1970-97
R2
= 56 %. Average values of regressions estimated per year are reported above. All variables are deflated
with price at the beginning of the return period (Pt-1). Note that the earnings coefficient values, and not the
dummy variable values (which are all significant at 1 %), are reported here.
A: High positive unexpected returns & high price-earnings ratio
B: High positive unexpected returns & low price-earnings ratio
C: Negative raw returns, positive earnings, and high price-earnings ratio
D: Negative raw returns, positive earnings, and low price-earnings ratio
E: Negative raw returns, and negative earnings
Column A and B include company years with positive unexpected earn-
ings, which means that they have positive changes in expectations about

CHAPTER 1 21
future pay-offs.
16
If these expectation changes are included in the current
year’s earnings, earnings are expected to be temporarily high and the
price-earnings ratio low. Consequently, column B characteristics proxy
for a low degree of permanence in earnings, and column A for a high
degree of permanence. Unexpected returns are usually not recorded in a
purely permanent or transitory manner in earnings and this price-
earnings based classification does not give a noise free partition of per-
manent vs. transitory, but on average column A probably includes a
larger degree of permanence than column B. The estimated coefficient
values are consistent with predictions based on this partitioning; column
A having a very large and column B a fairly large value.
Columns C, D, and E contain observations with negative changes in
expectations about future earnings. Following reasoning of Basu (1997)
17
,
Easton et al. (2000) expect negative changes to be recorded promptly in
accounting earnings and consequently to have a transitory earnings ef-
fect. This is especially the case when earnings are negative, which indi-
cate that the negative news have largely been incorporated in the current
income statement. In the valuation framework below it is noted that ef-
fects of negative transitory earnings surprises can motivate very different
earnings coefficient values. The very low coefficient value in column E is
consistent with this. It is more difficult to have clear ideas about columns
C and D.
16
This way to find positive changes in expectations about future pay-offs is different from
the one in the present study. In the present study partitions are based on differences be-
tween observed and analysts’ expected earnings for the current year and on changes in
expectations about the next year. One potentially different consequence is that the pre-
sent study will not identify return influencing changes in expectations about future pay-
offs that do not affect current earnings, while Easton et al (2000) will. The classification of
permanent vs. transitory will also be operationalized in a different manner.
17
Basu (1997) means that due to the conservatism/prudence of accounting, negative news
about the future tends to be recognized in a more timely fashion in earnings than positive
news.

1.5.6 The Present Study in Relation to Previous Research
The present study belongs to the fundamental valuation based research
tradition that has had a revival since late 1980s and early 1990s. The
study has its base in a valuation framework that specifies a relation be-
tween stock returns and current and future earnings. It explores the fact
that annual returns can be explained by (a) the value effect of having all
future dividends (as a share of earnings) one year closer and (b) the value
effects of changes in expectations about future earnings and dividends. A
number of special cases, based on earnings growth and types of earnings
surprises, are developed and used as points of reference for the statistical
tests.
Models for both the relation between returns and current earnings
and between returns and current and future earnings are developed in
the valuation framework. If future earnings are perfectly correlated with
current earnings, current earnings are a sufficient explanatory variable
for returns. The framework specifies conditions when there should be a
one-to-one relation between returns and current earnings as well as con-
ditions that imply an earnings multiple above one.
Effects of transitory and permanent earnings surprises are incorpo-
rated into this framework and given no growth or unbiased accounting
the same expected earnings coefficients as in Easton et al. (2000) are re-
ceived for transitory and permanent earnings surprises. However, the
derived earnings multiples become larger when conditions for growth
and conservative accounting are introduced.
When, on the other hand, future earnings are not perfectly correlated
with current earnings, future earnings add to the explanation of current
returns. This study adds to previous research by modeling relations
where returns are explained by earnings for both the current and future
years.
In the empirical part below, both the relations with current earnings
alone and together with future earnings are tested. The results of the
univariate regression are similar to those of previous studies. The analysis
of possible explanations for the earnings coefficient being larger than

CHAPTER 1 23
one, which relates to the valuation framework in the present study, is an
addition to previous research. Following tests for cases with close-to-zero
earnings growth and earnings surprises are also new.
In the multivariate tests, the present study will touch on issues of both
Warfield & Wild (1992) and Lundholm & Myers (2002). The analysis
below will, however, build on the modeling and special cases from the
valuation framework that follow in the next chapter. Only (current and
future) earnings are modeled and used as independent variables, like in
Warfield & Wild (1992). More attention is paid to the earnings coeffi-
cients, though. Also, other aspects than industry effects are studied – as
e.g. effects of different earnings surprises, close-to-zero earnings growth,
and different periods.
In the earnings-surprise-area, the present study investigates questions
that are similar to those of Easton et al. (2000). A difference is that while
Easton et al. (2000) use unexpected returns to identify unexpected eco-
nomic events, the present study uses observed earnings surprises. Also,
the present study uses analysts’ one-year-ahead earnings forecasts to
identify earnings surprises, and two-years-ahead earnings forecasts to
identify permanent and transitory earnings surprises.

Chapter 2
2. Valuation Framework
A framework on which to base the empirical tests for the study of the re-
lationship between returns and earnings will be provided in the present
chapter. A starting point in this framework is the present-value-of-
expected-dividends model, generally accepted as a generic fundamental
valuation model. From this model a linkage between current stockholder
returns and current and future earnings will be derived.
2.1 The Generic Valuation Model
A theoretically well-founded and widely accepted valuation model speci-
fies the value of owners' equity as the present value of the expected future
net cash transactions with the company's owners. These net transactions
equal the net of dividends paid to, stock repurchases paid to, and stock
issue payments from owners; henceforth called net dividends. The pre-
sent value of expected future net dividends can be expressed as follows
18
:
(1)
[ ]
( )
∞
=τ
τ
τ+
+
=
1 E
t,jt
t,j
r1
D~E
V
Vj,t = value of owners' equity of company j at time t
18
In order to simplify the formulas, the valuation specifications presume a flat interest and
risk premium term structure.

Dj,t = net dividends paid by company j at time t
rE,j = required rate of return on owners' equity of company j
Et[...] = expectations operator conditioned on the available information at
time t
2.2 Returns and Earnings
In order to establish a linkage between stock return and accounting earn-
ings, the term for expected net dividends in (1) can be replaced with ex-
pected earnings multiplied with a payout ratio. The valuation formula
can thus, suppressing the firm index j, be reformulated as:
(2)
[ ]
( )
∞
=τ
τ
τ+τ+
+
⋅
=
1 E
ttt
t
r1
rp~X~E
V
Xt = earnings in period t
prt = payout ratio at time t, i.e. net dividends at time t in relation to earn-
ings in period t
In order to simplify the analysis, the expected payout ratio will be treated
as a constant. With this simplification, (2) can be re-written as:
(2’)
[ ]
( )
∞
=τ
τ
τ+
+
⋅
=
1 E
tt
t
r1
prX~E
V
Based on (2’), Vt and Vt+1 can hence be expanded as:
(2’a)
( )
[ ]
( )
[ ]
( )
[ ]PttP
E
2tt2
E
1tt
E
t X~E
r1
pr
X~E
r1
pr
X~E
r1
pr
V +++ ⋅
+
++⋅
+
+⋅
+
=  ,
P → ∞
(2’b)
( )
[ ]
( )
[ ] +⋅
+
+⋅
+
= +++++ 3t1t2
E
2t1t
E
1t X~E
r1
pr
X~E
r1
pr
V

CHAPTER 2 27
( )
[ ]1Pt1tP
E
X~E
r1
pr
+++⋅
+
+ , P → ∞
Calculating the difference between Vt+1 and Vt and adding Dt+1 generates
an expression for the stock returns in period t+1. Replacing the realized
Dt+1 with pr⋅Xt+1, returns can thus be expressed in the following way:
(3)
( )
[ ]
( )
[ ]
( )
[ ] 













⋅
+
+
+⋅
+
+⋅
+
+=+Δ
+++
++++
+++
1Pt1tP
E
3t1t2
E
2t1t
E
1t1t1t
X~E
r1
pr
X~E
r1
pr
X~E
r1
pr
DDV

( )
[ ]
( )
[ ]
( )
[ ]
=














⋅
+
+
+⋅
+
+⋅
+
−
+
++
PttP
E
2tt2
E
1tt
E
X~E
r1
pr
X~E
r1
pr
X~E
r1
pr

[ ]
( )
[ ] [ ]






+
−⋅
+
+





+
−= +
++
+
+
E
2tt
2t1t
EE
1tt
1t
r1
X~E
X~E
r1
pr
r1
X~E
Xpr
( )
[ ] [ ]
( )
[ ] [ ]
( )
[ ]1Pt1tP
E
E
Ptt
Pt1t1P
E
E
3tt
3t1t2
E
X~E
r1
pr
r1
X~E
X~E
r1
pr
r1
X~E
X~E
r1
pr
+++
+
++−
+
++
⋅
+
+






+
−⋅
+
+
+





+
−⋅
+
+ 
ΔVt+1 + Dt+1 = return, i.e. change in value of owners' equity during period
t+1 plus net dividends at time t+1
As P goes towards infinity the last term can be expected to approach ze-
ro, leaving:
(3’)
( )
[ ] [ ]
( ) 





+
−⋅
+
=+Δ τ+
τ++
∞
=τ
−τ++  E
tt
t1t
1
1
E
1t1t
r1
X~E
X~E
r1
pr
DV

Formula (3’) implies that returns come from two sources. First, earnings
come one year closer in time, including the realization of earnings for the
first period t+1. Second, changes in earnings expectations influence re-
turns. This effect comes from the fact that [ ]kt1t X~E ++ may be different
from [ ]ktt X~E + . Required rate of return and payout ratio are constant in
formula (3’).
The change in earnings expectations refer to changes during a year;
from the beginning to the end of year t+1. Regarding the term
[ ]1t1t XE ++ in formula (3’), it is assumed that when expectations are
formed in the end of year t+1 earnings for year t+1 are known; i.e.
[ ] 1t1t1t XXE +++ = .
All modeling that follows is based on formula (3’), as are the hypothe-
ses that are developed for the empirical tests. These empirical tests use
regression analysis to investigate the relationship between returns for one
period and earnings for the same and future periods. The two main cate-
gories of regressions – univariate and multivariate – will in principle have
the following form:
1t1t101t1t XDV ++++ ε+α+α=+Δ
1tKtK2t21t101t1t XXXDV ++++++ ε+α++α+α+α=+Δ 
Formula (3’) can, however, not be directly used as a basis for these re-
gressions, since each factor contains the difference between earnings for
some period as expected at time t+1 and (the present value of) earnings
for the same period as expected at time t. In order to enable an investiga-
tion of the relationship between returns and future earnings it is neces-
sary to have models that contain the expected earnings levels, instead of
the difference between expected earnings.
By making assumptions about how earnings expectations change
over time, it will be possible to re-write formula (3’). In order to represent
three different kinds of earnings surprises, the following analysis uses
three general forms for the relation between earnings expectations at
time t+1 and time t.

CHAPTER 2 29
In the three sub-sections 2.2.1 to 2.2.3 below, three different time se-
ries cases for earnings are modeled. In the first case earnings are ex-
pected to be constant over time. In the second case earnings are expected
to grow at a constant rate. In the third, and final, case earnings are al-
lowed to vary stochastically over time.
Each of the three cases is in turn analyzed for three different types of
earnings surprises during the current period. First, the returns-earnings
relations during a period when observed earnings are equal to what was
expected in the beginning of the year are modeled under each case.
These sub-cases with no observed earnings surprise in period t+1 also
assume that expectations about future periods remain unchanged. Sec-
ond, the relations are modeled for a situation when observed earnings for
the current period differ from expected, but expectations regarding fu-
ture periods remain unchanged. These are the sub-cases with an ob-
served transitory earnings surprise. Third, the modeling deals with sub-
cases with and observed permanent earnings surprise – i.e. when ob-
served earnings differ from expected and expectations about future earn-
ings are revised with the same relation.
Consequently, a total of nine different special cases are modeled in
the following three sub-sections 2.2.1 to 2.2.3.
Table 6: Structure of sub-sections with different earnings time series and earnings
surprises
No earnings
surprise
Transitory earn-
ings surprise
Permanent earn-
ings surprise
Constant expected future earnings Sub-part 2.2.1.1 Sub-part 2.2.1.2 Sub-part 2.2.1.3
Constant expected future earnings
growth rate
Sub-part 2.2.2.1 Sub-part 2.2.2.2 Sub-part 2.2.2.3
Variations in expected future earnings Sub-part 2.2.3.1 Sub-part 2.2.3.2 Sub-part 2.2.3.3
In sub-section 2.2.4 a connection between the returns-earnings relation
and conservative accounting and growth is modeled. This is an extension
of the modeling with constant earnings growth rate in sub-section 2.2.2.
Finally, modeling with truncation combines the third case with constant
growth rate from a future point in time is developed in sub-section 2.2.5.

2.2.1 The First Case: Constant Expected Future Earnings
This first of three cases is the most restrictive case. It is assumed that fu-
ture earnings are expected to be constant. Using the above notation,
constant expected future earnings can be expressed as:
(4a) [ ] [ ] [ ] === +++ 3tt2tt1tt X~EX~EX~E
(4b) [ ] [ ] [ ] === ++++++ 4t1t3t1t2t1t X~EX~EX~E
Assuming constant earnings implies that the company is not growing and
that no part of earnings is retained. Hence, earnings and dividends are
assumed to be equal in this case:
(5) ktkt XD ++ =
By replacing net dividends in valuation model (1) with earnings accord-
ing to (5) and recognizing that earnings are expected to be constant, the
value of owners' equity can be formulated as:
(6a)
[ ]
( )
[ ]
E
1tt
1 E
tt
t
r
X~E
r1
X~E
V +
∞
=τ
τ
τ+
=
+
= 
(6b)
[ ]
( )
[ ]
E
2t1t
1 E
1t1t
1t
r
X~E
r1
X~E
V ++
∞
=τ
τ
+τ++
+ =
+
= 
Based on (6a) and (6b), formulas relating returns to earnings will be de-
veloped in the three following sub-parts. Three different relations be-
tween current period observed and expected earnings, and change in
expectations from t to t+1 are considered:
• No earnings surprise: observed earnings are equal to expected
earnings, and expected future earnings remain unchanged
• Transitory earnings surprise: observed earnings are different
from expected earnings, but expected future earnings remain
unchanged

CHAPTER 2 31
• Permanent earnings surprise: observed earnings are different
from expected earnings, and expected future earnings change
in accordance with the observed relative difference
2.2.1.1 No Earnings Surprise at Time t+1
In this study, the case of no earnings surprise implies both that observed
earnings are equal to expected and that expectations about future earn-
ings are unchanged from time t to t+1:
(7a) [ ]1tt1t X~EX ++ =
(7b) [ ] [ ]kttkt1t X~EX~E +++ = for k ≥ 2
The graph below illustrates this case. The dashed lines illustrate earnings
as expected at time t, while the full lines show observed earnings for pe-
riod t+1 and future earnings as expected at time t+1.
= earnings as expected at time t
= earnings as observed or expected at time t+1
Since future earnings are expected to be constant and since there is no
change in expectations, Vt and Vt+1 in (6a) and (6b) are equal:
(8) [ ] [ ] t1t1tt2t1t VVX~EX~E == ++++
Hence, the formula for returns reduces to:
(9) 1t1tt1t1t1t1t1t XXVVXVDV +++++++ =+−=+Δ=+Δ
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+k

That is, when future earnings are expected to be constant and no earn-
ings surprise is observed in the current period, returns are equal to cur-
rent earnings.
2.2.1.2 Transitory Earnings Surprise at Time t+1
In this study, the case of transitory earnings surprise implies both that
observed current earnings are different from expected and that expecta-
tions about future earnings remain unchanged from time t to t+1. This
can be expressed in the following way:
(10a) [ ]1tt1t XEX ++ ≠
(10b) [ ] [ ]kttkt1t XEXE +++ = for k ≥ 2
The graph below illustrates this case with transitory earnings surprise in
period t+1.
Since earnings expectations remain unchanged, the above relation (8)
holds also for transitory earnings surprises. Given (6a) and (6b), the con-
clusion then becomes the same as for the no-surprise-case above. When
future earnings are expected to be constant and a transitory earnings
surprise is observed in the current period, returns are equal to current
earnings:
(11) 1t1t1t XDV +++ =+Δ
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+k

CHAPTER 2 33
It can be noted that this relation is the same as Easton et al. (2000) de-
rived for transitory earnings and Kormendi & Lipe (1987) for transitory
unexpected earnings.
19
2.2.1.3 Permanent Earnings Surprise at Time t+1
In this study and for this constant earnings case, the case of permanent
earnings surprise implies both that observed current earnings are differ-
ent from expected and that expectations about future earnings change to
the observed earnings value. This can be expressed in the following way:
(12a) [ ]1tt1t XEX ++ ≠
(12b) [ ] 1tkt1t XXE +++ = for k ≥ 2
The graph below illustrates this case with permanent earnings surprise in
period t+1.
By substituting (12b) into (6b) and using (6a), a linkage between return
and current earnings can be derived. The returns-earnings relation can
now be expressed in the following way:
(13)
[ ]
1t
E
1tt
E
1t
1t1t1t1t X
r
X~E
r
X
XVDV +
++
++++ +−=+Δ=+Δ
[ ]
[ ]








+
⋅
−⋅=+−= ++
++
1
Gr
1
r
1
XX
r
GX
r
X
XEEE
1t1t
E
XE1t
E
1t
19
See sub-section 1.5.2, ”Valuation Models and the Relation between Returns and Earn-
ings”.
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9 t+k

[ ]
[ ]
[ ]





 −
+⋅=








⋅
−
+⋅= ++
E
XE
1t
EXE
XE
1t
r
G11
1X
rG
1G
1X
GE[X] = [ ]1tt1t X~EX ++ , i.e. one plus the relative earnings surprise
That is, when future earnings are expected to be constant and a perma-
nent earnings surprise is observed in the current period, returns are ex-
pected to be larger (smaller) than earnings when the surprise is positive
(negative). More exactly, returns equal current earnings plus the capital-
ized difference between observed and expected earnings.
20
When the relative earnings surprise is positive and very large (GE[X] →
∞), the expected earnings coefficient becomes equal to 1 + 1/rE. This is
the same upper limit as Easton et al. (2000) derived for permanent earn-
ings and Kormendi & Lipe (1987) for permanent unexpected earnings.
21
The case of no earnings surprise can viewed as a special case by setting
GE[X] = 1. The earnings coefficient in formula (13) then reduces to 1. Ta-
ble 7 illustrates expected earnings coefficients for different values of the
relative permanent earnings surprise and the required rate of return.
20
By multiplying Xt
into the parenthesis and replacing Xt
/GE[X]
with [ ]1tt X~E + formula (13)
can also be written as: [ ]( ) E1tt1t1t1t1t rX~EXXDV +++++ −+=+Δ .
21
See sub-section 1.5.2, ”Valuation Models and the Relation between Returns and Earn-
ings”. Note that when GE[X]
goes towards infinity, Xt+1
goes towards being equal to the
earnings surprise; i.e. [ ]1tt1t1t X~EXX +++ −→ when [ ] ∞→XEG .

CHAPTER 2 35
Table 7: Earnings coefficient as specified in (13) – constant expected future earn-
ings and permanent earnings surprise
5% 8% 10% 12% 15% 20%
0.50 -19.00 -11.50 -9.00 -7.33 -5.67 -4.00
0.70 -7.57 -4.36 -3.29 -2.57 -1.86 -1.14
0.90 -1.22 -0.39 -0.11 0.07 0.26 0.44
0.95 -0.05 0.34 0.47 0.56 0.65 0.74
1.00 1.00 1.00 1.00 1.00 1.00 1.00
1.05 1.95 1.60 1.48 1.40 1.32 1.24
1.10 2.82 2.14 1.91 1.76 1.61 1.45
1.30 5.62 3.88 3.31 2.92 2.54 2.15
1.50 7.67 5.17 4.33 3.78 3.22 2.67
2.00 11.00 7.25 6.00 5.17 4.33 3.50
3.00 14.33 9.33 7.67 6.56 5.44 4.33
5.00 17.00 11.00 9.00 7.67 6.33 5.00
∞ 21.00 13.50 11.00 9.33 7.67 6.00
GE[X]
r E
In the table, the special case of no earnings surprise can be seen as a
“line” between positive and negative permanent earnings surprises. The
table illustrates that the present value of a positive (negative) permanent
surprise is recognized via an earnings coefficient above (below) one.
Since the present value is larger when the required rate of return is lower
the coefficients in columns more to the left vary more.
It should be noted that permanent earnings surprises can have a
large impact on the coefficient for current earnings. If the required rate
of return on owners' equity is 10 %, a positive revision of future earnings
with 10 % means that returns will be almost twice as large as current
earnings; while a negative revision of future earnings with 10 % would
make the coefficient negative. When GE[X] = 1/(1+rE) the coefficient will
be equal to zero; as e.g. when rE is equal to 10 % and GE[X] is equal to
0.91.

2.2.2 The Second Case: Constant Expected Future
Earnings Growth Rate
In this second case, the previous restriction that earnings are expected to
be constant is relaxed and replaced with the assumption that earnings
are expected to grow with a constant rate. Assuming constant earnings
growth rate and payout ratio, valuation formula (2’) can be simplified as:
(14a)
[ ]
XE
1tt
t
gr
prX~E
V
−
⋅
= +
gX = future growth rate in earnings;
[ ] [ ] 1XXE1XXE kt1kt1tjt1jtt −=− +++++++ , for k ≥ 2
22
The value of owners' equity at the end of the return period can be ex-
pressed correspondingly:
(14b)
[ ]
XE
2t1t
1t
gr
prX~E
V
−
⋅
= ++
+
The analysis of the constant earnings growth case will hence be based on
the following formulation of returns:
(15)
[ ] [ ]
1t
XE
1tt
XE
2t1t
1t1t D
gr
prX~E
gr
prX~E
DV +
+++
++ +
−
⋅
−
−
⋅
=+Δ
The previous case of constant earnings is a special case of this constant
growth rate case. In the case of no earnings growth all future earnings
are equal and full payout is implied, meaning that future dividends are
also equal to future earnings. Replacing both earnings and the dividend
22
The expected growth rate is assumed not to change between time t and time t+1. In or-
der for this constant growth case to be meaningful, gX
need to be lower than rE
and earn-
ings for the next period expected to be positive.

CHAPTER 2 37
in (15) with Xt+1 the formula reduces to the relation that was derived for
the constant earnings case (in formula (9)).
The case of no earnings surprise implies both that observed earnings are
equal to expected and that expectations about future earnings are un-
changed from time t to t+1. In this constant earnings growth case, no
earnings surprise can be expressed as:
(16a) [ ]1tt1t X~EX ++ =
(16b) [ ] [ ] 1k
X1tkttkt1t GXXEX~E −
++++ ⋅== for k ≥ 2
GX = 1 + gX
The following graph illustrates this case with no earnings surprise in pe-
riod t+1.
Under these conditions, and assuming that actual payout ratio at time
t+1 equals expected pr, return formula (15) can be re-written as follows:
(17)
XE
E
1t1t
XE
1t
XE
X1t
1t1t
gr
r
prXprX
gr
prX
gr
prGX
DV
−
⋅⋅=⋅+
−
⋅
−
−
⋅⋅
=+Δ ++
++
++
Formula (17) expresses that with constant expected earnings and divi-
dend growth and during a period with neither any earnings surprise nor
any changes in earnings expectations, the return is equal to the value at
the beginning of the period [(Xt+1 · pr) / (rE - gX)] times the required re-
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9

turn. Formula (17) also expresses that – ceteris paribus – the earnings
coefficient is expected to be larger when the payout ratio is higher, the
earnings growth higher, or the required return lower
23
. Table 8 illustrates
expected earnings coefficients for different values of payout ratio, re-
quired rate of return, and earnings growth rate.
ings growth rate and no earnings surprise
pr: 0.5
5% 8% 10% 12% 15% 20%
2% 0.833 0.667 0.625 0.600 0.577 0.556
4% 2.500 1.000 0.833 0.750 0.682 0.625
6% n/a 2.000 1.250 1.000 0.833 0.714
8% n/a n/a 2.500 1.500 1.071 0.833
pr: 0.6
5% 8% 10% 12% 15% 20%
2% 1.000 0.800 0.750 0.720 0.692 0.667
4% 3.000 1.200 1.000 0.900 0.818 0.750
6% n/a 2.400 1.500 1.200 1.000 0.857
8% n/a n/a 3.000 1.800 1.286 1.000
pr: 0.8
5% 8% 10% 12% 15% 20%
2% 1.333 1.067 1.000 0.960 0.923 0.889
4% 4.000 1.600 1.333 1.200 1.091 1.000
6% n/a 3.200 2.000 1.600 1.333 1.143
8% n/a n/a 4.000 2.400 1.714 1.333
gXgXgX
r E
r E
r E
With constant earnings growth, the coefficient to be multiplied with
earnings can even in the case of no earnings surprise be different from
one. E.g., the coefficient is larger than one when rE · (1 - pr) < gX. As-
sumptions involving conservatism in accounting will be added below in
sub-section 2.2.4 and its three sub-parts.
23
Assuming that: 0 < gX
< rE
.

CHAPTER 2 39
As above, the case of transitory earnings surprise implies both that ob-
served current earnings are different from expected and that expectations
about future earnings remain unchanged from time t to t+1. For this
constant earnings growth rate case, transitory earnings surprise can be
expressed in the following way:
(18a) [ ] [ ]XE1tt1t GX~EX ⋅= ++
(18b) [ ] [ ] [ ] 1k
X1ttkttkt1t GX~EX~EX~E −
++++ ⋅== for k ≥ 2
The following graph illustrates transitory earnings surprise in period t+1.
Using the constant steady-state payout ratio for the observed period t+1
earnings and still not changing the earnings expectations for future years
would not be totally satisfying. If period t+1 e.g. sees a large positive
earnings surprise, more value than expected is created. If not all of this
extra value is distributed, any cash in the retained part could at least be
used to create interest income or reduce loans and interest expenses.
24
The following modeling assumes that the amount that is retained in pe-
riod t+1 is the same as was expected in the beginning of the period:
(19) [ ] [ ]( )1tt1t1tt1t X~EXprX~ED ++++ −+⋅=
Given expressions (18a) and (18b), (19) can be re-written as:
24
This would be the case if the company’s investment plan is fixed, as in Modigliani & Mil-
ler (1958).
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9

(19’)
[ ] [ ] [ ]
[ ]
[ ] [ ]
=








−+⋅=−+⋅= +
+
+
+
+
XEXE
XE
XE
1t
XE
1t
1t
XE
1t
1t
G
1
G
G
G
pr
X
G
X
Xpr
G
X
D
[ ]( ) [ ]XEXE1t GgprX +⋅= +
gE[X] = GE[X] - 1
Under these conditions, return formula (15) can be re-written as follows:
(20)
[ ] [ ] [ ]( )
[ ]
=
+⋅
+
−
⋅
−
−
⋅⋅
=+
+++
++
XE
XE1t
XE
XE1t
XE
XXE1t
1t1t
G
gprX
gr
prGX
gr
prGGX
DV
[ ]
[ ]XE
XE
XE
X
1t
G
gpr
gr
gpr
X






++
−
⋅
⋅= +
Table 9 illustrates expected earnings coefficients for different values of
the transitory earnings surprise, payout ratio, and earnings growth rate.

CHAPTER 2 41
ings growth rate and transitory earnings surprise
r E g X pr G E[X] Coeff r E g X pr G E[X] Coeff
0.12 0.08 0.50 2.0 1.250 0.12 0.04 0.50 2.0 0.875
0.12 0.08 0.50 1.3 1.385 0.12 0.04 0.50 1.3 0.808
0.12 0.08 0.50 1.0 1.500 0.12 0.04 0.50 1.0 0.750
0.12 0.08 0.50 0.7 1.714 0.12 0.04 0.50 0.7 0.643
0.12 0.08 0.50 0.1 6.000 0.12 0.04 0.50 0.1 -1.500
0.12 0.08 0.50 -0.1 -4.000 0.12 0.04 0.50 -0.1 3.500
0.12 0.08 0.50 -2.0 0.750 0.12 0.04 0.50 -2.0 1.125
0.12 0.08 0.60 2.0 1.400 0.12 0.04 0.60 2.0 0.950
0.12 0.08 0.60 1.3 1.615 0.12 0.04 0.60 1.3 0.923
0.12 0.08 0.60 1.0 1.800 0.12 0.04 0.60 1.0 0.900
0.12 0.08 0.60 0.7 2.143 0.12 0.04 0.60 0.7 0.857
0.12 0.08 0.60 0.1 9.000 0.12 0.04 0.60 0.1 0.000
0.12 0.08 0.60 -0.1 -7.000 0.12 0.04 0.60 -0.1 2.000
0.12 0.08 0.60 -2.0 0.600 0.12 0.04 0.60 -2.0 1.050
0.12 0.08 0.80 2.0 1.700 0.12 0.04 0.80 2.0 1.100
0.12 0.08 0.80 1.3 2.077 0.12 0.04 0.80 1.3 1.154
0.12 0.08 0.80 1.0 2.400 0.12 0.04 0.80 1.0 1.200
0.12 0.08 0.80 0.7 3.000 0.12 0.04 0.80 0.7 1.286
0.12 0.08 0.80 0.1 15.000 0.12 0.04 0.80 0.1 3.000
0.12 0.08 0.80 -0.1 -13.000 0.12 0.04 0.80 -0.1 -1.000
0.12 0.08 0.80 -2.0 0.300 0.12 0.04 0.80 -2.0 0.900
Table 9 illustrates that positive transitory earnings surprises (GE[X] > 1)
are not associated with any extreme levels on the earnings coefficient – it
does e.g. not become negative or very large. As the table illustrates and
as can be seen from formula (20), the larger the positive earnings surprise
is, the closer to one the earnings coefficient gets.
25
Negative transitory
earnings surprises (GE[X] < 1) have a more complex effect on the earnings
coefficient. The table illustrates that the coefficient sometimes receives
large positive values and sometimes very negative values. The different
signs depend on the sign on observed earnings and on whether the nega-
tive surprise is negative enough to make returns negative. The large coef-
ficients – positive or negative – are associated with situations when
25
GE[X]
→ ∞  Coeff → 1

observed earnings are close to zero (i.e. when GE[X] is close to zero) while
returns are not as close to zero. Assumptions involving conservatism in
accounting will be added below in sub-section 2.2.4 and its three sub-
parts.
The case of permanent earnings surprise implies both that observed cur-
rent earnings are different from expected and that expectations about
future earnings change with the observed relative earnings surprise. This
can be expressed in the following way:
(21a) [ ] [ ]XE1tt1t GX~EX ⋅= ++
(21b) [ ] [ ] [ ]XEkttkt1t GX~EX~E ⋅= +++ for k ≥ 2
The following graph illustrates permanent earnings surprise in period
t+1.
(21a) can be re-arranged to [ ] [ ]1tt1tXE X~EXG ++= , which together with
(21b) gives:
(21c) [ ] [ ] [ ] [ ]
[ ] X1t
1tt
1t
2ttXE2tt2t1t GX
X~E
X
X~EGX~EX~E ⋅=⋅=⋅= +
+
+
++++
Assuming that the actual payout ratio at time t+1 equals expected pr and
using the re-arranged version [ ] [ ]XE1t1tt GXX~E ++ = of (21a), return
formula (15) can be re-written as:
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+9

CHAPTER 2 43
(22)
( ) [ ]( )
=⋅+
⋅⋅⋅
=+Δ +
++
++ prX
gr
prG
gr
prGX
DV 1t
XE
XE
XE
X1t
1t1t
-
X
-
-
1t
[ ] ( )
=








+
⋅
⋅⋅= + 1
grG
1
gr
G
prX
XEXEXE
X
1t
-
-
-
[ ]
XE
EXE
1t
gr
rG
prX
-
1-1 +
⋅⋅= +
Based on (22), table 10 illustrates different earnings coefficient values for
different sizes of permanent earnings surprise, rates of growth, and pay-
out ratios.
Table 10: Earnings coefficient as specified in (22) – constant expected future
earnings growth rate and permanent earnings surprise
r E g X pr G E[X] Coeff r E g X pr G E[X] Coeff
0.12 0.08 0.50 1.3 4.385 0.12 0.04 0.50 1.3 2.192
0.12 0.08 0.50 1.0 1.500 0.12 0.04 0.50 1.0 0.750
0.12 0.08 0.50 0.7 -3.857 0.12 0.04 0.50 0.7 -1.929
0.12 0.08 0.60 1.3 5.262 0.12 0.04 0.60 1.3 2.631
0.12 0.08 0.60 1.0 1.800 0.12 0.04 0.60 1.0 0.900
0.12 0.08 0.60 0.7 -4.629 0.12 0.04 0.60 0.7 -2.314
0.12 0.08 0.80 1.3 7.015 0.12 0.04 0.80 1.3 3.508
0.12 0.08 0.80 1.0 2.400 0.12 0.04 0.80 1.0 1.200
0.12 0.08 0.80 0.7 -6.171 0.12 0.04 0.80 0.7 -3.086
0.12 0.06 0.50 1.3 2.923
0.12 0.06 0.50 1.0 1.000
0.12 0.06 0.50 0.7 -2.571
0.12 0.06 0.60 1.3 3.508
0.12 0.06 0.60 1.0 1.200
0.12 0.06 0.60 0.7 -3.086
0.12 0.06 0.80 1.3 4.677
0.12 0.06 0.80 1.0 1.600
0.12 0.06 0.80 0.7 -4.114
As was also noted for the case with constant earnings, table 10 highlights
that permanent earnings surprises can have considerable influence on
the earnings coefficient. The larger the positive surprise, the larger the

coefficient. The more negative the surprise, the lower the coefficient –
only very small negative surprises do not motivate a negative coefficient.
26
Assumptions involving conservatism in accounting will be added below
in sub-section 2.2.4 and its three sub-parts.
2.2.3 The Third Case: Variations in Expected Future
Earnings
The previous two cases are based on stable patterns of expected future
earnings. This third case does not make any such assumption about the
development of expected future earnings – future earnings are here al-
lowed to follow any pattern.
As above, the case of no earnings surprise implies both that observed
earnings are equal to expected and that expectations about future earn-
ings are unchanged from time t to t+1:
(23a) [ ]1tt1t X~EX ++ =
The graph below illustrates the case when expected future earnings can
vary over time, when there is no earnings surprise for period t+1, and
when expectations about future earnings remain unchanged.
26
Stock values are assumed to be positive, which implies that the growing future earnings
are assumed to be positive. This in turn implies that a permanent earnings surprise cannot
be based on negative observed earnings, which means that GE[X]
in this purely permanent
earnings surprise case is implied to be larger than zero.
t+2t+1 t+3 t+4 t+5 t+6 t+7 t+8 t+k

CHAPTER 2 45
This scenario implies that the terms within the large brackets in formula
(3’) can be specified in the following way:
(24) [ ] [ ] [ ] ( ) [ ] [ ]
E
E
kt
E
ktEkt
E
kt
kt
r1
r
X~E
r1
X~Er1X~E
r1
X~E
X~E
+
⋅=
+
−+⋅
=
+
− +
+++
+
Substituting into (3’) gives the following expression for returns:
(25) [ ]
( )
[ ]
( )
+
+
⋅
⋅+
+
⋅
⋅+
+
⋅
⋅=+Δ +++++ 3
E
E
3t2
E
E
2t
E
E
1t1t1t
r1
rpr
X~E
r1
rpr
X~E
r1
rpr
XDV
[ ]
( )P
E
E
Pt
r1
rpr
X~E
+
⋅
⋅+ + , P → ∞
Allowing current and future earnings to be uncorrelated, the right hand
side does not reduce to only including current earnings. Under these
conditions future earnings add to the linkage between returns and earn-
ings. The earnings coefficients depend on the remoteness of earnings, the
required rate of return and on the payout ratio.
The effect of earnings on returns equals the present value of having
the dividend part of each period's earnings one period closer in time.
The first earnings coefficient results from discounting one period, the
second coefficient from two periods of discounting etc. Earnings coeffi-
cients are hence expected to continuously decrease with the remoteness
of earnings.
The required rate of return is a company specific factor that is ex-
pected to have an impact on the size of the coefficients. The higher the
required rate of return, the higher the effect of earnings close in time and
the lower the effect of earnings remote in time on returns. The intuition
is that with a high required rate of return, more is gained from having
future earnings one period closer in time. However, if the gain is far into
the future, its present value will be lower with a high rate of return. Eve-

rything else being constant, this mean that returns for high-risk compa-
nies are expected to be more sensitive to the size of expected earnings
that are relatively close in time. Also, the coefficient-size for earnings fur-
ther away in the future would be expected to decrease faster for high-risk
companies than for low-risk companies.
Another company specific factor affecting the size of the coefficients
is the payout ratio. As can be seen from formula (25) the higher the pay-
out ratio, the larger the effect of earnings on returns. More is earned
from having the earnings one year closer in time if a larger share of earn-
ings is paid as dividends.
The following tables 11a-b illustrate the size of the coefficients for
earnings for different future periods, different values of the required rate
of return, and payout ratio. The calculations are based on formula (25).

CHAPTER 2 47
Case: variable future earnings, no earnings surprise [based on formula (25)]
Table 11a (rE=10 %): Earnings coefficients for the current (k=1) and nine future
periods (k=2 to 10)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 0 0.009 0.018 0.027 0.036 0.045 0.055 0.064 0.073 0.082 0.091
2 0 0.008 0.017 0.025 0.033 0.041 0.050 0.058 0.066 0.074 0.083
3 0 0.008 0.015 0.023 0.030 0.038 0.045 0.053 0.060 0.068 0.075
4 0 0.007 0.014 0.020 0.027 0.034 0.041 0.048 0.055 0.061 0.068
5 0 0.006 0.012 0.019 0.025 0.031 0.037 0.043 0.050 0.056 0.062
6 0 0.006 0.011 0.017 0.023 0.028 0.034 0.040 0.045 0.051 0.056
7 0 0.005 0.010 0.015 0.021 0.026 0.031 0.036 0.041 0.046 0.051
8 0 0.005 0.009 0.014 0.019 0.023 0.028 0.033 0.037 0.042 0.047
9 0 0.004 0.008 0.013 0.017 0.021 0.025 0.030 0.034 0.038 0.042
10 0 0.004 0.008 0.012 0.015 0.019 0.023 0.027 0.031 0.035 0.039
Payout ratio (pr)
kperiodsintothefuture
Table 11b (rE=20 %): Earnings coefficients for the current (k=1) and nine future
periods (k=2 to 10)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 0 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167
2 0 0.014 0.028 0.042 0.056 0.069 0.083 0.097 0.111 0.125 0.139
3 0 0.012 0.023 0.035 0.046 0.058 0.069 0.081 0.093 0.104 0.116
4 0 0.010 0.019 0.029 0.039 0.048 0.058 0.068 0.077 0.087 0.096
5 0 0.008 0.016 0.024 0.032 0.040 0.048 0.056 0.064 0.072 0.080
6 0 0.007 0.013 0.020 0.027 0.033 0.040 0.047 0.054 0.060 0.067
7 0 0.006 0.011 0.017 0.022 0.028 0.033 0.039 0.045 0.050 0.056
8 0 0.005 0.009 0.014 0.019 0.023 0.028 0.033 0.037 0.042 0.047
9 0 0.004 0.008 0.012 0.016 0.019 0.023 0.027 0.031 0.035 0.039
10 0 0.003 0.006 0.010 0.013 0.016 0.019 0.023 0.026 0.029 0.032
Payout ratio (pr)
Firstly, tables 11a-b illustrate the previously mentioned decay in the size
of the coefficient for earnings further into the future. E.g. for a payout
ratio of 0.6, the coefficients start at 0.055 and 0.100 for current earnings
and decreases to 0.023 and 0.019 for earnings nine years later for re-
quired rates of return of 10 % and 20 %, respectively.

Secondly, the effect of different levels of the required rate of return is
present in the tables. Earnings close in time have higher coefficients for
higher required rates of return, for all values of the payout ratio. For cur-
rent earnings the coefficient is almost twice as large when the required
rate of return is 20 % as when it is 10 %. Differences in the size of the
coefficients become smaller for earnings more remote in time, and finally
the differences shift.
Finally, the previously discussed effect of the payout ratio can be il-
lustrated in the tables. The ratio of two compared levels of payout ratios,
gives the ratio of the coefficients. See e.g. table 11b, period one; where
payout ratios 0.3, 0.6, and 0.9 are associated with coefficient sizes of re-
spectively 0.050, 0.100, and 0.150.
With transitory earnings surprise is meant that observed current earnings
are different from expected and that expectations about future earnings
remain unchanged from time t to t+1, which can be expressed as:
(26a) [ ] [ ]XE1tt1t GX~EX ⋅= ++
A graphical illustration of this sub-case:
Since expectations about future earnings are unchanged in this case, a
similar derivation as in the no surprise case can be made here. The dif-
ference is that here (24) is substituted into the large brackets in formula
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+k

CHAPTER 2 49
(3’) only for future periods (i.e. k ≥ 2). For the current period (k = 1) the
following expression is substituted into the large brackets in formula (3’):
(27) [ ] [ ] [ ]
E
XE1t
1t
E
1tt
1t1t
r1
GX
X
r1
XE
XE
+
−=
+
−
+
+
+
++
This results in the following returns formula:
27
(28)
[ ] ( )
[ ]
( )2
E
E
2t
EXE
1t1t1t
r1
rpr
X~E
r1G
1
1prXDV
+
⋅
⋅+








+⋅
−⋅=+Δ ++++
[ ]
( )
[ ]
( )P
E
E
Pt3
E
E
3t
r1
rpr
X~E
r1
rpr
X~E
+
⋅
⋅++
+
⋅
⋅+ ++  , P → ∞
If GE[X] in formula (28) is set to one, the formula reduces to the special
case with no earnings surprise as in formula (25). As is previously known
from permanent earnings surprise cases, a very large surprise (GE[X] → ∞)
also in this transitory surprise case makes the coefficient for current earn-
ings (1+rE)/rE times larger than in the no earnings surprise case.
28
Finally,
a special case when the coefficient for current earnings is expected to
equal zero is worth noting – this occurs when GE[X] = 1/(1+rE).
Using formula (28) instead of (25) will obviously change the coeffi-
cient for the first period (k = 1). If realized earnings are higher (lower)
than expected, the coefficient will be larger (smaller) than as previously
specified in tables 11a-b, and vice versa. Tables 12a-b below illustrate
27
The difference between the coefficient for current earnings in formula (28) and formula
(25) is equal to
[ ]
( )E
XE
r1
G11
pr
+
−
⋅ . With a high payout ratio a large share of the earnings
surprise will be paid out as dividends and therefore the surprise has a large effect on re-
turns. Large earnings surprises also have noticeable effects on the coefficient. Finally, the
effect of an earnings surprise is smaller when the required rate of return is high.
28
The ratio between corresponding coefficients in formula (30) and (25) is equal to
[ ]
E
XE
r
G11
1
−
+ .

coefficient values for current earnings for different degrees of transitory
earnings surprise.
Case: variable future earnings, transitory earnings surprise [based on for-
mula (28)]
Table 12a (rE=10 %): Coefficient for current earnings
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.5 0 -0.082 -0.164 -0.245 -0.327 -0.409 -0.491 -0.573 -0.655 -0.736 -0.818
0.7 0 -0.030 -0.060 -0.090 -0.119 -0.149 -0.179 -0.209 -0.239 -0.269 -0.299
0.9 0 -0.001 -0.002 -0.003 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009 -0.010
1.0 0 0.009 0.018 0.027 0.036 0.045 0.055 0.064 0.073 0.082 0.091
1.1 0 0.017 0.035 0.052 0.069 0.087 0.104 0.121 0.139 0.156 0.174
1.3 0 0.030 0.060 0.090 0.120 0.150 0.180 0.210 0.241 0.271 0.301
1.6 0 0.043 0.086 0.130 0.173 0.216 0.259 0.302 0.345 0.389 0.432
2.0 0 0.055 0.109 0.164 0.218 0.273 0.327 0.382 0.436 0.491 0.545
3.0 0 0.070 0.139 0.209 0.279 0.348 0.418 0.488 0.558 0.627 0.697
4.0 0 0.077 0.155 0.232 0.309 0.386 0.464 0.541 0.618 0.695 0.773
5.0 0 0.082 0.164 0.245 0.327 0.409 0.491 0.573 0.655 0.736 0.818
Payout ratio (pr)
GE[X]
Table 12b (rE=20 %): Coefficient for current earnings
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.5 0 -0.067 -0.133 -0.200 -0.267 -0.333 -0.400 -0.467 -0.533 -0.600 -0.667
0.7 0 -0.019 -0.038 -0.057 -0.076 -0.095 -0.114 -0.133 -0.152 -0.171 -0.190
0.9 0 0.007 0.015 0.022 0.030 0.037 0.044 0.052 0.059 0.067 0.074
1.0 0 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167
1.1 0 0.024 0.048 0.073 0.097 0.121 0.145 0.170 0.194 0.218 0.242
1.3 0 0.036 0.072 0.108 0.144 0.179 0.215 0.251 0.287 0.323 0.359
1.6 0 0.048 0.096 0.144 0.192 0.240 0.288 0.335 0.383 0.431 0.479
2.0 0 0.058 0.117 0.175 0.233 0.292 0.350 0.408 0.467 0.525 0.583
3.0 0 0.072 0.144 0.217 0.289 0.361 0.433 0.506 0.578 0.650 0.722
4.0 0 0.079 0.158 0.238 0.317 0.396 0.475 0.554 0.633 0.713 0.792
5.0 0 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 0.833
GE[X]
Payout ratio (pr)
The coefficients for current earnings for the no earnings surprise case are
shown on the row for GE[X] = 1.0. These are obviously the same as the
coefficients for k = 1 in tables 11a-b. In addition to this, tables 12a-b

CHAPTER 2 51
show that positive earnings surprises (GE[X] > 1) increase the size of the
coefficient while negative earnings surprises (GE[X] < 1) decrease the size
of the coefficient. The situation when the coefficient is close to zero is
illustrated in the table for rE = 10 % by the row for GE[X] = 0.9.
As in the previous permanent earnings surprise case, permanent earnings
surprise means that observed current earnings are different from ex-
pected and that expectations about future earnings change with the ob-
served relative earnings surprise. This can be expressed in the following
way:
(29a) [ ] [ ]XE1tt1t GX~EX ⋅= ++
(29b) [ ] [ ] [ ]XEkttkt1t GX~EX~E ⋅= +++ for k ≥ 2
The following graph illustrates this permanent earnings surprise in peri-
od t+1.
Substituting the re-arranged version [ ]ktt X~E + = [ ] [ ]XEkt1t GX~E ++ of
(29b) into formula (3’) gives:
t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 t+k

(30)
[ ] ( )







+⋅
−⋅⋅=+Δ +++
EXE
1t1t1t
r1G
1
1prXDV
[ ]
[ ] ( )







+⋅
−⋅
+
⋅+ ++
EXEE
2t1t
r1G
1
1
r1
pr
X~E
[ ]
( ) [ ] ( )
+








+⋅
−⋅
+
⋅+ ++
EXE
2
E
3t1t
r1G
1
1
r1
pr
X~E
[ ]
( ) [ ] ( )







+⋅
−⋅
+
⋅+ −++
EXE
1P
E
Pt1t
r1G
1
1
r1
pr
X~E , P → ∞
As in the previous sub-part, setting GE[X] in formula (30) to one reduces
the formula to the special case with no earnings surprise as in formula
(25). In the previous transitory surprise case a very large surprise (GE[X] →
∞) made the coefficient for current earnings (1+rE)/rE times larger than in
the no surprise case. Formula (30) shows that with a very large perma-
nent earnings surprise all earnings coefficients are influenced in this way.
Also, the earnings coefficients are expected to be equal to zero when GE[X]
= 1/(1+rE).
Formula (30) also illustrates that permanent earnings surprises create
larger return effects when rates of return are low. The reason for this is
that the revisions of expected future earnings are discounted with a
smaller factor.
Tables 13a-h below present expected coefficients for four different
degrees of permanent earnings surprises (GE[X] = 1.2, GE[X] = 1.1, GE[X] =
0.9, and GE[X] = 0.8) and two different required rates of return (10 % and
20 %).

CHAPTER 2 53
Case: variable future earnings, permanent earnings surprise [based on for-
mula (30)]
Table 13a (rE=10 %; GE[X]=1.2): Earnings coefficients for the current (k=1) and
nine future periods (k=2 to 10)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 0 0.024 0.048 0.073 0.097 0.121 0.145 0.170 0.194 0.218 0.242
2 0 0.022 0.044 0.066 0.088 0.110 0.132 0.154 0.176 0.198 0.220
3 0 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0.180 0.200
4 0 0.018 0.036 0.055 0.073 0.091 0.109 0.127 0.146 0.164 0.182
5 0 0.017 0.033 0.050 0.066 0.083 0.099 0.116 0.132 0.149 0.166
6 0 0.015 0.030 0.045 0.060 0.075 0.090 0.105 0.120 0.135 0.151
7 0 0.014 0.027 0.041 0.055 0.068 0.082 0.096 0.109 0.123 0.137
8 0 0.012 0.025 0.037 0.050 0.062 0.075 0.087 0.100 0.112 0.124
9 0 0.011 0.023 0.034 0.045 0.057 0.068 0.079 0.090 0.102 0.113
10 0 0.010 0.021 0.031 0.041 0.051 0.062 0.072 0.082 0.093 0.103
Payout ratio (pr)
Table 13b (rE=10 %; GE[X]=1.1): Earnings coefficients for the current (k=1) and
nine future periods (k=2 to 10)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 0 0.017 0.035 0.052 0.069 0.087 0.104 0.121 0.139 0.156 0.174
2 0 0.016 0.032 0.047 0.063 0.079 0.095 0.110 0.126 0.142 0.158
3 0 0.014 0.029 0.043 0.057 0.072 0.086 0.100 0.115 0.129 0.143
4 0 0.013 0.026 0.039 0.052 0.065 0.078 0.091 0.104 0.117 0.130
5 0 0.012 0.024 0.036 0.047 0.059 0.071 0.083 0.095 0.107 0.119
6 0 0.011 0.022 0.032 0.043 0.054 0.065 0.075 0.086 0.097 0.108
7 0 0.010 0.020 0.029 0.039 0.049 0.059 0.069 0.078 0.088 0.098
8 0 0.009 0.018 0.027 0.036 0.045 0.053 0.062 0.071 0.080 0.089
9 0 0.008 0.016 0.024 0.032 0.040 0.049 0.057 0.065 0.073 0.081
10 0 0.007 0.015 0.022 0.029 0.037 0.044 0.052 0.059 0.066 0.074
Payout ratio (pr)

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