Empirical Testing of Parsimonious
Equity Valuation Models1
Carl Fredrik Danielson2, Martin Grund3 and John Gyllenhammar4
18 December 2007
Master’s Thesis in Finance/Accounting and Financial Management
Stockholm School of Economics
Tutor: Professor Kenth Skogsvik
Abstract
This paper empirically evaluates the ability among different parsimonious equity
valuation models to withstand factors causing valuation errors and to estimate the
fair market value. The asset-based book value of owners’ equity and the discounted
cash flow based capitalised earnings model are empirically evaluated along with the
terminal value constrained versions of Residual Income Valuation and Abnormal
Earnings Growth valuation models. Extended and altered versions of these models
are also evaluated. The empirical testing is performed by estimating and comparing
the valuation errors for a sample of publicly traded Swedish companies over the time
period 1998-2007. The constrained versions of Residual Income Valuation and
Abnormal Earnings Growth valuation models generally provide smaller absolute
valuation errors than the book value and capitalised earnings respectively. Adjusting
the Residual Income Valuation model for the valuation bias at the horizon point of
time is found to be a feasible extension of the model under the provision that an
accurate estimation of the valuation bias is available. Evaluating the Abnormal
Earnings Growth valuation model against the Residual Income Valuation model
shows that the abnormal earnings-based approach generally seems to capture
valuation biases to a larger extent and on average provides a smaller average absolute
valuation error.
1
The authors gratefully acknowledge Professor Kenth Skogsvik for helpful comments and guidance.
[email protected]
3 [email protected]
4 [email protected]
2
1
Table of Contents
1. Introduction and Purpose .......................................................................................................................4
2. Summary ....................................................................................................................................................6
3. Valuation Models and Hypotheses ........................................................................................................8
3.1. Assumptions and Notations.............................................................................................................8
3.2. Introduction to Models...................................................................................................................10
3.3. Book Value of Owners’ Equity .....................................................................................................10
3.4. The Residual Income Valuation Model and Its Terminal Value Constrained Version........11
3.5. The Terminal Value Constrained Residual Income Valuation Model Extended with
Permanent Measurement Bias Adjustment.........................................................................................12
3.6. The Capitalised Earnings Model in Two Versions.....................................................................13
3.7. The Abnormal Earnings Growth Valuation Model and Its Terminal Value Constrained
Version......................................................................................................................................................14
3.8. Hypotheses........................................................................................................................................15
4. Data...........................................................................................................................................................19
4.1. Data Set, Descriptive Statistics and Consistency Checks ..........................................................19
5. Empirical Analysis ..................................................................................................................................22
5.1. Modelling Assumptions ..................................................................................................................22
5.2. Book Value of Owners’ Equity .....................................................................................................26
5.3. The Terminal Value Constrained Residual Income Valuation Model ....................................27
5.4. The Permanent Measurement Bias Extended Version of RIV(TVC).....................................28
5.5. The Capitalised Earnings Model (Required Rate of Return on Equity) .................................32
5.6. The Capitalised Earnings Model (The Risk-free Interest Rate) ...............................................33
5.7. The Terminal Value Constrained Abnormal Earnings Growth Valuation Model................35
5.8. Testing of Hypothesis 1..................................................................................................................37
5.9. Testing of Hypothesis 2 and Sub-Hypothesis.............................................................................38
5.10. Testing of Hypothesis 3................................................................................................................41
5.11. Testing of Hypothesis 4................................................................................................................42
5.12. Testing of Hypothesis 5................................................................................................................44
5.13. Summary of Empirical Results and Statistical Testing ............................................................46
6. Discussion of Empirical Results and Concluding Comments ........................................................50
6.1. Discussion of Empirical Results....................................................................................................50
6.2. The Validity and Robustness of the Empirical Results .............................................................56
7. References................................................................................................................................................59
8. Appendix..................................................................................................................................................60
8.1. Appendix 1: Derivation of AEG(TVC) from PVED................................................................60
2
8.2. Appendix 2: GICS Industry Sectors and GICS Level 1 Sector Group Indexes....................61
8.3. Appendix 3: Data Sample...............................................................................................................62
8.4. Appendix 4: Valuation error in RIV(TVC)..................................................................................65
8.5. Appendix 5: Valuation error in RIV(PMB) .................................................................................66
8.6. Appendix 6: Valuation error in AEG(TVC)................................................................................67
8.7. Appendix 7: Comparison Between the Valuation Error in AEG(TVC) and RIV(TVC) ....68
8.8. Appendix 8: Beta Calculations.......................................................................................................69
8.9. Appendix 9: Average Absolute Valuation errors per Sector and Year......................................70
8.10. Appendix 10: Empirical Results 1998-2002 ..............................................................................72
8.11. Appendix 11: Empirical Results 2003-2007 ..............................................................................75
8.12. Appendix 12: Empirical Results Five or More Consensus Estimates (1998-2007) ............78
8.13. Appendix 13: Empirical Results 5% Equity Risk Premium (1998-2007) .............................81
8.14. Appendix 14: Statistical Testing 1998-2002...............................................................................84
8.15. Appendix 15: Statistical Testing 2003-2007...............................................................................86
8.16. Appendix 16: Statistical Testing Five or More Consensus Estimates (1998-2007).............88
8.17. Appendix 17: Statistical Testing 5% Equity Risk Premium (1998-2007) .............................90
8.18. Appendix 18: Summary of Empirical Results and Statistical Testing: 1998-2002...............92
8.19. Appendix 19: Summary of Empirical Results and Statistical Testing: 2003-2007...............96
8.20. Appendix 20: Summary of Empirical Results and Statistical Testing: 5 or More Consensus
Estimates (1998-2007) ......................................................................................................................... 100
8.21. Appendix 21: Summary of Empirical Results and Statistical Testing: 5% Equity Risk
Premium (1998-2007) .......................................................................................................................... 104
3
1. Introduction and Purpose
In the practice of equity valuation, straightforward valuation models with few assumptions
and an ability to withstand factors that have strong impact on the valuation are attractive. A
review of the most frequently applied equity valuation models would show that the Discounted
Cash Flow (DCF) valuation models are commonly used. In DCF modelling, explicit forecasts of
the company’s future performance and growth are used to calculate the present value of future
cash flows. A DCF model relies on strong assumptions and the mechanical valuation technique is
sensitive for alterations in these assumptions. More straightforward valuation models less
dependent on crucial assumptions and with an ability to withstand factors that have strong
impact on the valuation are therefore desirable.
The Residual Income Valuation (RIV) model has made a great impact on accounting-based
valuation practice. RIV modelling anchors residual earnings to book value of owners’ equity as a
possible measure of a firm’s value creation. Current value of owners’ equity is defined as the sum
of book value of owners’ equity and the present value of future residual earnings.
Similar to the RIV model, but anchoring value to the capitalised earnings, the Abnormal
Earnings Growth (AEG) model has recently been introduced by Ohlson and Juettner-Nauroth
(2005). AEG focuses on future earnings and earnings growth, and the AEG model defines
current value of owners’ equity as the sum of capitalised earnings and the present value of future
abnormal earnings growth.
Parsimonious versions of both the RIV and AEG models, where the terminal value is set to
zero at some horizon point of time, are considered as practical benchmark models for equity
valuation based on financial statement information and forecasts of the future. The terminal value
constrained versions of RIV (RIV(TVC)) and AEG (AEG(TVC)) modelling are, however, more
or less affected by conservative accounting and the company’s distance to steady state at the
valuation point of time.
Under the assumption of steady state, the valuation bias from conservative accounting of the
RIV(TVC) model is proposed by Skogsvik and Juettner-Nauroth (2007) to be non-positive and
dependent on the conservative bias of owners’ equity at the terminal point of time, whereas the
valuation bias of the AEG(TVC) model depends on the capitalised growth of the conservative
bias in the terminal period. If the growth of the conservative bias coincides with the general
growth in a company that has entered the steady state, the measurement error in the terminal
value constrained AEG model is typically smaller than in the corresponding RIV model.
(Skogsvik and Juettner-Nauroth, 2007)
The purpose of this paper is to empirically evaluate the ability among different types of
parsimonious equity valuation models to withstand factors causing valuation error. The reasoning
will be based on the theoretical framework presented in the working paper by Skogsvik and
4
Juettner-Nauroth (2007). The valuation error in the empirical analysis is, however, not solely
attributable to conservative accounting; other factors, e.g. the distance to steady state, will also
provide a valuation bias. The evaluation will cover the asset-based book value of equity (Bv), the
discounted cash flow based capitalised earnings (PVEE) along with the accounting-based
parsimonious valuation models RIV(TVC) and AEG(TVC). Extended versions of the RIV(TVC)
model will also be evaluated. The evaluation will be performed by estimating and comparing the
valuation errors to make inferences about the models’ ability to reflect the fair value of owners’
equity.
This paper is organized as follows. In section 2 the main results of this paper are summarised.
In section 3, assumptions and valuation models are specified together with the hypotheses that
will underpin the empirical testing and discussion. In section 4, the data is discussed together with
descriptive statistics and consistency checks. Section 5 presents the empirical analysis of the
models’ measurement error and testing of hypotheses. Section 6 discusses the results and its
validity, and finally summarises the results with concluding comments. The Appendixes provide
detailed and explaining tables, charts and information.
5
2. Summary
The major results of this paper are:
Result 1:
The RIV(TVC) model [on average] provides a smaller absolute
valuation error than book value of owners’ equity for 9 out of 9
industry sectors.
Result 2:
The RIV(PMB) model [on average] provides a smaller absolute
valuation error than RIV(TVC) for 5 out of 9 industry sectors.
RIV(TVC) [on average] provides a smaller absolute valuation
error than RIV(PMB) for 2 out of 9 industry sectors.
Result 3:
The PVEE(rf) model [on average] provides a smaller absolute
valuation error than PVEE(rE) for 1 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation
error than PVEE(rf) for 8 out of 9 industry sectors.
Result 4:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than PVEE(rE) for 5 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation
error than AEG(TVC) for 3 out of 9 industry sectors.
Result 5:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than RIV(TVC) for 7 out of 9 industry sectors.
RIV(TVC) [on average] provides a smaller absolute valuation
error than AEG(TVC) for 2 out of 9 industry sectors.
The main results imply that the models show varying levels of abilities to capture biases in
the valuation of equity. RIV(TVC) and AEG(TVC) generally provide smaller absolute valuation
errors than the book value and PVEE respectively. Adjusting the RIV(TVC) valuation for the
conservative bias at the horizon point of time is found to be a feasible extension of the model
provided that an accurate estimation of the permanent measurement bias is available. Estimating
Q to adjust for conservative bias as well as the firm-specific goodwill/badwill at T<T* does not
provide a smaller valuation error than the PMB extension. Evaluating the AEG(TVC) model
against RIV(TVC) shows that the abnormal earnings-based approach generally seems to provide
a smaller average absolute valuation error.
6
In general, the empirical results and statistical testing can be seen as robust over time and for
critical modelling assumptions. These are attractive features that would separate the parsimonious
valuation models from more complex valuation models. The volatile and relatively large average
valuation errors in the empirical evaluation, however, shed light on the difficulties in finding
appropriate rules of thumb to apply on industry sectors and over a long period of time.
7
3. Valuation Models and Hypotheses
3.1. Assumptions and Notations
The notations used in this paper (in alphabetical order):
Bvt =
Book value of owners’ equity at time t, after capital transactions
between the company and the owners at time t.
Cbt =
Conservative valuation bias in owners’ equity at time t.
Divt =
Expected dividend paid to the shareholders less any new issue of
equity capital at time t.
Et(…) = Expectation operator, conditioned on available information at
time t.
g
=
kt =
Company growth rate in earnings.
Net payout ratio as a percentage of earnings, i.e. the net of
dividends and new issue of equity capital divided by earnings.
Nt =
New issue of equity capital at time t.
Pt =
Market value of owners’ equity at time t after capital transactions
(dividend and/or new issue of equity capital) between the
company and the owners at time t.
q=
The relation between the market value and the book value of
owners’ equity.
rE =
Required rate of return on owners’ equity, i.e. the cost of equity
capital.
RE =
(1+ rE).
rm –rf =
The market risk premium, i.e. the incremental return that
investors require from holding risky equities rather than risk-free
securities.
rf
=
The risk-free interest rate, i.e. the interest rate at which an
investor could invest with no default risk.
T* =
The firm specific point in time where only zero net present value
(NPV) project are executed, i.e. steady state.
…(UB) = Unbiased accounting.
Vt =
Value of owners’ equity according to the applied valuation model
at time t, after transactions between the company and the owners
at time t.
Xt =
Accounting net earnings accumulated over the period.
8
The following assumptions are assumed to hold:
1.
The valuation point of time coincide with t=0 (t0) throughout the
whole paper.
2.
Dividends and new issues of equity capital are marked to market and
settled at the end of future periods.
3.
The investment risk associated with the (net) dividends payments is
incorporated in the required rate of return on owners’ equity.
4.
The required rate of return on owners’ equity is non-stochastic and
has a flat term structure.
5.
The deviations from the clean surplus relation (CSR) in future
financial statements are expected to be zero, i.e. net income,
dividends, and new issues of equity capital account for all changes in
the book value of owners’ equity:
E 0 [Bv t +1 − ( Bv t + X t +1 − Div t +1 )] = 0
⇔
E 0 ( Bv t +1 ) = E 0 ( Bv t ) + E 0 ( X t +1 ) − E 0 ( DIVt +1 )
6.
(CSR)
This relationship of conservative accounting (Cbt) could be denoted:
Bv (0UB ) − Bv 0 = Cb 0 ≥ 0
E 0 ( Bv (t UB ) ) − Bv t = E 0 ( Cb t ) ≥ 0
(Cbt)
E 0 ( X t ) = E 0 [ X (t UB ) − ( Cb t − Cb t −1 )] = E 0 ( X (t UB ) ) − E 0 [ ∆( Cb t )]
(Skogsvik and Juettner-Nauroth, 2007)
The reasoning above implies that when steady state is reached,
the book value of owners’ equity equals market value if accounting is
unbiased. Conservative accounting implies that the book value will be
lower than the market value when steady state is not yet reached.
However, it should be noted that the impact on earnings is
ambiguous.
9
3.2. Introduction to Models
The evaluated models [with some reservation for book value of owners’ equity] can be
derived from the present value of expected dividend (PVED) valuation. In PVED, the value of
owners’ equity equals the present value of all future dividends paid by the firm to its equity
holders:
∞
V0 = ∑
E 0 ( Div t )
R ET
t =1
(PVED)
By inserting a horizon point in time t=T, an unconstrained version of the PVED can be
obtained:
V0 = ∑
T
E 0 ( Div t ) E 0 ( PT )
+
R tE
R ET
t =1
(PVED)
PVED requires explicit forecasts of dividends for T periods and a forecast of the terminal
price PT at the end of period T.
3.3. Book Value of Owners’ Equity
Book value is determined by the current book value of equity on the balance sheet and
represents the shareholders’ investments in the firm:
V0 = Bv 0
(Bv)
The book value of owners’ equity does not, however, capture the future expected earnings
associated with the shareholders’ investments and thus the measure does not fully reflect the
intrinsic value of owners’ equity. In a company with future earnings, the intrinsic value of equity
must therefore equal the sum of book value of owner’s equity and a premium. This fits with the
idea that investors pay for future earnings today5. (Penman, 2007)
5
The relationship between the market valuation of owners’ equity and book value of owners’ equity is
often referred to as the Market-to-Book ratio.
10
3.4. The Residual Income Valuation Model and Its Terminal Value Constrained Version
The RIV model clarifies the linkage between accounting-based measures of owners’ equity,
earnings and the intrinsic value of owners’ equity (Ohlson, 2005). With book value of owners’
equity as an anchor, the RIV model uses residual earnings as a measure of a firm’s value creation.
The intrinsic value of owners’ equity is defined in RIV modelling as the sum of book value of
equity and the present value of future residual income. Under the assumption that CSR holds,
E0(Divt) can be rewritten in accounting terms and incorporated in the PVED to develop the RIV
model:
V0 = ∑
T
E 0 ( Div t ) E 0 ( PT )
+
R tE
R ET
t =1
(PVED)
E 0 ( Bv t +1 ) = E 0 ( Bv 0 ) + E 0 ( X t +1 ) − E 0 ( Div t +1 )
T
V0RIV = Bv 0 + ∑
t =1
E 0 ( X t − rE ⋅ Bv t −1 ) E 0 ( PT − Bv T )
+
R tE
R ET
(RIV)
The formula above shows that the value of owners’ equity is driven by three factors:
1.
Opening book value of owners’ equity, excluding dividend and
including any new issue of share capital:
Bv 0
2.
Present value of the expected residual income until the horizon
point in time. The residual income is calculated as the difference
between earnings and the return on equity:
T
∑
t =1
3.
E 0 ( X t − rE ⋅ Bv t −1 )
R tE
The present value of the goodwill/badwill of owners’ equity at the
horizon point in time, which can be explained by the present value
of all future residual incomes:
E 0 ( PT − Bv T )
R TE
11
The unconstrained RIV valuation model is conditioned on the assumption of CSR, which
implies that the function is unaffected by the choice of accounting principles. Provided that the
accounting is done in compliance with CSR, the model will yield the same result as PVED. If the
accounts are prepared with conservative accounting principles, higher excess profits will be
created and a constantly higher residual income will be produced at the horizon point of time.
Given unbiased accounting and if T≥T* (i.e. the company is in steady state and there is no
business goodwill/badwill at the horizon point of time) the terminal value in the unconstrained
version of RIV drops out and could be set to zero in a parsimonious terminal value constrained
version of the model:
T
( TVC )
V0RIV
= Bv 0 + ∑
,CB
t =1
E 0 ( X t − r ⋅ Bv t −1 )
R tE
(RIV(TVC))
If accounting is conservatively biased and/or if T<T*, the RIV(TVC) model is affected by
the valuation bias of the terminal value, and will consequently provide a valuation error in the
valuation of owners’ equity. (Skogsvik and Juettner-Nauroth, 2007)
3.5. The Terminal Value Constrained Residual Income Valuation Model Extended with
Permanent Measurement Bias Adjustment
If accounting is biased and/or if T* is not reached at the terminal point of time (T),
RIV(TVC) will provide a valuation error. An adjustment aimed to decrease this error could be
made by extending the parsimonious terminal value constrained version of RIV with an
estimation of the business goodwill/badwill at T:
T
V0RIV ( PMB ) = Bv 0 + ∑
t =1
E 0 ( X t − rE ⋅ Bv t −1 ) q ⋅ Bv T
+
R tE
R ET
(RIV(PMB))
where:
q ⋅ Bv T E 0 ( PT − Bv T )
=
R TE
R TE
An estimate for the q-measure that defines the valuation bias as a fraction of book value at
t=T could be obtained from financial literature for a swift extension of the RIV(TVC) model.
12
The estimation of q if T=T* (i.e. the estimation of conservative accounting) is often referred to as
the permanent measurement bias (PMB)6. (Runsten, 1998)
3.6. The Capitalised Earnings Model in Two Versions
The discounted cash flow approach and earnings-based capitalised earnings model (PVEE)
can be derived from PVED using, the dividend payout ratio (k):
V0 =
k 1 X 1 (1 + g ) k 1 X 1
=
rE − g
rE − g
(PVEE)
Assuming that all earnings are paid out as dividends (kt=1), a firm will not make any
investments and hence the growth could be assumed to equal zero (g=0):
V0 =
X1
rE
(PVEE(rE))
As an attractive model feature, PVEE does not depend on any choice of particular
parameters relating to dividend policies. Rather, it focuses on the more easily forecasted next year
earnings. The major drawback of PVEE, however, is the focus on next year earnings solely to
value owners’ equity. This approach could potentially lead to valuation errors if next year earnings
are not representative for future earnings and earnings growth, e.g. as a result of conservative
bias.
PVEE(rE) by its definition does not capture the value of growth in future earnings, and thus
the model could be expected to underestimate the value of owners’ equity for companies with
growth in earnings. By removing the risk adjustment from the cost of equity capital in the
denominator and under the assumption that the growth and risk parameters are of equal size (or
that the growth factor is greater than the risk parameter), capitalising the earnings with the riskfree interest rate would potentially imply a more accurate estimation of owners’ equity7:
V0 =
6
X1
rf
(PVEE(rf))
The observant reader notes that the estimated PMB value must not necessarily equal q, and thus, the
extension of the model will not always neutralise the valuation bias. The implications of this will be
discussed in connection with the evaluation of RIV(PMB).
7
This valuation approach is often used on aggregate market capitalisation over the world and is popularly
referred to as the Fed Model.
13
3.7. The Abnormal Earnings Growth Valuation Model and Its Terminal Value
Constrained Version
With PVEE(rE) as an anchor, the AEG model focuses on future earnings and earnings
growth in the short- and the long-run. The intrinsic value of equity depends on forward earnings
and the subsequent growth8. Analogously with the PVEE, the unconstrained AEG model is
immune to dividend policy:
V0AEG =
E 0 ( X 1 ) T −1 E 0 ( X t +1 + rE ⋅ Div t − X t ⋅ R E ) r E
+∑
+
rE
R tE
t =1
E ( P + Div T − X T ⋅ R E r E )
+ 0 T
R TE
(AEG)
The unconstrained AEG model is a restatement of PVED9 and similar to the RIV model, the
valuation of owners’ equity is driven by three factors:
1.
Capitalised expected value of earnings in the first period t=1
(PVEE):
E0 ( X1 )
rE
2.
The present value of capitalised expected abnormal earnings
growth over the periods t = 2,3,…,T:
T −1
∑
t =1
3.
E 0 ( X t +1 + rE ⋅ Div t − X t ⋅ R E ) r E
R tE
The present value of the expected difference between the market
value of owners’ equity and capitalised value of earnings at the
horizon point in time t=T:
E 0 ( PT + Div T − X T ⋅ R E r E )
R TE
The abnormal earnings growth model embodies the idea that the value of equity is based on
what the firm can earn. Given that the assumption of CSR holds, the measures of abnormal
8
Cf. Penman (2007) for further discussion of AEG modelling.
9
Cf. Appendix 1 for the axiomatic rewriting of PVED to AEG valuation model.
14
earnings growth in the AEG model will be clearly linked to the measure of residual income in the
RIV model10.
Given unbiased accounting and that T≥T*+1, the terminal value in AEG is equal to zero.
Hence, the model can be rewritten to obtain a terminal value constrained version:
V0AEG( TVC ) =
E 0 ( X 1 ) T −1 E 0 ( X t +1 + rE ⋅ Div t − X t ⋅ R E ) r E
+∑
rE
R tE
t =1
(AEG(TVC))
As in the corresponding RIV(TVC) model, the AEG(TVC) will provide a valuation error in
the valuation of owners’ equity if accounting is conservatively biased and/or if T<T*+1.
(Skogsvik and Juettner-Nauroth, 2007)
3.8. Hypotheses
Under the assumption of steady state, Skogsvik and Juettner-Nauroth (2007) suggest that the
unconstrained versions of RIV and AEG modelling are immune to accounting conservatism.
This does not, however, hold for book value of owners’ equity and PVEE, or for the
parsimonious versions of RIV and AEG modelling.
Conservative accounting in book value provides a valuation error (-Cb0) of owners’ equity
that is equal to the difference between the book value at t=0 (Bv0) and unbiased book value
(Bv0(UB)) at t=0 :
V0 − P0 = Bv 0 − Bv (0UB ) = −Cb 0
The valuation error in the RIV(TVC) is a function of the expected conservative bias of
owners’ equity at horizon point of time11:
V0 − P0 = −
10
E 0 ( Cb T* )
R ET*
The following expression shows on the equality between the abnormal earnings growth for period t + 1
and the difference between residual income in period t + 1 and period t:
E 0 ( X t +1 + rE ⋅ Div t − X t ⋅ R E = E 0 [( X t +1 − rE ⋅ Bv t ) − ( X t − rE ⋅ Bv t −1 )]
(Skogsvik and Juettner-Nauroth, 2007)
11
Cf. Appendix 4 for derivation of the measurement error in RIV(TVC).
15
This implies an expected non-positive bias if E0(CbT*) ≥ 0 and that RIV(TVC)
accommodates conservative accounting with no valuation error if E0(CbT*) = 0. If t0 < T* it
could be expected that
E 0 ( Cb T * )
is smaller than Cb 0 .
R TE*
The RIV(TVC) model [on average] provides a smaller absolute
Hypothesis 1:
valuation error than the book value of owners’ equity.
The valuation error in RIV(PMB) is a function of the error in the estimation of q (PMB) and
the book value of owners’ equity at T*12:
V0 − P0 = −
( PMB − q ) ⋅ Bv T*
R TE*
RIV(PMB) will consequently provide a smaller valuation error than RIV(TVC) if:
( PMB − q ) ⋅ Bv T *
E ( Cb )
< 0 T* T*
T*
RE
RE
Hypothesis 2:
The RIV(PMB) model [on average] provides a smaller absolute
valuation error than the RIV(TVC) model.
The PVEE(rE) valuation model provides a valuation error of owners’ equity equal to
difference between capitalised earnings at t=1 and capitalised unbiased earnings at t=1:
V0 − P0 =
X 1 X 1UB
−
rET* rET*
According to the reasoning in section 2, the PVEE model could be used together with the
risk-free interest rate. By capitalising next year estimated earnings with the risk-free interest rate
(rf), the denominator is adjusted downwards to adjust for the absence of growth in the
numerator. This could potentially capture the value of growth in future earnings that is omitted in
PVEE(rE) when capitalising with rE. The adjustment would produce a smaller valuation error if
the growth rate of the company is larger than the difference between rE and rf:
12
Cf. Appendix 5 for derivation of the measurement error in RIV(PMB).
16
V0 − P0 =
X 1 X 1UB
− T
rfT
rf
Under the assumptions above, the following must hold:
rf > rE − g
PVEE(rf) underestimates fair value (always smaller
⇔
g > β ⋅ ( rm − rf )
valuation error than PVEE(rE)).
rf < rE − g
PVEE(rf) overestimates fair value (valuation error
⇔
g < β ⋅ ( rm − rf )
size unclear relative to PVEE(rE)).
rf = rE − g
PVEE(rf) captures growth in earnings.
⇔
g = β ⋅ ( rm − rf )
Hypothesis 3:
The Capitalised Earnings Model where earnings are capitalised
with the risk-free interest rate [on average] provides a smaller
valuation error than earnings capitalised with the required rate of
return on equity.
The valuation error in AEG(TVC) is equal to the negative present value of the capitalised
growth of the conservative bias in period (T*+1) and thus, if the expected change in the
conservative bias in (T*+1) equals zero, the AEG(TVC) model could accommodate conservative
accounting principles with no valuation error in the valuation of owners’ equity13:
V0 − P0 = −
Cb T* +1 − Cb T* / rE
T*
RE
If t0 < T* it could be expected that:
13
Cf. Appendix 6 for derivation of the measurement error in AEG(TVC).
17
Cb T* +1 − Cb T* / rE
X 1UB X 1
<
−
.
R TE*
rET* rET*
Hypothesis 4:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than PVEE(rE).
Skogsvik and Juettner-Nauroth (2007) suggest that the valuation error in the terminal value
constrained AEG model is typically smaller than in the corresponding RIV model if the growth
of the conservative bias lies within a certain interval of “normal” values. The RIV(TVC) model,
on the other hand, provides a smaller valuation error than the AEG(TVC) only when the growth
of the conservative bias exhibits more “extreme” values14:
Given CSR and steady state, the valuation bias of AEG(TVC) is
smaller than in RIV(TVC) only if:
-E0(CbT*) · rE < E0[(CbT*+1-CbT*)] < E0(CbT*) · rE
Reversely, the RIV(TVC) model is superior to AEG(TVC) only if:
E0[(CbT*+1-CbT*)] < -E0(CbT*) · rE or E0[(CbT*+1-CbT*)] >E0(CbT*)
(Skogsvik and Juettner-Nauroth, 2007)
Under an assumption of steady state, this supports the reasoning in
Hypothesis 5:
Hypothesis 5:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than RIV(TVC).
In the next section, the models’ ability to reflect market value and to withstand conservative
accounting biases will be empirically evaluated. The results will be discussed on basis of the
theoretical reasoning and by testing hypotheses 1-5.
14
Cf. Appendix 7 for a comparison between the measurement errors in RIV(TVC) and AEG(TVC).
18
4. Data
4.1. Data Set, Descriptive Statistics and Consistency Checks
Monthly observations of yearly data for 190 currently traded companies on the Stockholm
Stock Exchange have been collected from DATASTREAM for the period July 1998 to October
2007. The companies have been categorised into nine industry sectors15 according to the Global
Industry Classification Standard (GICS)16:
GICS Sector
1998
1999
2000
2001
2002
2003
Consumer Discretionary
5
8
9
11
7
15
Consumer Staples
0
3
3
3
2
3
Energy
1
1
2
2
1
2
Financials
4
10
15
12
6
14
Health Care
2
3
4
3
2
7
Industrials
18
26
33
31
12
33
Information Technology
5
11
15
15
2
19
Materials
5
5
6
6
2
6
Telecommunication Services
1
1
1
2
2
2
Total
41
68
88
85
36
101
Table 1: Sample size measured as number of companies per industry sector and year.
2004
18
3
2
16
7
36
24
9
2
117
2005
19
4
2
15
8
39
21
8
3
119
2006
23
6
3
19
7
44
26
10
4
142
2007
25
7
4
24
8
49
32
9
3
161
Evidently, the number of firms in any year does not total 190. This is explained by the fact
that companies enter the sample at different points of time over the studied period. Limitations
in analyst coverage further reduce the sample size, and the possible implications from this will be
discussed later. Together with Institutional Brokers Estimate System (IBES) consensus
estimates17, reported accounting data has served as a starting point in the empirical valuation
modelling18. The analyst estimates have been used as a proxy for the market’s expectations on
company future book value, earnings and dividends. The average number of estimates available
per company and parameter varies with sector and time, e.g. estimates for fiscal period (FY) 4 are
rarely observed:
15
The categorisation of companies into industry sector is made to allow for a deeper understanding and
discussion of the empirical results. Cf. Appendix 2-3 for more detailed information on the studied sample
and the different industry sector characteristics.
16
GICS is an industry classification that consists of 10 sectors, 24 industry groups, 62 industries, and 132
sub-industries. GICS assigns an industry sector name to each company according to its principal business
activity, and the standard is widely accepted as a framework for investment research, portfolio management
and asset allocation.
17
18
The consensus estimates are the arithmetic average of estimates for the fiscal period indicated.
IBES is a system which monitors and gathers the different estimates made by stock analysts on
companies of interest to institutional investors. The IBES database covers over 18 000 companies in 60
countries.
19
Fiscal Year 1
Fiscal Year 2
GICS Sector
BPS
EPS
DPS
BPS
EPS
DPS
Consumer Discretionary
6.9
8.1
8.9
6.5
8.0
8.5
Consumer Staples
5.8
7.6
7.9
5.2
7.5
7.6
Energy
2.2
3.3
2.8
2.0
2.9
2.6
Financials
7.1
9.9
10.5
6.5
9.7
9.8
Health Care
4.5
5.4
5.8
4.2
5.3
5.5
Industrials
6.7
8.7
9.2
6.2
8.6
8.6
Information Technology
4.8
6.2
5.8
4.4
6.0
5.4
Materials
8.0
10.6
11.2
7.4
10.5
10.6
Telecommunication Services
11.8
14.8
16.7
10.9
15.0
16.0
Table 2: Average number of estimates per company, estimated parameter and fiscal year.
BPS
4.6
3.9
1.5
4.4
3.2
4.5
3.1
5.1
8.1
Fiscal Year 3
EPS
DPS
5.4
5.8
5.4
5.7
2.0
1.8
6.3
6.5
3.9
4.0
5.9
6.0
3.9
3.6
7.0
7.2
11.1
11.6
BPS
1.2
1.0
0.9
1.0
1.1
1.1
1.1
1.1
1.7
Fiscal Year 4
EPS
DPS
1.0
1.0
1.0
1.0
0.1
0.1
0.8
0.7
0.6
0.6
0.8
0.8
0.6
0.6
0.9
1.0
2.4
2.5
Reported accounting information and consensus estimates used in the empirical analysis:
Book Value Per Share (BPSt) = BPSt is the net asset value of a company’s
securities, expressed in per share terms. BPSt
is used as an estimation of Bvt.
Earnings Per Share (EPSt)
= EPSt is the amount of a company’s profit
allocated to each outstanding share of
common stock, thus this serves as an
indicator of a company’s profitability. EPSt is
used as an estimation of Xt.
Dividends Per Share (DPSt) = DPSt consists of a company’s common stock
dividends on an annualized basis, divided by
the weighted average number of common
shares outstanding for the year. DPSt is used
as an estimation of Divt.
Price Per Share (PPSt)
= The last price per share represents the market
value of owners’ equity per common share
outstanding. PPSt is used as an estimation of
P t.
To ensure comparability and to improve the validity of the empirical results, extensive
consistency checks have been carried out to find error in the data. The consistency checks and
adjustments include:
Currency translations have been made from exchange rate time series where reported
information or consensus estimates are reported in other currencies than SEK.
20
Observations with negative earnings or book value forecasts have been excluded19 along with
missing observations.
BPSt has been estimated where the value is missing. Estimation of BPSt is performed in
accordance with CSR and based on information from the previous fiscal period. Consequently,
the estimation can only be performed for FY1-FY4 where both EPS and DPS estimates are
observed in the previous period:
BPS FYt = BPS FYt −1 + EPS FYt − DPS FYt −1
To empirically evaluate the models and to allow for a paired sample t-test of the hypotheses,
the data has been limited to observations with complete accounting information and consensus
estimates for three fiscal periods. The terminal point of time is set to t=T=3 because of the
limited number of analyst estimates for FY4.
The total number of complete observations in the data sample is 8 504:
GICS Sector
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Total
Consumer Discretionary
28
88
99
63
76
153
174
197
234
231
1343
Consumer Staples
0
28
36
25
4
32
36
46
64
55
326
Energy
5
2
4
5
5
16
10
4
24
34
109
Financials
23
93
127
79
65
133
139
137
192
202
1190
Health Care
12
25
31
14
18
63
79
80
82
67
471
Industrials
98
234
315
194
112
296
365
395
485
453
2947
Information Technology
23
81
139
68
7
127
218
171
225
230
1289
Materials
25
52
71
33
24
63
94
76
100
87
625
Telecommunication Services
5
12
12
15
20
24
24
29
37
26
204
Total
219
615
834
496
331
907
1139
1135
1443
1385
8504
Table 3: Total number of complete observations per industry sector and year (e.g. 7 companies were observed in Consumer Discretionary
sector in 2002. If full accounting information and estimates would have been available for all companies and months this year, the number
of complete observations would have been 84. With missing information, however, the number of complete observations is only 76).
The number of observations per sector and year increases from 1998 to 2007, and any biases
that this may induce on the results will be discussed and empirically tested.
19
The reasoning behind the exclusion of negative observations is self-evident, e.g. valuing owners’ equity
with negative earnings forecasts would imply a negative value in the capitalised earnings model. Naturally,
this can not hold.
21
5. Empirical Analysis
In this section, the models’ accuracy in determining the market value of owners’ equity and
the impact of conservative accounting will be evaluated. Hypotheses 1-5 will be tested.
5.1. Modelling Assumptions
The market value (Pt) is assumed to reflect the fair value of owners’ equity at the valuation
point of time (t=0) given all available information. In order to isolate the valuation error, it is
assumed that the valuation of owners’ equity would be correct if the accounting was unbiased and
the company had reached steady state at t0. Consequently, any deviations from Pt are explained by
conservative bias and/or the business goodwill/badwill (i.e. T<T*). The valuation error (V.E.)
will be calculated as the difference between the market value of owners’ equity at time t=0
(estimated by PPSt) (P0) and the estimated value (V0):
V.E. = V0 − P0
(V.E.)
To allow for comparison between models and over industry sectors, the absolute valuation
error (Abs(V.E.)) will be computed:
Abs( V.E.) = V0 − P0
(Abs(V.E.))
All valuation errors will be normalised using the market value at t=0, and the normalised
valuation errors will henceforth be referred to as the valuation errors in the models:
V.E. V0 − P0
=
P0
P0
Abs( V.E.) V0 − P0
=
P0
P0
The differences in average absolute valuation errors between models will be tested with paired
t-tests on the equality of means20, and at the 5 percent (**) level. Significance is also reported for
the 1 (***) and 10 percent (*) levels. All results will be presented with 3 different alternative
20
The t-test rests on an assumption of normal distribution in data.
22
hypotheses, the computed t-statistics and the associated p-values as well as a computed 95
percent confidence interval for the mean values.
To calculate the cost of equity capital for companies, an estimate of the equity risk premium
is central. The required return on equity will be the risk-free interest rate plus a risk premium. The
risk premium will be the equity risk premium for the market, adjusted for the risk of the
company. This requires an estimate of the prospective equity risk premium, whereas by definition
the only premium which can be measured is the historical risk premium. In practice therefore, the
historical risk premium is used as a starting point for assumptions about the future. Generally, in
inferring the future risk premium from historical data, the implicit assumption is made that the
historical risk premium, measured over many years, is an unbiased estimate of the future
premium21. Over a 105-year period between 1900 and 2004, the annualized geometric equity risk
premium, relative to bills, was 5.5 percent in Sweden. Averaged across the world index, the risk
premium relative to bills was 4.7 percent. Across the world index, the risk premium relative to
bonds averaged 4.0 percent, while for Sweden it was 5.0 percent22. (Dimson et. al., 2005)
The historical estimates should be considered to be too high as forecasts of the future.
Increased diversification, for example, has decreased the required risk premium for investors and
the past returns have therefore been advantaged by the decline in the risk faced by investors. This
means that when developing forecasts for the future, the historical risk premium should be
adjusted downward for the impact of these factors. (Dimson et. al., 2005)
An estimate of a plausible, forward-looking risk premium for the Swedish market would
consequently be on the order of 4.0 percent (rm - rf = 4.0%). This assumption will later be
robustness tested to infer its impact on the empirical results.
The nominal risk-free interest rate at the time for valuation (t=0) is given by the midpoint
between the bid and offered rates for the 10-year Swedish Government zero coupon.
The risk adjustment of the equity market risk premium is measured by the systematic risk of
a company (beta). Beta is used as a measure of the extent to which a share’s performance
fluctuates with the market, relative to average. A raw beta is estimated at each time for valuation
(t=0) by regressing 400 points of daily returns of the relevant GICS Level 1 Sector Group index23
21
An unbiased estimate of the risk premium required by investors would tell what future returns can be
expected from the equity market, relative to risk-free investments. A low (high) risk premium would
automatically imply low (high) future returns from equities. If this were not the case, then the stock market
would ensure that share prices rapidly rose (fell) until promised returns were aligned with required returns.
22
This historical risk premium is summarised by the geometric mean of historic returns. The forward-
looking risk premium, however, should more appropriately be measured by the arithmetic mean, since it
represents the mean of all returns that may possibly occur.
23
Cf. Appendix 2 for detailed information on the GICS Level 1 Sector Group indexes.
23
against the market proxy return Affarsvarlden General Index (AFGX)24. The industry sector
estimated beta is applied to all companies in the specific industry sector at the time for
valuation25:
GICS Sector
1998
1999
Consumer Discretionary
0.9272 0.9313
Consumer Staples
0.3979
Energy
0.8651 0.8464
Financials
0.8789 0.9144
Health Care
0.8365 0.7170
Industrials
0.8687 0.8064
Information Technology
1.5740 1.6932
Materials
0.8042 0.7479
Telecommunication Services
1.0981 1.1438
Table 4: Average beta values per sector and year.
2000
0.7403
0.2182
0.3718
0.6868
0.3538
0.4254
1.8373
0.4068
1.2231
2001
0.6383
0.1134
0.3845
0.6221
0.1109
0.3752
1.9835
0.3038
1.1501
2002
0.8589
0.0996
0.7542
0.8779
0.4046
0.6816
1.9807
0.5130
1.2016
2003
0.8786
0.2045
0.8645
1.0167
0.6593
0.8705
2.0107
0.6295
1.2447
2004
0.7507
0.2786
0.9503
0.9267
0.7169
0.9573
2.0587
0.6749
1.0413
2005
0.7104
0.3777
0.9954
0.8103
0.5603
0.9764
2.0658
0.6275
1.0100
2006
0.8150
0.5132
1.1527
0.9969
0.6733
1.1285
1.2986
0.9587
0.9124
2007
0.8852
0.5723
1.1704
1.0552
0.6488
1.1684
1.0151
1.1475
0.8280
Under the assumption that the Capital Asset Pricing Model (CAPM) holds, the
index model is used to derive the equity cost of capital by risk adjustment of the equity
market risk premium:
E( rE ) = rf + β ⋅ [E(rm ) − rf ]
(CAPM)
The PMB values used in the testing of RIV(PMB) has been obtained from Runsten (1998).
Runsten (1998) discusses the sources and factors that primarily influence the level of expected
business goodwill/badwill at t=T*, and provides a calculation of PMB values for different
industry sectors. Runsten’s (1998) industry sector categorisation differs from GICS, and thus,
assumptions about applicable sectors have been required. The assumptions are based on
expectations about e.g. balance sheet composition and business models, which are factors that
influence the expected level of PMB:
GICS Sector
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Table 5: PMB values used in
ranked in ascending order.
24
Runsten (1998) Classification
PMB
Rank
Consumer Goods
0.72
7
Consumer Goods
0.72
7
Shipping
0.65
6
Real Estate
0.56
3
Pharmaceuticals
1.74
9
Engineering
0.33
1
Consultants and Computer
0.59
4
Chemicals
0.44
2
Consultants and Computer
0.59
4
the empirical modelling per GICS industry sector and
AFGX measures the Stockholm Stock Exchange and was started in 1937. Base: 28 December 1979 =
100. AFGX is a capital-weighted index and it is calculated by multiplying the number of shares in each
company with the bid price of the most numerous type of share in the company.
25
Cf. Appendix 8 for the historical beta values estimated at (t=0) and for each industry sector.
24
Runsten (1998) does not provide estimates of PMB for companies in the Financials sector,
and thus the closest match in terms of balance sheet composition and business model has been
assumed to be Real Estate companies (n.b. Real Estate companies are included in the GICS
Financials industry sector). It should also be noted that Runsten’s (1998) research did not have
any possibility to cover the evolvement of the Information Technology sector from 1998 and
forward. The applied PMB value from Runsten (1998) for this sector is therefore potentially
misleading.
Parallel to using Runsten’s (1998) PMB values, an estimation of q values including the
valuation bias from companies not being in steady state (Q) is performed in the empirical
modelling. The estimation is obtained through reverse-engineering the q-value for each
observation that would imply zero valuation error in RIV(TVC) if the extension was added to the
valuation:
( P0 − V0RIV ( TVC ) ) ⋅ R TE
Qi =
Bv T
(Q)
Q is subsequently calculated as the average of all reverse-engineered values per industry
sector.
The discounting of present values in the modelling is performed by adjusting the yearly
interest rate at t=0 to fit with the monthly data and the assumptions about when in time
transactions occur.
25
5.2. Book Value of Owners’ Equity
The book value of owners’ equity is given in the modelling by the company reported
information at t=0 (V0 = Bv0 = BPS0). As stipulated in section 2, the valuation error provided in
book value of owners’ equity with conservative accounting is equal to the difference between the
book value at t=0 and unbiased book value at t=0 (-Cb0). A negative (positive) valuation error
would consequently imply that book value on average underestimates (overestimates) the correct
value of owners’ equity:
1.00
1.40
0.80
1.20
0.60
1.00
0.40
V.E.
0.80
0.00
0.60
-0.20
-0.40
0.40
-0.60
0.20
-0.80
Abs(V.E.(BV))
Chart 1: Average valuation error and absolute valuation error in book
value measured per sector.
2007
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 2: Average absolute valuation error in book value, measured
per sector and historically.
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.5640
0.0109
-0.5854 -0.5426 0.6350
0.0074
0.6205 0.6496
6
Consumer Staples
-0.7367
0.0077
-0.7518 -0.7215 0.7367
0.0077
0.7215 0.7518
8
Energy
-0.1504
0.0448
-0.2393 -0.0616 0.4412
0.0204
0.4007 0.4817
2
Financials
-0.4181
0.0091
-0.4361 -0.4002 0.4745
0.0064
0.4619 0.4871
4
Health Care
-0.7305
0.0174
-0.7647 -0.6964 0.8050
0.0077
0.7900 0.8200
9
Industrials
-0.5293
0.0062
-0.5415 -0.5172 0.5857
0.0041
0.5776 0.5938
5
Information Technology
-0.5603
0.0135
-0.5868 -0.5338 0.6639
0.0092
0.6459 0.6819
7
Materials
-0.3073
0.0117
-0.3304 -0.2843 0.3620
0.0089
0.3446 0.3795
1
Telecommunication Services
-0.4065
0.0251
-0.4560 -0.3569 0.4524
0.0209
0.4112 0.4936
3
Table 6: Average valuation error and absolute valuation error in book value with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
The average valuation error shows that the book value underestimates the fair value of
owners’ equity across all industry sectors. The average valuation error is the smallest for Energy
and Materials companies. The industry sectors with the largest valuation error are Consumer
Staples and Health Care. Evaluating the absolute valuation error shows that Materials and Energy
together with Telecommunication Services have the smallest valuation error. Health Care,
Consumer Staples, and Information Technology have the largest average absolute valuation error.
Putting a 95 percent confidence interval on all mean absolute values would imply an absolute
deviation from the fair value between 34.46 percent and 82.00 percent.
26
2006
2005
2004
2003
2002
2001
2000
1999
1998
Materials
Information
Technology
Industrials
Health Care
Financials
Energy
Consumer Staples
V.E.(BV)
Telecommunication
Services
0.00
-1.00
Consumer
Discretionary
V.E.
0.20
M.E.
95 % C.I.
Abs(M.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.5189
0.0041
-0.5270 -0.5108 0.5862
0.0029
0.5805 0.5919
Table 7: Average valuation error and absolute valuation error in book value with standard error and a 95 percent
confidence interval (C.I.).
Aggregated for all industry sectors, the average valuation error in book value is -51.89 (52.70;-51.08) percent. The average absolute valuation error is 58.62 percent and ranges between
58.05 and 59.19 percent within a 95 percent confidence interval.
5.3. The Terminal Value Constrained Residual Income Valuation Model
RIV(TVC) is calculated by using company reported information and available consensus
estimates at t=0. As stipulated in section 2, the valuation error provided in RIV(TVC) with
conservative accounting is a function of the conservative bias of owners’ equity at horizon point
of time. A negative (positive) valuation error would consequently imply that RIV(TVC) on
average underestimates (overestimates) the correct value of owners’ equity:
0.80
1.20
0.60
1.00
0.40
0.80
V.E.
0.00
-0.20
0.60
0.40
-0.40
0.20
-0.60
Abs(V.E.(RIV(TVC)))
Chart 3: Average valuation error and absolute valuation error in
RIV(TVC) per sector.
2007
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 4: Average absolute valuation error in RIV(TVC) measured
per sector and historically.
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.4334
0.0119
-0.4568 -0.4101 0.5544
0.0073
0.5402 0.5686
6
Consumer Staples
-0.5808
0.0066
-0.5938 -0.5678 0.5808
0.0066
0.5678 0.5938
7
Energy
-0.1020
0.0431
-0.1874 -0.0165 0.4141
0.0191
0.3761 0.4520
3
Financials
-0.3629
0.0080
-0.3786 -0.3471 0.4105
0.0058
0.3991 0.4219
2
Health Care
-0.6358
0.0169
-0.6690 -0.6027 0.7095
0.0086
0.6927 0.7264
9
Industrials
-0.4113
0.0064
-0.4238 -0.3988 0.4873
0.0042
0.4791 0.4955
5
Information Technology
-0.5046
0.0132
-0.5304 -0.4788 0.6052
0.0093
0.5869 0.6235
8
Materials
-0.1928
0.0110
-0.2144 -0.1711 0.2834
0.0072
0.2692 0.2976
1
Telecommunication Services
-0.3764
0.0238
-0.4233 -0.3294 0.4148
0.0204
0.3745 0.4551
4
Table 8: Average valuation error and absolute valuation error in RIV(TVC) with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
The average valuation error shows that the RIV(TVC) underestimates the fair value of
owners’ equity across all industry sectors. The average valuation error in RIV(TVC) is the
smallest for Energy and Materials companies. The industry sectors with the largest valuation error
27
2006
2005
2004
2003
2002
2001
2000
1999
1998
Materials
Information
Technology
Industrials
Health Care
Financials
Energy
Consumer Staples
V.E.(RIV(TVC))
Telecommunication
Services
0.00
-0.80
Consumer
Discretionary
V.E.
0.20
are Health Care and Consumer Staples. Evaluating the absolute valuation error shows that
Materials and Financials together with Energy have the smallest valuation error. Health Care,
Information Technology, and Consumer Staples have the largest average absolute valuation error.
Putting a 95 percent confidence interval on all mean values would imply an absolute deviation
from the fair value between 26.92 percent and 72.64 percent.
Comparing the results from RIV(TVC) with the results from book value of owners’ equity
shows that RIV(TVC) seems to provide a smaller absolute valuation error across all the sectors.
This supports the theoretical reasoning in previous sections and is suggested in hypothesis 1.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.4202
0.0041
-0.4283 -0.4121 0.5033
0.0028
0.4977 0.5088
Table 9: Average valuation error and absolute valuation error in RIV(TVC) with standard error and a 95 percent
confidence interval (C.I.).
Aggregated for all industry sectors, the average valuation error in RIV(TVC) is -42.02 (42.83;-41.21) percent. The average absolute valuation error is 50.33 percent and ranges between
49.77 and 50.88 percent within a 95 percent confidence interval.
5.4. The Permanent Measurement Bias Extended Version of RIV(TVC)
RIV(PMB) is calculated by using company reported information and available consensus
estimates at t=0 together with PMB values from Runsten (1998). As stipulated in section 2, the
valuation error provided in RIV(PMB) with conservative accounting is a function of the
difference between the applied PMB value and the q-value that would imply zero valuation error.
A negative (positive) valuation error would consequently imply that RIV(PMB) on average
underestimates (overestimates) the correct value of owners’ equity:
0.80
2.50
0.60
2.00
0.40
V.E.
1.00
0.00
0.50
-0.20
Abs(V.E.(RIV(PMB)))
Chart 5: Average valuation error and absolute valuation error in
RIV(PMB) per sector.
28
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
Materials
Information
Technology
Industrials
Health Care
Financials
Energy
Consumer Staples
V.E.(RIV(PMB))
Telecommunication
Services
0.00
-0.40
Consumer
Discretionary
V.E.
1.50
0.20
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 6: Average absolute valuation error in RIV(PMB) measured
per sector and historically.
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.0946
0.0183
-0.1304 -0.0587 0.5383
0.0112
0.5163 0.5603
8
Consumer Staples
-0.3466
0.0116
-0.3695 -0.3237 0.3498
0.0113
0.3275 0.3721
3
Energy
0.5070
0.0787
0.3510 0.6631
0.6480
0.0685
0.5122 0.7838
9
Financials
-0.0406
0.0114
-0.0629 -0.0182 0.2820
0.0080
0.2662 0.2977
1
Health Care
-0.1164
0.0275
-0.1704 -0.0624 0.4266
0.0199
0.3874 0.4657
6
Industrials
-0.2473
0.0079
-0.2628 -0.2318 0.4083
0.0052
0.3982 0.4185
5
Information Technology
-0.2419
0.0192
-0.2797 -0.2042 0.5322
0.0140
0.5047 0.5596
7
Materials
0.1147
0.0151
0.0850 0.1444
0.3202
0.0092
0.3020 0.3383
2
Telecommunication Services
-0.0734
0.0328
-0.1381 -0.0087 0.3967
0.0181
0.3610 0.4325
4
Table 10: Average absolute valuation error in RIV(PMB) with standard error and a 95 percent confidence interval (C.I.) per sector
and ranked in ascending order.
The average valuation error shows that the RIV(PMB) underestimates the fair value of
owners’ equity for all industry sectors with the exception for Energy and Materials. The average
valuation error in RIV(PMB) is the smallest for Financials and Telecommunication Services. The
industry sectors with the largest valuation error are Energy and Consumer Staples. Evaluating the
absolute valuation error shows that Financials and Materials, together with Consumer Staples have
the smallest valuation error. Energy, Consumer Discretionary, and Information Technology, have
the largest average absolute valuation error. Putting a 95 percent confidence interval on all mean
values would imply an absolute deviation from the fair value between 26.62 percent and 78.38
percent.
Comparing the results from RIV(PMB) with the results from RIV(TVC) shows that
RIV(PMB) seem to provide a smaller absolute valuation error across all the sectors with exception
for Energy and Materials.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1495
0.0059
-0.1611 -0.1380
0.425
0.004
0.4172 0.4328
Table 11: Average valuation error and absolute valuation error in RIV(PMB) with standard error and a 95 percent
confidence interval (C.I.).
Aggregated for all industry sectors, the average valuation error in RIV(PMB) is -14.95 (16.11;-13.80) percent. The average absolute valuation error is 42.50 percent and ranges between
41.72 and 43.28 percent within a 95 percent confidence interval.
As shown, the adjustment of RIV(TVC) with Runsten’s (1998) PMB values does not
eliminate valuation errors. This could be explained by the fluctuation over time in the factors that
influence the level of business goodwill/badwill at time t=T*. Ideally, the PMB should therefore
be calculated specifically for each company and year. (Runsten, 1998) An alternative approach
could be to make an extension to the RIV(TVC) model with estimated q values (Q) that capture
not only the conservative bias (i.e. the assumption of steady state is released). This could
potentially improve the accuracy of the parsimonious RIV(TVC) model:
29
GICS Sector
1998
1999
2000
2001
2002
2003
Consumer Discretionary
2.9925 5.0637 2.9190 2.7656 1.7971 1.0825
Consumer Staples
1.8209 1.2385 1.7823 2.2079 1.5433
Energy
-0.2589 -0.2224 -0.3752 -0.4610 -0.3425 -0.1156
Financials
0.9593 1.1643 1.6864 0.8864 0.8998 0.6246
Health Care
-0.9127 1.0154 1.4695 1.2846 2.3460 2.2909
Industrials
1.5278 1.6377 1.4173 1.0635 0.6796 0.4801
Information Technology
3.4601 4.2168 9.5600 1.7779 1.7180 1.0137
Materials
0.4895 0.5333 0.2473 0.1940 0.3412 0.2221
Telecommunication Services
5.3307 6.1903 7.1655 2.5016 0.7805 0.2745
Table 12: Q estimated per industry sector and year.
2004
1.8457
1.8594
0.3508
0.8847
3.1286
0.9753
2.5582
0.3333
0.3417
2005
2.2272
2.3799
0.7540
0.8610
3.8374
1.2712
2.0303
0.3718
0.1172
2006
2.4948
3.7260
0.9783
1.0079
4.2589
1.7798
2.1712
0.8015
1.0612
2007
3.1321
4.6575
0.8008
1.1461
4.0137
2.4021
2.4691
0.7353
1.8053
Over time, the average Q values have varied, and since 2002 the estimated values have
generally increased across all sectors. Notably, Telecommunication Services, Information
Technology and Consumer Discretionary show extremely high Q values during year 1998-2000.
The average levels of the calculated Q values are higher than the PMB values obtained from
Runsten (1998). Runsten’s (1998) PMB values are calculated with a horizon point of time beyond
FY3. With a shorter horizon it is more likely that the companies have not reached steady state
and is therefore still earning abnormal profits, which would explain the higher Q values and make
direct comparisons between the estimated values difficult.
The average overestimation in
RIV(PMB) for Energy and Materials, could be explained by flawed assumption about the industry
sector categorisation. Hence, the applicability of Runsten’s (1998) PMB values could lead to
inaccurate adjustment of the RIV(TVC) model.
Rank
Rank
PMB
Q
GICS Sector
Runsten (1998) Classification
PMB
Q
Consumer Discretionary
Consumer Goods
0.72
7
2.50
6
Consumer Staples
Consumer Goods
0.72
7
2.67
7
Energy
Shipping
0.65
6
0.44
1
Financials
Real Estate
0.56
3
1.03
3
Health Care
Pharmaceuticals
1.74
9
3.05
8
Industrials
Engineering
0.33
1
1.43
4
Information Technology
Consultants and Computer
0.59
4
3.08
9
Materials
Chemicals
0.44
2
0.46
2
Telecommunication Services
Consultants and Computer
0.59
4
1.69
5
Table 13: Comparison between Runsten’s (1998) PMB values and estimated Q, both ranked in ascending order.
The industry sectors with the lowest Q values are Energy and Materials together with
Financials. Information Technology, Health Care, and Consumer Staples provide the highest Q
values on average.
Analogously with RIV(PMB), the valuation error in RIV(Q) is a function of the error in the
estimation (Q) of q and the book value of owners’ equity at T:
V0 − P0 = −
( Q − q ) ⋅ Bv T
R ET
With positive PMB values, RIV(Q) will consequently provide a smaller valuation error than
RIV(PMB) if ( Q − q ) < ( PMB − q ) .
30
The RIV(Q) model [on average] provides a smaller valuation
Sub-Hypothesis:
error than RIV(PMB).
RIV(Q) is calculated by using company reported information and available consensus
estimates at t=0. As stipulated in section 2, the valuation error provided in RIV(Q) is a function
of the difference between the applied Q value and the q-value that would imply zero valuation
error. A negative (positive) valuation error would consequently imply that RIV(Q) on average
3.00
1.00
2.50
0.80
2.00
Abs(V.E.(RIV(Q)))
Chart 7: Average valuation error and absolute valuation error in
RIV(Q) per sector.
2007
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 8: Average absolute valuation error in RIV(Q) measured per
sector and historically.
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
0.7448
0.0349
0.6763 0.8134
0.9979
0.0299
0.9393 1.0565
8
Consumer Staples
0.2868
0.0268
0.2341 0.3395
0.4654
0.0174
0.4312 0.4997
3
Energy
0.3117
0.0671
0.1786 0.4448
0.5239
0.0535
0.4178 0.6300
6
Financials
0.2282
0.0145
0.1997 0.2568
0.3934
0.0112
0.3714 0.4153
2
Health Care
0.2748
0.0368
0.2024 0.3471
0.5015
0.0313
0.4400 0.5631
4
Industrials
0.2990
0.0135
0.2726 0.3255
0.5109
0.0111
0.4891 0.5327
5
Information Technology
0.8676
0.0456
0.7782 0.9570
1.0643
0.0422
0.9815 1.1470
9
Materials
0.1313
0.0153
0.1011 0.1614
0.3282
0.0095
0.3095 0.3469
1
Telecommunication Services
0.4906
0.0508
0.3905 0.5908
0.7571
0.0307
0.6965 0.8177
7
Table 14: Average valuation error and absolute valuation error in RIV(Q) with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
The average valuation error shows that the RIV(Q) on average overestimates the fair value of
owners’ equity for all industry sectors. The average valuation error in RIV(Q) is the smallest for
Materials and Financials. The industry sectors with the largest valuation error are Information
Technology and Consumer Discretionary. Evaluating the absolute valuation error shows that
Materials and Financials together with Consumer Staples have the smallest valuation error.
Information Technology, Consumer Discretionary, and Telecommunications Services, have the
largest average absolute valuation error. Putting a 95 percent confidence interval on all mean values
would imply an absolute deviation from the fair value between 30.95 percent and 114.70 percent.
31
2006
2005
2004
2003
2002
1998
Materials
Telecommunication
Services
V.E.(RIV(Q))
Information
Technology
0.00
Industrials
0.00
Health Care
0.50
Financials
0.20
Energy
1.00
Consumer Staples
0.40
2001
1.50
2000
0.60
1999
V.E.
1.20
Consumer
Discretionary
V.E.
underestimates (overestimates) the correct value of owners’ equity:
Comparing the results from RIV(Q) with the results from RIV(PMB) shows that RIV(Q)
seems to provide a larger absolute valuation error across all the sectors, with exception for Energy
companies. This contradicts the sub-hypothesis.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.4363
0.0110
0.4148 0.4578
0.6456
0.0097
0.6266 0.6646
Table 15: Average valuation error and absolute valuation error in RIV(Q) with standard error and a 95 percent confidence
interval (C.I.).
Aggregated for all industry sectors, the average valuation error in RIV(Q) is 43.63
(41.48;45.78) percent. The average absolute valuation error is 64.56 percent and ranges between
62.66 and 66.46 percent within a 95 percent confidence interval.
5.5. The Capitalised Earnings Model (Required Rate of Return on Equity)
PVEE(rE) is calculated by using consensus estimates for next year’s earnings at t=0 and the
estimated company required rate of return on equity. As stipulated in section 2, the valuation
error provided in PVEE(rE) with conservative accounting is the difference between capitalised
earnings and capitalised unbiased earnings at t=0. A negative (positive) valuation error would
consequently imply that PVEE(rE) on average underestimates (overestimates) the correct value
of owners’ equity:
3.50
0.60
3.00
0.40
2.50
0.20
2.00
Abs(V.E.(PVEE(rE)))
Chart 9: Average valuation error and absolute valuation error in
PVEE(rE) per sector.
32
2007
2006
2005
2004
2003
2002
2001
2000
1998
Telecommunication
Services
V.E.(PVEE(rE))
Materials
0.00
Information
Technology
-0.60
Industrials
0.50
Health Care
-0.40
Financials
1.00
Energy
-0.20
Consumer Staples
1.50
Consumer
Discretionary
0.00
1999
V.E.
V.E.
0.80
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 10: Absolute average valuation error in PVEE(rE) measured
per sector and historically.
V.E.
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Consumer Discretionary
0.0109
0.0170
-0.0224 0.0443
Consumer Staples
0.2039
0.0188
0.1669 0.2410
Energy
0.2217
0.0972
0.0292 0.4143
Financials
-0.1045
0.0091
-0.1223 -0.0867
Health Care
-0.3514
0.0167
-0.3843 -0.3185
Industrials
-0.0343
0.0093
-0.0525 -0.0161
Information Technology
-0.4500
0.0114
-0.4723 -0.4278
Materials
0.2990
0.0291
0.2418 0.3561
Telecommunication Services
-0.3902
0.0230
-0.4356 -0.3449
Table 16: Average valuation error and absolute valuation error in PVEE(rE)
interval (C.I.) per sector and ranked in ascending order.
Abs(V.E.)
Mean Std. Error
0.4399
0.0120
0.2971
0.0145
0.6696
0.0758
0.2581
0.0059
0.4536
0.0102
0.3334
0.0070
0.5237
0.0086
0.4829
0.0248
0.4191
0.0203
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4163 0.4635
5
0.2685 0.3257
2
0.5194 0.8198
9
0.2464 0.2697
1
0.4336 0.4737
6
0.3197 0.3470
3
0.5069 0.5405
8
0.4341 0.5316
7
0.3790 0.4592
4
and a 95 percent confidence
The average valuation error shows that the PVEE(rE) underestimates or overestimates the
fair value of owners’ equity depending on industry sector. On average, the valuation error is
relatively small and negative in Industrials and Financials, whereas for Consumer Discretionary
companies the model shows small but positive average errors. Information Technology,
Telecommunication Services, and Health Care all show large negative valuation errors.
The lowest average absolute valuation error is provided in Financials, Consumer Staples and
Industrials. Energy, Information Technology and Materials, however, have the largest average
absolute valuation error. Putting a 95 percent confidence interval on all mean values would imply
an absolute deviation from the fair value between 24.64 percent and 81.98 percent.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.0892
0.0059
-0.1008 -0.0776
0.3911
0.0042
0.3828 0.3994
Table 17: Average valuation error and absolute valuation error in PVEE(rE) with standard error and a 95 percent
confidence interval (C.I.).
Aggregated for all industry sectors, the average valuation error in PVEE(rE) is -8.92 (-10.08;7.76) percent. The average absolute valuation error is 39.11 percent and ranges between 38.28 and
39.94 percent within a 95 percent confidence interval.
5.6. The Capitalised Earnings Model (The Risk-free Interest Rate)
PVEE(rf) is calculated by using consensus estimates for next year’s earnings at t=0 and
the risk-free interest rate at t=0. The valuation error provided in PVEE(rf) with conservative
accounting is analogue with the V.E. in PVEE(rE) and equals the difference between capitalised
earnings and capitalised unbiased earnings at t=0. A negative (positive) valuation error would
consequently imply that PVEE(rf) on average underestimates (overestimates) the correct value of
owners’ equity:
33
1.40
7.00
1.20
6.00
1.00
5.00
V.E.(PVEE(rf))
Abs(V.E.(PVEE(rf)))
Chart 11: Average valuation error and absolute valuation error in
PVEE(rf) per sector.
2007
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 12: Absolute average valuation error in PVEE(rf) measured per
sector and historically.
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
0.7884
0.0291
0.7313 0.8454
0.9235
0.0259
0.8726 0.9744
7
Consumer Staples
0.6116
0.0210
0.5703 0.6528
0.6225
0.0199
0.5832 0.6617
2
Energy
1.2600
0.1609
0.9410 1.5790
1.4204
0.1480
1.1270 1.7139
9
Financials
0.6572
0.0170
0.6237 0.6906
0.7346
0.0141
0.7069 0.7624
5
Health Care
0.0313
0.0249
-0.0177 0.0803
0.4127
0.0162
0.3809 0.4445
1
Industrials
0.7506
0.0140
0.7232 0.7779
0.8263
0.0124
0.8019 0.8506
6
Information Technology
0.3955
0.0284
0.3398 0.4512
0.7018
0.0233
0.6560 0.7476
4
Materials
1.1402
0.0417
1.0582 1.2222
1.1860
0.0397
1.1081 1.2638
8
Telecommunication Services
0.2360
0.0489
0.1395 0.3324
0.6274
0.0269
0.5743 0.6805
3
Table 18: Average valuation error and absolute valuation error in PVEE(rf) with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
The average valuation error shows that the PVEE(rf) overestimates the fair value of owners’
equity across all industry sectors. The average valuation error in PVEE(rf) is the smallest for
Health Care, Telecommunication Services together with Information Technology. The industry
sectors with the largest valuation error are Energy, Materials and Consumer Discretionary.
Evaluating the absolute valuation error shows that Health Care, Consumer Staples and
Telecommunication Services have the smallest valuation error. Energy, Materials and Consumer
Discretionary have the largest average absolute valuation error. Putting a 95 percent confidence
interval on all mean values would imply an absolute deviation from the fair value between 38.03
percent and 171.39 percent.
Comparing the results from PVEE(rf) with the results of PVEE(rE) shows that PVEE(rf)
seem to provide a smaller absolute valuation error only for the Health Care sector. The difference
in valuation errors between PVEE(rf) and PVEE(rE) is tested in hypothesis 3.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.6673
0.0097
0.6483 0.6863
0.8085
0.0083
0.7922 0.8248
Table 19: Average valuation error and absolute valuation error in PVEE(rf) with standard error and a 95 percent
confidence interval (C.I.).
34
2006
2005
2004
2003
2002
1998
Telecommunication
Services
0.00
Materials
0.00
Information
Technology
1.00
Industrials
0.20
Health Care
2.00
Financials
0.40
Energy
3.00
Consumer Staples
0.60
2001
4.00
2000
0.80
1999
V.E.
8.00
Consumer
Discretionary
V.E.
1.60
Aggregated for all industry sectors, the average valuation error in PVEE(rf) is 66.73
(64.83;68.63) percent. The average absolute valuation error is 60.65 percent and ranges between
79.22 and 82.48 percent within a 95 percent confidence interval.
5.7. The Terminal Value Constrained Abnormal Earnings Growth Valuation Model
AEG(TVC) is calculated by using company reported information and available consensus
estimates at t=0. As stipulated in section 2, the valuation error provided in AEG(TVC) with
conservative accounting is a function of the conservative bias of owners’ equity at horizon point
of time. A negative (positive) valuation error would consequently imply that AEG(TVC) on
2.00
0.60
1.80
0.50
1.60
0.40
1.40
0.30
1.20
Chart 13: Average valuation error and absolute measurement in
AEG(TVC) measured per sector.
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.2316
0.0177
Consumer Staples
0.3983
0.0231
Energy
0.2674
0.0749
Financials
-0.0652
0.0090
Health Care
-0.0721
0.0174
Industrials
0.1675
0.0104
Information Technology
-0.1816
0.0169
Materials
0.3226
0.0229
Telecommunication Services
-0.1809
0.0218
Table 20: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
2007
Consumer Discretionary
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
Chart 14: Absolute average valuation error in AEG(TVC) measured
per sector and historically.
95 % C.I.
Lower
Upper
0.1969 0.2662
0.3529 0.4437
0.1189 0.4159
-0.0829 -0.0476
-0.1064 -0.0378
0.1472 0.1879
-0.2147 -0.1485
0.2776 0.3675
-0.2239 -0.1379
error in AEG(TVC)
Abs(V.E.)
Mean Std. Error
0.4580
0.0140
0.4314
0.0212
0.5817
0.0560
0.2505
0.0056
0.3118
0.0104
0.3424
0.0088
0.4304
0.0129
0.4028
0.0207
0.2793
0.0159
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4306 0.4854
8
0.3898 0.4731
7
0.4706 0.6928
9
0.2394 0.2616
1
0.2913 0.3323
3
0.3251 0.3597
4
0.4051 0.4557
6
0.3621 0.4436
5
0.2480 0.3106
2
and a 95 percent confidence
The average valuation error shows that the AEG(TVC) underestimates the fair value of
owners’ equity for Telecommunications Services, Information Technology, Health Care, and
Financials and overestimates the fair value of owners’ equity for Consumer Staples, Materials,
Consumer Discretionary, Industrials, and Energy. The AEG(TVC) provides the smallest
valuation error on average for Financials and Health Care. The industry sectors with the largest
valuation error are Consumer Staples and Materials. Evaluating the absolute valuation error shows
35
2006
2005
2004
2003
2002
1998
Materials
Abs(V.E.(AEG(TVC)))
Telecommunication
Services
V.E.(AEG(TVC))
Information
Technology
0.00
Industrials
-0.30
Health Care
0.20
Financials
0.40
-0.20
Energy
0.60
-0.10
Consumer Staples
0.80
0.00
2001
1.00
0.10
2000
0.20
1999
V.E.
0.70
Consumer
Discretionary
V.E.
average underestimates (overestimates) the correct value of owners’ equity:
that Financials, Telecommunication Services, and Health Care have the smallest valuation error.
Putting a 95 percent confidence interval on all mean values would imply an absolute deviation
from the fair value between 23.94 percent and 69.28 percent. Energy, Consumer Discretionary,
and Consumer Staples have the largest average absolute valuation error.
Comparing the results from AEG(TVC) with the results from PVEE(rE) shows that
AEG(TVC) seem to provide a smaller absolute valuation error across all the sectors with exception
for Industrials, Consumer Discretionary, and Consumer Staples. Comparing the results with
those from RIV(TVC), the AEG(TVC) seems to provide a smaller valuation error of the fair
value of owners’ equity with exception for Energy and Materials.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.0920
0.0062
0.0799 0.1042
0.3688
0.0048
0.3594 0.3783
Table 21: Average valuation error and absolute valuation error in AEG(TVC) with standard error and a 95 percent
confidence interval (C.I.).
Aggregated for all industry sectors, the average valuation error in AEG(TVC) is 9.20
(7.99;10.42) percent. The average absolute valuation error is 36.88 percent and ranges between
35.94 and 37.83 percent within a 95 percent confidence interval.
36
5.8. Testing of Hypothesis 1
Hypothesis 1 suggests that the absolute valuation error in RIV(TVC) [on average] is smaller
than the absolute error provided in the book value of owners’ equity. To test hypothesis 1 the
difference between the absolute valuation error in RIV(TVC) and book value of owners’ equity is
calculated for each observation:
DiffRIV(TVC)-Bv = Abs(V.E.)RIV(TVC) - Abs(V.E.)Bv
(DiffRIV(TVC)-Bv)
The mean difference is tested with a paired t-test where significant negative (positive) mean
values would imply that the absolute valuation error in RIV(TVC) [on average] is smaller (greater)
than in book value of owners’ equity:
0.90
1
0.80
0.8
0.70
0.6
0.60
Diff
0.40
0.2
2007-05-14
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
1998-06-30
Materials
Information
Technology
Abs(V.E.(BV))
Telecommunication
Services
Abs(V.E.(RIV(TVC)))
Industrials
-0.6
Health Care
-0.4
0.00
Financials
0.10
Energy
-0.2
Consumer Staples
0.20
1999-06-25
0
0.30
Consumer
Discretionary
V.E.
0.4
0.50
Abs(V.E.(RIV(TVC)))-Abs(V.E.(BV))
Chart 15: Comparison of the absolute average valuation error in
RIV(TVC) and BV per sector.
Chart 16: The difference between the absolute valuation errors in
the models, calculated for each observation.
Number of
H0: RIV(TVC)-BV = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0806*** -24.1501
0.0000
0.0000
1.0000
1343
Consumer Staples
-0.1559*** -48.1293
0.0000
0.0000
1.0000
326
Energy
-0.0271**
-2.3290
0.0109
0.0217
0.9891
109
Financials
-0.0640*** -28.3670
0.0000
0.0000
1.0000
1190
Health Care
-0.0955*** -35.9340
0.0000
0.0000
1.0000
471
Industrials
-0.0984*** -55.9340
0.0000
0.0000
1.0000
2947
Information Technology
-0.0587*** -24.8607
0.0000
0.0000
1.0000
1289
Materials
-0.0787*** -19.0168
0.0000
0.0000
1.0000
625
Telecommunication Services
-0.0376*** -9.8045
0.0000
0.0000
1.0000
204
Table 22: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(TVC)-BV = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0830*** -79.1652
0.0000
0.0000
1.0000
8504
Table 23: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Testing of hypothesis 1 show that the mean absolute valuation error in RIV(TVC) is smaller
than in book value. The largest absolute differences can be observed in Consumer Staples and
37
Health Care. For Energy and Telecommunication, the mean absolute differences are found to be
the smallest. All results are significant at the 1 percent level, except for Energy companies where
the difference is significantly less than zero at the 5 percent level.
Over time, the volatility in DiffRIV(TVC)-Bv has decreased and the differences in the sample
have converged.
The RIV(TVC) model [on average] provides a smaller absolute
Result 1:
valuation error than book value of owners’ equity for 9 out of 9
industry sectors.
5.9. Testing of Hypothesis 2 and Sub-Hypothesis
Hypothesis 2 suggests that the absolute valuation error in RIV(PMB) [on average] is smaller
than the absolute error provided in RIV(TVC). To test hypothesis 2 the difference between the
absolute valuation error in RIV(PMB) and RIV(TVC) is calculated for each observation:
DiffRIV(PMB)-RIV(TVC) = Abs(V.E.)RIV(PMB) - Abs(V.E.)RIV(TVC)
(DiffRIV(PMB)RIV(TVC))
The mean difference is subsequently tested with a paired t-test where significant negative
(positive) mean values would imply that the absolute valuation error in RIV(PMB) [on average] is
3
0.70
2.5
0.60
2
0.50
1.5
Diff
0.80
0.40
1
0.30
0.5
0.20
0
0.10
-0.5
2007-05-14
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
1999-06-25
1998-06-30
Materials
Information
Technology
Abs(V.E.(RIV(TVC)))
-1
Telecommunication
Services
Abs(V.E.(RIV(PMB)))
Industrials
Health Care
Financials
Energy
Consumer Staples
0.00
Consumer
Discretionary
V.E.
smaller (greater) than in RIV(TVC):
Abs(V.E.(RIV(PMB)))-Abs(V.E.(RIV(TVC)))
Chart 17: Comparison of the absolute average valuation error in
RIV(PMB) and RIV(TVC) per sector.
38
Chart 18: The difference between the absolute valuation errors in the
models, calculated for each observation.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0161*
-1.5582
0.0597
0.1194
0.9403
1343
Consumer Staples
-0.2311*** -41.0754
0.0000
0.0000
1.0000
326
Energy
0.2339***
3.8472
0.9999
0.0002
0.0001
109
Financials
-0.1286*** -15.7197
0.0000
0.0000
1.0000
1190
Health Care
-0.2830*** -15.7283
0.0000
0.0000
1.0000
471
Industrials
-0.0790*** -26.4430
0.0000
0.0000
1.0000
2947
Information Technology
-0.0730*** -8.0700
0.0000
0.0000
1.0000
1289
Materials
0.0368***
3.3154
0.9995
0.0010
0.0005
625
Telecommunication Services
-0.0181
-0.9548
0.1704
0.3408
0.8296
204
Table 24: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0782*** -24.5064
0.0000
0.0000
1.0000
8504
Table 25: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Testing of hypothesis 2 shows that the mean absolute valuation error in RIV(PMB) is smaller
than in RIV(TVC) for all sectors except Materials and Energy. The largest absolute differences can
be observed in Health Care and Energy and the smallest absolute difference is found in Consumer
Discretionary and Telecommunication Services. The results for Telecommunication Services are
not significant at the 10 percent level. The remaining sectors have significant results at the 1
percent or 10 percent (Consumer Discretionary) level. Over time, the volatility in the differences
has decreased.
The RIV(PMB) model [on average] provides a smaller absolute
Result 2:
valuation error than RIV(TVC) for 5 out of 9 industry sectors.
RIV(TVC) [on average] provides a smaller absolute valuation
error than RIV(PMB) for 2 out of 9 industry sectors.
In RIV(Q) the RIV(TVC) model is extended using PMB values estimated for the sample over
the whole period (Q). To test the sub-hypothesis that RIV(Q) [on average] provides a smaller
valuation error than RIV(PMB), the difference between the absolute valuation error in RIV(Q) and
RIV(PMB) is calculated for each observation:
DiffRIV(Q)-RIV(PMB) = Abs(V.E.)RIV(Q) - Abs(V.E.)RIV(PMB)
(DiffRIV(Q)RIV(PMB))
The mean difference is tested with a paired t-test where significant negative (positive) mean
values would imply that the absolute valuation error in RIV(Q) [on average] is smaller (greater)
than in RIV(PMB):
39
14
1.20
12
1.00
10
0.80
Diff
6
4
0.40
2
0.20
0
2007-05-14
Chart 20: The difference between the absolute valuation errors in the
models, calculated for each observation.
H0: RIV(Q )-RIV(PMB) = 0
t
p (<0)
p (≠0)
19.0887
1.0000
0.0000
4.4038
1.0000
0.0000
-6.7938
0.0000
0.0000
15.8932
1.0000
0.0000
4.0221
1.0000
0.0001
10.1091
1.0000
0.0000
15.4071
1.0000
0.0000
12.8344
1.0000
0.0000
11.0948
1.0000
0.0000
Significant at the 1 percent level, **
Number of
Observations
p(>0)
0.0000
1343
0.0000
326
1.0000
109
0.0000
1190
0.0000
471
0.0000
2947
0.0000
1289
0.0000
625
0.0000
204
Significant at the 5 percent
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.2206*** 27.9585
1.0000
0.0000
0.0000
8504
Table 27: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Testing of the sub-hypothesis to hypothesis 2 shows that the mean absolute valuation error in
RIV(Q) is smaller than in RIV(PMB) only for Energy companies. For all other industry sectors,
the RIV(PMB) model provides the smallest average absolute valuation error. All results are
significant at the 1 percent level. The largest absolute differences can be observed in Information
Technology, Consumer Discretionary and Telecommunication Services. The smallest absolute
difference is found in Materials and Health Care. Over time, the volatility in the difference has
been relatively constant with more extreme values concentrated around year 2000-2001.
With exception for Energy, the results contradict the sub-hypothesis for all sectors:
Sub-Result:
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
Abs(V.E.(RIV(Q)))-Abs(V.E.(RIV(PMB)))
Chart 19: Comparison of the absolute average valuation error in
RIV(Q) and RIV(PMB) per sector.
GICS Sector
Mean
Consumer Discretionary
0.4596***
Consumer Staples
0.1157***
Energy
-0.1241***
Financials
0.1114***
Health Care
0.0749***
Industrials
0.1025***
Information Technology
0.5321***
Materials
0.0080***
Telecommunication Services
0.3603***
Table 26: Paired t-test of DiffRIV(Q)-RIV(PMB). ***
level, * Significant at the 10 percent level.
1999-06-25
1998-06-30
Materials
Information
Technology
Abs(V.E.(RIV(PMB)))
-2
Telecommunication
Services
Abs(V.E.(RIV(Q)))
Industrials
Health Care
Financials
Energy
Consumer Staples
0.00
Consumer
Discretionary
V.E.
8
0.60
The RIV(Q) model [on average] provides a smaller absolute
valuation error than RIV(PMB) for 1 out of 9 industry sectors.
RIV(PMB) [on average] provides a smaller absolute valuation
error than RIV(Q) for 8 out of 9 industry sectors.
40
5.10. Testing of Hypothesis 3
Hypothesis 3 suggests that the absolute valuation error in PVEE(rf) [on average] is smaller
than the absolute error provided in PVEE(rE).
To test hypothesis 3 the difference between the absolute valuation error in PVEE(rf) and
PVEE(rE) is calculated for each observation:
DiffPVEE(rf)-PVEE(rE) = Abs(V.E.)PVEE(rf) - Abs(V.E.)PVEE(rE)
(DiffPVEE(rf)PVEE(rE))
The mean difference is tested with a paired t-test where significant negative (positive) mean
values would imply that the absolute valuation error in PVEE(rf) [on average] is smaller (greater)
than in PVEE(rE):
1.40
9
8
1.20
7
6
1.00
5
0.80
Diff
V.E.
4
0.60
3
2
0.40
1
0
0.20
-1
2007-05-14
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
1999-06-25
1998-06-30
Materials
Information
Technology
Abs(V.E.(PVEE(rE)))
-2
Telecommunication
Services
Abs(V.E.(PVEE(rf)))
Industrials
Health Care
Financials
Energy
Consumer Staples
Consumer
Discretionary
0.00
Abs(V.E.(PVEE(rf)))-Abs(V.E.(PVEE(rE)))
Chart 21: Comparison of the absolute average valuation error in
PVEE(rf) and PVEE(rE) per sector.
Chart 22: The difference between the absolute valuation errors in the
models, calculated for each observation.
H0: PVEE(rf)-PVEE(rE) = 0
GICS Sector
Mean
t
p (<0)
p (≠0)
Consumer Discretionary
0.4836*** 25.5524
1.0000
0.0000
Consumer Staples
0.3254*** 23.7195
1.0000
0.0000
Energy
0.7508***
7.8110
1.0000
0.0000
Financials
0.4765*** 29.6847
1.0000
0.0000
Health Care
-0.0410**
-2.2602
0.0121
0.0243
Industrials
0.4929*** 47.5434
1.0000
0.0000
Information Technology
0.1781***
7.5452
1.0000
0.0000
Materials
0.7031*** 30.1305
1.0000
0.0000
Telecommunication Services
0.2083***
5.1504
1.0000
0.0000
Table 28: Paired t-test of DiffPVEE(rE)-PVEE(rf). *** Significant at the 1 percent level, **
level, * Significant at the 10 percent level.
Number of
Observations
p(>0)
0.0000
1343
0.0000
326
0.0000
109
0.0000
1190
0.9879
471
0.0000
2947
0.0000
1289
0.0000
625
0.0000
204
Significant at the 5 percent
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.4174*** 58.9518
1.0000
0.0000
0.0000
8504
Table 29: Paired t-test of DiffPVEE(rE)-PVEE(rf). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
41
Testing of hypothesis 3 shows that the mean absolute valuation error in PVEE(rf) is smaller
than in PVEE(rE) only for Health Care companies. This is significant at the 5 percent level. For
all other industry sectors, the PVEE(rE) model provides the smallest average absolute valuation
error, and the results are significant at the 1 percent level. The largest absolute differences can be
observed in Energy, Materials and Industrials. The smallest absolute difference is found in Health
Care, Information Technology and Telecommunication Services. Over time, the volatility in the
difference has been relatively constant with more extreme values concentrated around year 20002001.
With exception for Health Care, the results contradict hypothesis 3 for all sectors
The PVEE(rf) model [on average] provides a smaller absolute
Result 3:
valuation error than PVEE(rE) for 1 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation
error than PVEE(rf) for 8 out of 9 industry sectors.
5.11. Testing of Hypothesis 4
Hypothesis 4 suggests that the absolute valuation error in AEG(TVC) [on average] is smaller
than the absolute error provided in PVEE(rE). To test hypothesis 4 the difference between the
absolute valuation error in AEG(TVC) and PVEE(rE) is calculated for each observation:
DiffAEG(TVC)-PVEE(rE) = Abs(V.E.)AEG(TVC) - Abs(V.E.)PVEE(rE)
(DiffAEG(TVC)PVEE(rE))
The mean difference is tested with a paired t-test where significant negative (positive) mean
values would imply that the absolute valuation error in AEG(TVC) [on average] is smaller (greater)
than in PVEE(rE):
42
0.80
5
0.70
4
3
0.60
2
1
Diff
0.40
0
0.30
-1
0.20
-2
0.10
-3
2007-05-14
Abs(V.E.(AEG(TVC)))-Abs(V.E.(PVEE(rE))
Chart 23: Comparison of the absolute average valuation error in
AEG(TVC) and PVEE(rE) per sector.
Chart 24: The difference between the absolute valuation errors in the
models, calculated for each observation.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.0181***
2.3763
0.9912
0.0176
0.0088
1343
Consumer Staples
0.1343*** 10.8061
1.0000
0.0000
0.0000
326
Energy
-0.0880
-1.0560
0.1467
0.2933
0.8533
109
Financials
-0.0076**
-1.7952
0.0364
0.0729
0.9636
1190
Health Care
-0.1419*** -12.2921
0.0000
0.0000
1.0000
471
Industrials
0.0090**
1.8258
0.9660
0.0680
0.0340
2947
Information Technology
-0.0933*** -9.5589
0.0000
0.0000
1.0000
1289
Materials
-0.0800*** -4.8402
0.0000
0.0000
1.0000
625
Telecommunication Services
-0.1397*** -9.0181
0.0000
0.0000
1.0000
204
Table 30: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0223*** -6.7949
0.0000
0.0000
1.0000
8504
Table 31: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Testing of hypothesis 4 shows that the mean absolute valuation error in AEG(TVC) is smaller
than in PVEE(rE) for all sectors with exception for Consumer Discretionary, Consumer Staples
and Industrials. The results are not significant at the 10 percent level for Energy. The largest
absolute differences can be observed in Health Care, Telecommunication Services and Consumer
Staples. The smallest absolute difference is found in Financials, Industrials and Consumer
Discretionary. Over time, the volatility in the difference has been relatively constant.
Result 4:
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
1999-06-25
1998-06-30
Materials
Information
Technology
Abs(V.E.(PVEE(rE)))
-4
Telecommunication
Services
Abs(V.E.(AEG(TVC)))
Industrials
Health Care
Financials
Energy
Consumer Staples
0.00
Consumer
Discretionary
V.E.
0.50
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than PVEE(rE) for 5 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation
error than AEG(TVC) for 3 out of 9 industry sectors.
43
5.12. Testing of Hypothesis 5
Hypothesis 5 suggests that the absolute valuation error in AEG(TVC) [on average] is smaller
than the absolute error provided in RIV(TVC). To test hypothesis 5 the difference between the
absolute valuation error in AEG(TVC) and RIV(TVC) is calculated for each observation:
DiffAEG(TVC)-RIV(TVC) = Abs(V.E.)AEG(TVC) - Abs(V.E.)RIV(TVC)
(DiffAEG(TVC)RIV(TVC))
The mean difference is tested with a paired t-test where significant negative (positive) mean
values would imply that the absolute valuation error in AEG(TVC) [on average] is smaller (greater)
than in RIV(TVC):
0.80
6
0.70
5
4
0.60
3
2
Diff
0.40
1
0.30
0
0.20
-1
0.10
-2
2007-05-14
2006-05-19
2005-05-24
2004-05-29
2003-06-04
2002-06-09
2001-06-14
2000-06-19
1999-06-25
1998-06-30
Materials
Information
Technology
Abs(V.E.(RIV(TVC)))
-3
Telecommunication
Services
Abs(V.E.(AEG(TVC)))
Industrials
Health Care
Financials
Energy
Consumer Staples
0.00
Consumer
Discretionary
V.E.
0.50
Abs(V.E.(AEG(TVC)))-Abs(V.E.(RIV(TVC)))
Chart 25: Comparison of the absolute average valuation error in
AEG(TVC) and RIV(TVC) per sector.
Chart 26: The difference between the absolute valuation errors in the
models, calculated for each observation.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0964*** -5.9113
0.0000
0.0000
1.0000
1343
Consumer Staples
-0.1494*** -6.2728
0.0000
0.0000
1.0000
326
Energy
0.1676***
3.2558
0.9992
0.0015
0.0008
109
Financials
-0.1600*** -19.9913
0.0000
0.0000
1.0000
1190
Health Care
-0.3978*** -27.0365
0.0000
0.0000
1.0000
471
Industrials
-0.1449*** -15.2183
0.0000
0.0000
1.0000
2947
Information Technology
-0.1748*** -19.9894
0.0000
0.0000
1.0000
1289
Materials
0.1195***
5.2066
1.0000
0.0000
0.0000
625
Telecommunication Services
-0.1355*** -7.7032
0.0000
0.0000
1.0000
204
Table 32: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.1344*** -26.0213
0.0000
0.0000
1.0000
8504
Table 33: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
44
Testing of hypothesis 5 shows that the mean absolute valuation error in AEG(TVC) is smaller
than in RIV(TVC) for all sectors with exception for Energy and Materials. All results are
significant at the 1 percent level. The largest absolute differences can be observed in Health Care,
Information Technology and Energy. The smallest absolute difference is found in Consumer
Discretionary, Materials and Telecommunication Services. Over time, the volatility in the
difference has converged from initially high levels during the years 1999-2001.
Result 5:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than RIV(TVC) for 7 out of 9 industry sectors.
RIV(TVC) [on average] provides a smaller absolute valuation
error than AEG(TVC) for 2 out of 9 industry sectors.
45
5.13. Summary of Empirical Results and Statistical Testing
4.00
3.20
2.40
V.E.
1.60
0.80
0.00
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 27: Average valuation error for each GICS industry sector and model over the whole period (1998-2007).
46
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
Consumer Staples
-1.60
Consumer Discretionary
-0.80
4.00
3.20
V.E.
2.40
1.60
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 28: Average absolute valuation error for each GICS industry sector and model over the whole period (1998-2007).
47
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
Consumer Staples
0.00
Consumer Discretionary
0.80
0.80
0.60
0.40
V.E.
0.20
0.00
-0.20
-0.40
-0.60
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 29: Average valuation error for each model over the whole period (1998-2007).
0.90
0.80
0.70
0.60
V.E.
0.50
0.40
0.30
0.20
0.10
0.00
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 30: Average absolute valuation error for each model over the whole period (1998-2007).
48
The empirical modelling in this section implies that:
Average
Valuation error
Average
Absolute Valuation error
Valuation
Model
Book Value
Over/underestimation
Underestimates
for all sectors.
Largest Error
Consumer Staples (-),
Health Care (-)
Smallest Error
Energy (-),
Materials (-)
Largest Error
Health Care,
Consumer
Staples
Smallest Error
Materials,
Energy
RIV(TVC)
Underestimates
for all sectors.
Health Care (-),
Consumer Staples (-)
Energy (-),
Materials (-)
Health Care,
Information
Technology
Materials,
Financials
RIV(PMB)
Underestimates
for 7/9 sectors.
Energy (+),
Consumer Staples (-)
Financials (-),
Telecommunication
Services (-)
Energy,
Consumer
Discretionary
Financials,
Materials
RIV(Q)
Overestimates
for all sectors.
Information
Technology (+),
Consumer
Discretionary (+)
Materials (+),
Financials (+)
Information
Technology,
Consumer
Discretionary
Materials,
Financials
PVEE(rE)
Underestimates
for 5/9 sectors.
Information
Technology (-),
Telecommunication
Services (-)
Consumer
Discretionary (+),
Industrials (-)
Energy,
Information
Technology
Financials,
Consumer Staples
PVEE(rf)
Overestimates
for all sectors.
Energy (+),
Materials (+)
Health Care (+),
Telecommunication
Services (+)
Energy,
Materials
Health Care,
Consumer Staples
AEG(TVC)
Overestimates
for 5/9 sectors.
Consumer Staples (+),
Materials (+)
Financials (-),
Health Care (-)
Energy,
Financials,
Consumer
Telecommunication
Discretionary
Services
Table 34: Overview of results from empirical modelling. (+) Positive average valuation error, (-) Negative average valuation error.
Summarised results from the statistical testing of hypotheses:
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
GICS Sector
Consumer Discretionary
***
*
(***)
(***)
(***)
***
Consumer Staples
***
***
(***)
(***)
***
***
Energy
**
(***)
***
(***)
(***)
Financials
***
***
(***)
(***)
**
***
Health Care
***
***
(***)
**
***
***
Industrials
***
***
(***)
(***)
(**)
***
Information Technology
***
***
(***)
(***)
***
***
Materials
***
(***)
(***)
(***)
***
(***)
Telecommunication Services
***
(***)
(***)
***
***
Table 35: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
Total
***
***
(***)
(***)
***
***
Table 36: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
In the next section, the results will be discussed and critically evaluated.
49
6. Discussion of Empirical Results and Concluding
Comments
6.1. Discussion of Empirical Results
Empirical testing of benchmark equity valuation models has been performed for seven
different valuation models on a data sample of 190 Swedish companies between 1998 and 2007
(Table 1-3). The models have differing approaches to obtain the fair value of owners’ equity, but
could [with some reservation for book value of owners’ equity] all be derived from the theory
that the value of a company’s equity capital equals the present value of expected future dividends.
The calculated differences between the fair (market) value of owners’ equity and the
estimated value in each model is referred to as the valuation error. In the empirical analysis, the
valuation error is assumed to be attributable to conservative accounting principles and the
business goodwill/badwill at t=T and the models’ failure to withstand these biases (cf. the
definition of valuation error in section 5.1.). The results show that the models’ ability to reflect
the market value of owners’ equity varies between industry sectors and over time.
Book value of owners’ equity constantly underestimates the market value of owners’ equity
for all sectors and over time, i.e. the valuation bias in book value of owners’ equity is non-positive
for all sectors. These implications fits well with the theoretical reasoning that the biased book
value at t=0 fails to capture the value of for example future earnings and that the market value of
owners’ equity should equal book value with a premium. Inferences about different levels of
conservative bias and business goodwill/badwill among the industry sectors could consequently
be made from the results. Materials and Energy sectors seem to be the sectors with the lowest
level of valuation bias. The Materials and Energy sectors comprise companies that manufacture
materials, paper, forest products and related products along with companies constructing or
providing oil rigs, drilling equipment and other energy related services and equipment. These
companies could be expected to have capital intensive business models with relatively large
proportions of the assets marked to market on the balance sheet. On the opposite side, Health
Care, Consumer Staples and Information Technology show the highest levels of conservative
accounting. These industry sectors could also be expected to have a relatively higher amount of
hidden assets that are not recorded on the balance sheet. The industries encompass companies
that are engaged in research, development and production of pharmaceuticals, development of
software application or provision of technology consulting services as well as manufacturers and
distributors of food and beverages. Examples of hidden assets on the companies’ balance sheets
could be operating assets that are recorded according to the principal of prudency and thus lead
to underestimation of the fair value of owners’ equity.
50
The RIV(TVC) model anchors the value of owners’ equity to book value, and links future
residual income to the value of equity capital to arrive at the estimated intrinsic value. RIV(TVC)
on average provides estimation below the market value for all sectors. In comparison with the
results for book value of owners’ equity the RIV(TVC) model on average results in smaller
absolute valuation errors for each sector and over time. Consequently, the anchoring of residual
income to the book value of owners’ equity seems to withstand valuation biases to a greater
extent than book value alone. The differences in valuation error across industry sectors are
comparable with the results discussed for book value of owners’ equity.
Hypothesis 1:
The RIV(TVC) model [on average] provides a smaller absolute
valuation error than the book value of owners’ equity.
Result 1:
The RIV(TVC) model [on average] provides a smaller absolute
valuation error than book value of owners’ equity for 9 out of 9
industry sectors.
Testing hypothesis 1 shows that the extension of book value in RIV(TVC) with future
residual income on average arrives at a more accurate estimation of the fair value of owners’
equity for companies in all industry sectors. This implies that RIV(TVC) is a more robust model
with a greater ability to withstand valuation bias than book value of owners’ equity (cf. the
reasoning in section 3.4.).
The valuation error in RIV(TVC) is a function of the business goodwill/badwill at the
chosen horizon point of time. To adjust for the average underestimation of the fair value in the
model, an extension of RIV(TVC) that aims to approximate the level of business
goodwill/badwill at T could be made. The extension is referred to as RIV(PMB) and uses an
estimated value per sector (the PMB value) to adjust for the conservative bias. Applying the PMB
values from Runsten (1998) (Table 5) in an extension of the RIV(TVC) model results in a varying
degree of adjustment in valuation errors. The extended residual income valuation does not
underestimate the value for all sectors; for Energy and Materials companies RIV(PMB) provide a
positive valuation error on average, i.e. the model overestimates the value of owners’ equity. For
all other sectors, however, RIV(PMB) shows lower absolute levels of valuation error and the
extension seem to have provided a better estimate of the fair value.
Hypothesis 2:
The RIV(PMB) model [on average] provides a smaller absolute
valuation error than the RIV(TVC) model.
Result 2:
The RIV(PMB) model [on average] provides a smaller absolute
valuation error than RIV(TVC) for 5 out of 9 industry sectors.
51
RIV(TVC) [on average] provides a smaller absolute valuation error
than RIV(PMB) for 2 out of 9 industry sectors.
Testing hypothesis 2 shows that the extension of RIV(TVC) provides better estimates than
RIV(TVC) for 5 out of 9 sectors, with exception for Materials and Energy. The two sectors
exhibited the lowest absolute (negative) levels of valuation error in RIV(TVC) modelling, and thus
it could be concluded that the applied PMB values from Runsten (1998) was a poor estimate
which overestimated the level of business goodwill at T for these sectors. The positive error in
the estimated level of business goodwill could possibly be explained by the different sector
categorisation used by Runsten (1998). Runsten (1998) also concludes that the factors that
influence the level of measurement bias varies over time and per company and thus the PMB
values should ideally be calculated per company and year rather than subjectively taken from a
static table. By reverse-engineering the residual value in the RIV(TVC) estimation, an estimate of
the q value that potentially would capture the valuation bias from a company that has not reached
steady state has been computed for each observation. To avoid “data mining” and explicit fitting
of parameters to the historical data sample, however, the estimated values (Q), have not been
computed on a yearly basis but as an average over the whole period. The extension of the
RIV(TVC) with the Q values results in a consequent overestimation of the market value for all
sectors. The results imply a weaker ability in RIV(Q) compared to RIV(PMB) to capture valuation
biases. The results also indicate that the level of business goodwill/badwill at T varies
considerably over time in the sample.
Sub-Hypothesis:
The RIV(Q) model [on average] provides a smaller valuation
error than RIV(PMB).
Sub-Result:
The RIV(Q) model [on average] provides a smaller absolute
valuation error than RIV(PMB) for 1 out of 9 industry sectors.
RIV(PMB) [on average] provides a smaller absolute valuation
error than RIV(Q) for 8 out of 9 industry sectors.
Testing the sub-hypothesis that the average estimations of Q values would more accurately
adjust the RIV(TVC) model than the adjustment of conservative bias with PMB values, shows
that this holds only for Energy companies. The poorly applied PMB value from Runsten (1998)
for this sector is more accurately estimated by an average Q value over the whole period (cf. the
comparison between PMB and Q in Table 10). The estimated Q values in general, however, seem
to be influenced by very high levels of business goodwill during some years in the beginning of
the period, and the effect from these extreme values could explain the poor adjustment of
RIV(TVC) and that the estimated values do not result in smaller valuation errors than in
52
RIV(PMB). The rejection of the sub-hypothesis for 8 out of 9 sectors harmonizes with the
comments in Runsten (1998) about varying levels of factors influencing the level of goodwill at T
over time as well as the difficulties in estimating the PMB values.
Estimating a company’s equity capital from an earnings-based valuation approach is most
easily achieved by capitalising the next year’s expected earnings with the company required rate of
return on equity. This model is referred to as the present value of expected earnings (PVEE(rE)),
and the valuation error from conservative accounting in PVEE(rE) equals the difference between
capitalised next year’s earnings and capitalised next year’s unbiased earnings. The results for
PVEE(rE), show varying levels of both under- and overestimation of the fair value of owners’
equity. The average absolute valuation error is the smallest for Financials, Consumer Staples and
Industrials companies. These industry sectors could consequently be anticipated to encompass
companies with relatively low levels of conservative bias in next year’s earnings. The results also
show that PVEE(rE) on average underestimates the fair value the most for Information
Technology, Telecommunication Services and Health Care Companies. Underlying assumptions
(cf. the assumption that all earnings are paid out as dividends in section 3.6.) in the PVEE(rE)
model make it difficult to attribute the valuation error in the model only to different levels of
conservative accounting principles. The industries, for which PVEE(rE) on average
underestimates the fair value the most, have all shown higher-than-steady-state levels of growth
over the period. Releasing the assumption that T=1=T* (i.e. that the company has entered steady
state and that the growth equals zero) could possibly add to the explanation that the calculated
valuation errors to some extent reflect the model’s failure to include future growth in its valuation
of owners’ equity. In Materials and Energy companies, on the other hand, owners’ equity is on
average overestimated by PVEE(rE); the implications of this (that next year’s earnings are heavily
biased by conservative accounting) could interestingly be compared with the results from the
empirical testing of the asset-based book value approach (where the same sectors in contrast
showed the smallest average absolute valuation error).
In section 3.6, the reasoning that the unconsidered effect of growth in earnings in PVEE(rE)
could possibly be adjusted for by replacing the denominator with the risk-free interest rate is
presented. The estimation rests on the assumption that the growth rate equals the risk adjusted
market risk premium, and would result in a more accurate estimation than PVEE(rE) for any
company or sector where this holds or where the growth rate is greater than the difference
between rE and rf:
Hypothesis 3:
The Capitalised Earnings Model where earnings are capitalised
with the risk-free interest rate [on average] provides a smaller
valuation error than earnings capitalised with the required rate of
return on equity.
53
The PVEE(rf) model [on average] provides a smaller absolute
Result 3:
valuation error than PVEE(rE) for 1 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation error
than PVEE(rf) for 8 out of 9 industry sectors.
Empirical testing shows that the results from PVEE(rf) on average provide an
overestimation of the value of owners’ equity for all sectors. The smallest overestimation and
average absolute valuation error is provided for Health Care companies, and this is also the only
sector for which PVEE(rf) provides a more accurate estimate of the value of owners’ equity on
average over time.
The assumption of no growth in the nominator for PVEE is a strong assumption that
evidently seems to result in underestimated values of owners’ equity. Adjusting the denominator
under the assumption that the growth rate would equal the difference between the risk-free
interest rate and the required rate of return on equity, however, does not seem to be an
appropriate adjustment for all sectors26.
The AEG(TVC) model anchors future abnormal earnings to capitalised earnings to arrive at
an estimation of the value of owners’ equity. AEG(TVC), on average provides the largest
estimations below the market value for Information Technology, Telecommunication Services
and Health Care companies. The valuation error in AEG(TVC) is a function of the growth in
expected level of conservative bias as T+1. Consequently, the growth in conservative bias for
companies in the three sectors could be anticipated to be high at T+1.
26
Suggesting an alternative approach could be to replace the assumption of no growth with an assumption
that the company growth rate in earnings equals the expected level of inflation (i.e. the company real
growth rate is zero) that is included in the nominal risk-free interest rate at t=0:
The relationship between inflation (i), real (r) and nominal (R) interest
rates can be described (1 + r)(1 + i) = (1 + R).
In this alternative approach, the next year’s earnings would consequently be capitalised using the
required rate of return on equity less the expected inflation rate (rE – i). Provided an expected inflation
greater than zero at t=0, this approach would result in a valuation somewhere between PVEE(rE) and
PVEE(rf).
Further research to empirically evaluate the reasoning presented in this alternative approach is
suggested by the authors. The impact of adopting the revised discount rate (rE – i) in the parsimonious
terminal value constrained version of the Abnormal Earnings Growth valuation model could possibly also
be researched.
54
Hypothesis 4:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than PVEE(rE).
Result 4:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than PVEE(rE) for 5 out of 9 industry sectors.
PVEE(rE) [on average] provides a smaller absolute valuation error
than AEG(TVC) for 3 out of 9 industry sectors.
The testing of hypothesis 4 indicates that the AEG(TVC) provides better estimates than the
PVEE(rE) of the fair value of owners’ equity with exception for Consumer Discretionary and
Industrials. These sectors would consequently include companies with relatively low growth
levels in conservatively biased future earnings. Consumer Discretionary and Industrials include
companies that manufacture automotive, household durable goods and capital goods including
aerospace and defence (Table 24). The results from testing hypothesis 4 suggest that AEG(TVC)
on average decreases the absolute valuation error for 5 out of 9 sectors. In line with the reasoning
above about anticipated levels of conservative accounting in the Health Care sector, and the
discussion of permanent measurement biases in Runsten (1998), the relatively large adjustment
for Health Care companies seems reasonable. Over the studied time period, the estimated Q
values for the Health Care sector have steadily increased (Table 9). This historical growth in
business goodwill at T could imply that the level of conservative accounting in the sector has
increased. AEG(TVC) focuses on earnings and earnings growth in the short and in the long run,
and thus the model could therefore be expected to provide a smaller valuation error than
PVEE(rE) for the Health Care sector (cf. the underestimation of fair value of owners’ equity in
PVEE(rE) for Health Care companies).
Skogsvik and Juettner-Nauroth (2007) suggest that the valuation error in the terminal value
constrained AEG model is typically smaller than in the corresponding RIV model if the growth
of the conservative bias lies within a certain interval of “normal” values.
Hypothesis 5:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than RIV(TVC).
Result 5:
The AEG(TVC) model [on average] provides a smaller absolute
valuation error than RIV(TVC) for 7 out of 9 industry sectors.
RIV(TVC) [on average] provides a smaller absolute valuation error
than AEG(TVC) for 2 out of 9 industry sectors.
The testing of hypothesis 5 shows that the AEG(TVC) model provides a smaller absolute
valuation error than the RIV(TVC) model for all sectors with exception for Energy and Materials.
55
As earlier touched upon, the Energy and Materials sectors encompass companies with relatively
low levels of expected exposure to conservative accounting principles. The empirical testing
shows that the largest absolute differences can be observed for Health Care and Information
Technology. Companies within these sectors generally possess characteristics of high Q values
and could consequently be expected to have a relatively higher exposure to conservative
accounting principles.
Comparing the average valuation errors show different levels of bias in the results (i.e. an
average valuation error close to zero). A relatively unbiased result such as the PVEE(rE)
valuation for Consumer Discretionary companies (1.09 percent) could be useful in the context of
portfolio valuation.
Comparing the total results aggregated over all industry sectors, shows that PVEE(rE) and
AEG(TVC) provide the smallest biases and average absolute valuation errors together with
RIV(PMB). Evaluating the aggregated results in an attempt to rank the models would, however,
imply a naïve approach to equity valuation modelling.
6.2. The Validity and Robustness of the Empirical Results
The empirical results should generally be robust to different data sources or sample selection
conditions. Strong assumptions and limited consistency of the data, however, motivates a
discussion of the validity and robustness of the results:
It should be noted that evaluation of equity valuation models revolve on a harsh treatment of
accounting numbers, e.g. the assumption that CSR holds is necessary in the valuation modelling.
This relation, however, could not be expected to hold in practice. The short horizon point of
time, where the truncation of the parsimonious valuation models occur (FY3) could be expected
to appear at a stage where T<T*, and thus the assumption of steady state could also be expected
to be violated. The impact of the short horizon point of time on the valuation models is
summarised in conjunction with the estimation of Q values (cf. Table 10 and the associated
discussion).
Cyclical market effects that appear over the time period could potentially lead to biased
results. To make inferences about the impact over time from periods with relatively extreme
conditions, the sample is divided into two sub-samples (1998-2002 and 2003-2007), for which the
empirical analysis and statistical testing is performed in a first robustness test:
The robustness test of the empirical results for the two time periods shows fairly similar
results (cf. Appendix 18-19 for empirical results and statistical testing) to the main results and
conclusions about historical fluctuations presented in the previous section.
The use of consensus estimates as a proxy for market expectations on the specific
companies’ future book value of owners’ equity, earnings and dividends requires accurate analyst
forecasts. Preferably, the number of estimates should be high enough to categorically motivate
56
this assumption. To test for the implications of few estimates, a sub-sample is empirically
evaluated in a second robustness test:
The sub-sample consists of all observations with five or more consensus estimates for each
parameter and fiscal period. When limiting he sample by adding restrictions to the sample criteria
on the minimum number of consensus estimates, the number of observations decreases to 2 705.
GICS Sector
1998
1999
2000
2001
2002
2003
2004
2005
Consumer Discretionary
0
36
49
30
11
36
70
49
Consumer Staples
0
8
13
1
0
7
19
13
Energy
0
0
0
0
0
0
0
0
Financials
0
37
44
42
24
46
61
41
Health Care
0
5
15
2
0
3
15
7
Industrials
0
47
118
89
36
95
156
121
Information Technology
0
7
32
22
2
8
47
23
Materials
0
19
32
28
3
24
52
49
Telecommunication Services
0
5
10
15
1
15
23
20
Total
0
164
313
229
77
234
443
323
Table 37: Total number of complete observation in robustness test sub-sample per industry sector and year.
2006
76
18
0
66
28
168
34
60
23
473
2007
79
13
1
71
28
156
30
52
19
449
Total
436
92
1
432
103
986
205
319
131
2705
The robustness test shows that the results are in line with the results for the whole sample.
With fewer degrees of freedom, however, the statistical significance in the results is affected
negatively (cf. Table 128-139, where the statistical results for the Energy sector are not
significant).
The estimated equity risk premium is used to infer the required rate of return on equity and,
thus, the assumption will have impacts on [some of] the evaluated models:
E( rE ) = rf + β ⋅ [E(rm ) − rf ]
(CAPM)
gives that
[E(rm ) − rf ] ↑⇒ E( rE ) ↑ ,
i.e. when the equity risk premium increases, this leads to a higher required rate of return on
equity and the models that comprise the required rate of return on equity will be affected
analogously. The robustness of the results, with regards to the assumption of the equity risk
premium, is consequently tested by repeating the empirical analysis with an assumed equity risk
premium of 5.0 percent. The results (cf. Appendix) show little deviations from the results
obtained with a 4.0 percent risk premium. Hence, the aggregated results could be viewed as
robust for the proposed risk premium. This reasoning could be applied to a discussion regarding
the impact of poorly estimated beta values; the estimation of industry sector beta values over time
shows a more or less volatile pattern (Chart 32) and this volatility could potentially affect the
empirical results. The direct link to the required rate of return on equity through CAPM and the
57
equity risk premium provides a possibility to estimate the impact of changes in beta on the results
without performing separate robustness tests: β ↑⇒ E( rE ) ↑ .
In conclusion, the results can generally [with exception for specific observations] be seen as
robust over time. The observed variations in the statistical results, however, recognize the
difficulties in finding appropriate rules of thumb to apply on industry sectors and over a long
period of time.
58
7. References
Dimson E., Marsh P., and Staunton M. (2005), “Global Investment Returns Yearbook 2005”,
London, London Business School., pp. 5-75.
Modigliani, F., and Miller, M. H. (1958), “The Cost of Capital, Corporation Finance, and the
theory of Investment”, American Economic Review, Vol. 48, No. 3, pp. 261-297.
Ohlson, J.A. (1995), “Earnings, Book Values and Dividends in Equity Valuation”, Contemporary
Accounting Research, Vol. 11.
Ohlson, J.A. (2005), “On Accounting-Based Valuation Formulae”, Review of Accounting Studies,
Vol. 10, No. 2-3.
Ohlson, J.A and Juettner-Nauroth, B. E. (2005), “Expected EPS and EPS Growth as
Determinants of Value”, Review of Accounting Studies, Vol. 10.
Penman, S.H. (2007), “Financial Statement Analysis and Security Valuation”, McGraw-Hill Irwin,
3rd ed., pp. 119-139, 177-224.
Runsten, M. (1998), “The Association between Accounting Information and Stock Prices”,
Stockholm: EFI., pp. 41-56, 140-173.
Skogsvik, K., and Jennergren, P. (2007), “The Abnormal Earnings Growth Model: Applicability
and Applications”, SSE/EFI Working Paper Series in Business Administration No.
2007:11, Stockholm School of Economics.
Skogsvik, K., and Juettner-Nauroth, B. E. (2007), “The Impact of Conservative Accounting in
Residual Income and Abnormal Earnings Growth Valuation Modelling”.
59
8. Appendix
Most of the formulas and derivations in the appendices are summarised from the working
paper by Skogsvik and Juettner-Nauroth (2007). Cf. Skogsvik and Juettner-Nauroth (2007) for
the full theoretical reasoning and derivations.
8.1. Appendix 1: Derivation of AEG(TVC) from PVED
T
V0 = ∑
t =1
=
E 0 ( X 1 ) E 0 ( Div 1 ) E 0 ( X 1 ) E 0 ( X 2 ) E 0 ( Div 2 ) E 0 ( X 2 )
+
−
+
+
−
rE
RE
rE
rE ⋅ R E
R 2E
rE ⋅ R E
+ ..... +
=
E 0 ( DIVt ) E o ( PT )
+
=
RE
RT
E 0 ( X T ) E 0 ( Div T ) E 0 ( X T ) E 0 ( PT )
+
−
+
=
rE ⋅ R ET −1
R TE
rE ⋅ R ET −1
R ET
E 0 ( X 1 ) T −1 E 0 ( X t +1 + rE ⋅ Div t − X t ⋅ R E ) rE E 0 ( PT + Div T − X T ⋅ R E ) rE
+∑
+
t =1
rE
R tE
R ET
(Skogsvik and Juettner-Nauroth, 2007)
60
8.2. Appendix 2: GICS Industry Sectors and GICS Level 1 Sector Group Indexes
GICS Sector
Description
GICS Level 1 Sector Group Index
Consumer
Discretionary
The GICS Consumer Discretionary Sector encompasses those
industries that tend to be the most sensitive to economic cycles. Its
manufacturing segment includes automotive, household durable
goods, textiles & apparel and leisure equipment. The services
segment includes hotels, restaurants and other leisure facilities,
media production and services, and consumer retailing and
services.
The Stockholmsborsen All-Share Consumer
Discretionary Sector Price Index is a
capitalization-weighted index. The index was
developed with a base value of 100 as of
December 31, 1995. The parent index is SAX.
Consumer
Staples
The GICS Consumer Staples Sector comprises companies whose
businesses are less sensitive to economic cycles. It includes
manufacturers and distributors of food, beverages and tobacco and
producers of nondurable household goods and personal products.
It also includes food & drug retailing companies as well as
hypermarkets and consumer super centres.
The Stockholmsborsen All-Share Consumer
Staples Sector Price Index is a capitalizationweighted index. The index was developed with
a base value of 100 as of December 31, 1995.
The parent index is SAX.
Energy
The GICS Energy Sector comprises companies whose businesses
are dominated by either of the following activities: The
construction or provision of oil rigs, drilling equipment and other
energy related service and equipment, including seismic data
collection. Companies engaged in the exploration, production,
marketing, refining and/or transportation of oil and gas products,
coal and other consumable fuels.
The Stockholmsborsen All-Share Energy
Sector Index is a capitalization-weighted index.
The index was developed with a base value of
100 as of December 31, 1995. The parent index
is SAX.
Financials
The GICS Financial Sector contains companies involved in
activities such as banking, mortgage finance, consumer finance,
specialized finance, investment banking and brokerage, asset
management and custody, corporate lending, insurance, and
financial investment, and real estate, including REITs.
The Stockholmsborsen All-Share Financial
Sector Price Index is a capitalization-weighted
index. The index was developed with a base
value of 100 as of December 31, 1995. The
parent index is SAX.
Health Care
The GICS Health Care Sector encompasses two main industry
groups. The first includes companies who manufacture health care
equipment and supplies or provide health care related services,
including distributors of health care products, providers of basic
health-care services, and owners and operators of health care
facilities and organizations. The second regroups companies
primarily involved in the research, development, production and
marketing of pharmaceuticals and biotechnology products.
The Stockholmsborsen All-Share Health Care
Sector Price Index is a capitalization-weighted
index. The index was developed with a base
value of 100 as of December 31, 1995. The
parent index is SAX.
Industrials
The GICS Industrials Sector includes companies whose businesses
are dominated by one of the following activities: The manufacture
and distribution of capital goods, including aerospace & defence,
construction, engineering & building products, electrical equipment
and industrial machinery. The provision of commercial services
and supplies, including printing, employment, environmental and
office services. The provision of transportation services, including
airlines, couriers, marine, road & rail and transportation
infrastructure.
The Stockholmsborsen All-Share Industrials
Sector Index is a capitalization-weighted index.
The index was developed with a base value of
100 as of December 31, 1995. The parent index
is SAX.
Information
Technology
The GICS Information Technology Sector covers the following
general areas: firstly, Technology Software & Services, including
companies that primarily develop software in various fields such as
the Internet, applications, systems, databases management and/or
home entertainment, and companies that provide information
technology consulting and services, as well as data processing and
outsourced services; secondly Technology Hardware & Equipment,
including manufacturers and distributors of communications
equipment, computers & peripherals, electronic equipment and
related instruments; and thirdly, Semiconductors & Semiconductor
Equipment Manufacturers.
The Stockholmsborsen All-Share Materials
Sector Price Index is a capitalization-weighted
index. The index was developed with a base
value of 100 as of December 31, 1995. The
parent index is SAX.
Materials
The GICS Materials Sector encompasses a wide range of
commodity-related manufacturing industries. Included in this
sector are companies that manufacture chemicals, construction
materials, glass, paper, forest products and related packaging
products, and metals, minerals and mining companies, including
producers of steel.
The Stockholmsborsen All-Share Information
Technology Sector Price Index is a
capitalization-weighted index. The index was
developed with a base value of 100 as of
December 31, 1995. The parent index is SAX.
Telecommunicat
ion Services
The GICS Telecommunications Services Sector contains
companies that provide communications services primarily through
a fixed-line, cellular, wireless, high bandwidth and/or fibber optic
able network.
The Stockholmsborsen All-Share
Telecommunication Services Sector Price Index
is a capitalization-weighted index. The index
was developed with a base value of 100 as of
December 31, 1995. The parent index is SAX.
Table 38: Description of GICS Industry Sectors and corresponding GICS Level 1 Sector Group indexes. Information retrieved from
BLOOMBERG.
61
8.3. Appendix 3: Data Sample
Company
GICS Sector
1998-2007
>=5 Estimates
AARHUSKARLSHAMN
Consumer Staples
17
0
ABB (OME)
Industrials
83
31
ACANDO 'B'
Information Technology
63
0
ADDTECH 'B'
Industrials
53
0
ALFA LAVAL
Industrials
56
47
ANGPANNEFORENINGEN 'B'
Industrials
71
0
ANOTO GROUP
Information Technology
2
0
ASPIRO
Information Technology
4
0
ASSA ABLOY 'B'
Industrials
100
63
ATLAS COPCO 'A'
Industrials
112
87
AUDIODEV 'B'
Information Technology
34
0
AUTOLIV SDB
Consumer Discretionary
105
67
AVANZA
Financials
16
0
AXFOOD
Consumer Staples
91
19
AXIS
Information Technology
31
0
B&B TOOLS 'B'
Industrials
107
0
BALLINGSLOV INTL.
Consumer Discretionary
61
0
BE GROUP
Industrials
5
0
BEIJER ALMA 'B'
Industrials
35
0
BETSSON 'B'
Consumer Discretionary
7
0
BILIA 'A'
Consumer Discretionary
84
2
BILLERUD
Materials
55
34
BIOVITRUM
Health Care
1
0
BJORN BORG
Consumer Discretionary
6
0
BOLIDEN
Materials
45
28
BONGS LJUNGDAHL 'B'
Industrials
53
0
BOSS MEDIA
Information Technology
45
0
BRINOVA FASTIGHETER
Financials
20
0
BROSTROM
Energy
51
1
BTS GROUP
Industrials
36
0
BURE EQUITY
Financials
19
0
CARDO
Industrials
75
27
CARL LAMM
Information Technology
9
0
CASHGUARD 'B'
Information Technology
6
0
CASTELLUM
Financials
67
38
CATENA
Financials
1
0
CISION
Industrials
65
6
CLAS OHLSON 'B'
Consumer Discretionary
77
22
CLOETTA FAZER 'B'
Consumer Staples
84
0
CONCORDIA MARITIME 'B'
Energy
35
0
CONNECTA
Information Technology
19
0
CTT SYSTEMS
Industrials
3
0
D CARNEGIE & CO
Financials
69
3
DIGITAL VISION
Information Technology
1
0
DIOS FASTIGHETER
Financials
9
0
DORO
Information Technology
22
0
ELANDERS 'B'
Consumer Discretionary
63
4
ELECTROLUX 'B'
Consumer Discretionary
112
74
ELEKTA 'B'
Health Care
89
16
ENEA
Information Technology
63
0
ENIRO
Consumer Discretionary
81
44
ERICSSON 'B'
Information Technology
84
72
EXPANDA 'B'
Industrials
15
0
FABEGE
Financials
63
12
FAGERHULT
Industrials
18
0
FASTIGHETS BALDER 'B'
Financials
6
0
FENIX OUTDOOR
Consumer Discretionary
28
0
G & L BEIJER
Industrials
22
0
GANT COMPANY
Consumer Discretionary
9
1
GETINGE
Health Care
88
51
GUNNEBO
Industrials
62
28
GUNNEBO INDUSTRIER
Industrials
17
0
HAKON INVEST AB
Consumer Staples
20
0
Table 39: Sample members, assigned GICS industry sector and total number of complete observations.
62
5% Risk Premium
17
83
63
53
56
71
2
4
100
112
34
105
16
91
31
107
61
5
35
7
84
55
1
6
45
53
45
20
51
36
19
75
9
6
67
1
65
77
84
35
19
3
69
1
9
22
63
112
89
62
81
84
15
63
18
3
28
22
9
88
62
17
20
Company
GICS Sector
1998-2007
>=5 Estimates
5% Risk Premium
HALDEX
Industrials
88
48
88
HEBA 'B'
Financials
26
0
25
HEMTEX
Consumer Discretionary
16
1
16
HENNES & MAURITZ 'B'
Consumer Discretionary
112
91
112
HEXAGON 'B'
Industrials
79
22
79
HIQ INTERNATIONAL
Information Technology
68
27
68
HL DISPLAY 'B'
Industrials
60
0
60
HOGANAS 'B'
Materials
86
44
86
HOLMEN 'B'
Materials
112
68
112
HOME PROPERTIES
Financials
55
0
55
HQ
Financials
8
0
8
HUFVUDSTADEN 'A'
Financials
54
13
54
IBS 'B'
Information Technology
71
13
71
INDL.& FINL.SYS.'B'
Information Technology
43
13
43
INDUSTRIVARDEN 'A'
Financials
11
0
11
INDUTRADE
Industrials
20
0
20
INTELLECTA 'B'
Industrials
7
0
7
INTRUM JUSTITIA
Industrials
56
3
56
INVESTOR 'B'
Financials
57
0
57
JEEVES INFO.SYSTEMS
Information Technology
9
0
9
JM
Consumer Discretionary
84
26
84
KABE HUSVAGNAR 'B'
Consumer Discretionary
11
0
11
KAPPAHL HOLDINGS
Consumer Discretionary
11
0
11
KAROLIN MACHINE TOOL
Industrials
47
0
47
KAUPTHING BANK
Financials
8
0
8
KLOVERN
Financials
23
0
23
KNOW IT
Information Technology
44
0
44
KUNGSLEDEN
Financials
53
1
53
LAGERCRANTZ 'B'
Information Technology
47
0
47
LATOUR INVESTMENT 'B'
Financials
4
0
4
LAWSON SOFTWARE (OME)
Information Technology
2
0
2
LINDAB INTERNATIONAL
Industrials
9
6
9
LINDEX
Consumer Discretionary
99
26
99
LUNDBERGFORETAGEN 'B'
Financials
9
0
9
LUNDIN MINING SDB
Materials
19
2
19
MALMBERGS ELEKTRISKA
Industrials
12
0
12
MEDA 'A'
Health Care
48
8
48
MEDIVIR 'B'
Health Care
2
0
2
MEKONOMEN
Consumer Discretionary
42
0
42
METRO INTL.SDB 'B'
Consumer Discretionary
32
0
32
MIDELFART SONESSON 'A'
Consumer Staples
1
0
1
MILLICOM INTL.CELU.SDB
Telecommunication Services
14
0
14
MOBYSON
Information Technology
11
0
11
MODERN TIMES GP.MTG 'B'
Consumer Discretionary
79
48
79
MODUL 1 DATA
Information Technology
23
0
23
MUNTERS
Industrials
86
17
86
NCC 'B'
Industrials
74
34
74
NEFAB 'B'
Industrials
46
0
46
NEONET
Financials
6
0
6
NET INSIGHT 'B'
Information Technology
2
0
2
NEW WAVE GROUP 'B'
Consumer Discretionary
56
16
56
NIBE INDUSTRIER 'B'
Industrials
73
1
73
NOBEL BIOCARE (OME)
Health Care
83
7
83
NOBIA
Consumer Discretionary
55
14
55
NOCOM 'B'
Information Technology
2
0
2
NOKIA (OME)
Information Technology
5
5
5
NOLATO 'B'
Information Technology
58
9
58
NORDEA BANK
Financials
104
90
104
NORDNET SECURITIES BANK
Financials
17
0
17
NOTE
Information Technology
6
0
6
NOVOTEK 'B'
Information Technology
6
0
6
OEM INTERNATIONAL 'B'
Industrials
10
0
10
OMX
Financials
76
40
76
Table 39 (cont’d): Sample members, assigned GICS industry sector and total number of complete observations.
63
Company
GICS Sector
1998-2007
>=5 Estimates
5% Risk Premium
ORC SOFTWARE
Information Technology
55
17
55
ORIFLAME COSMETICS SDB
Consumer Staples
32
17
32
ORTIVUS 'B'
Health Care
13
0
13
PA RESOURCES 'B'
Energy
6
0
6
PARTNERTECH
Information Technology
56
0
56
PEAB 'B'
Industrials
68
5
68
POOLIA 'B'
Industrials
63
0
63
PREVAS 'B'
Information Technology
13
0
13
PROACT IT GROUP
Information Technology
9
0
9
PROFFICE 'B'
Industrials
52
0
52
PROFILGRUPPEN 'B'
Materials
35
0
35
Q-MED
Health Care
55
21
55
RATOS 'B'
Financials
10
0
10
RAYSEARCH LABORATORIES
Health Care
28
0
28
READSOFT 'B'
Information Technology
36
0
36
REJLERKONCERNEN 'B'
Industrials
1
0
1
RNB RETAIL AND BRANDS
Consumer Discretionary
35
0
35
ROTTNEROS
Materials
61
17
61
SAAB 'B'
Industrials
78
23
78
SANDVIK
Industrials
112
82
112
SAS
Industrials
40
22
40
SCA 'B'
Materials
112
69
112
SCANIA 'B'
Industrials
87
63
87
SCRIBONA 'B'
Information Technology
49
0
49
SEB 'A'
Financials
112
77
112
SECO TOOLS 'B'
Industrials
79
0
79
SECTRA 'B'
Health Care
64
0
64
SECURITAS 'B'
Industrials
108
90
108
SECURITAS SYSTEMS
Industrials
8
3
8
SEMCON
Information Technology
59
0
59
SENSYS TRAFFIC
Information Technology
11
0
11
SIGMA B
Information Technology
28
0
28
SKANSKA 'B'
Industrials
108
56
108
SKF 'B'
Industrials
109
95
109
SKISTAR 'B'
Consumer Discretionary
20
0
20
SSAB 'A'
Materials
89
57
89
STORA ENSO 'A' (OME)
Materials
11
0
11
STUDSVIK
Industrials
10
0
10
SWECO 'B'
Industrials
49
0
49
SWEDBANK 'A'
Financials
112
79
112
SVEDBERGS 'B'
Industrials
35
0
35
SWEDISH MATCH
Consumer Staples
81
56
81
SVENSKA HANDBKN.'A'
Financials
112
78
112
SWITCHCORE
Information Technology
3
0
3
TELE2 'B'
Telecommunication Services
99
65
99
TELECA 'B'
Information Technology
87
30
87
TELELOGIC
Information Technology
53
17
53
TELIASONERA
Telecommunication Services
81
66
81
TELIGENT
Information Technology
11
0
11
THALAMUS NETWORKS 'B'
Telecommunication Services
10
0
10
TICKET TRAVEL
Consumer Discretionary
40
0
40
TIETOENATOR (OME)
Information Technology
10
0
10
TRADEDOUBLER
Information Technology
19
2
19
TRANSCOM WWD.SDB.B
Industrials
47
0
47
TRELLEBORG 'B'
Industrials
82
45
82
UNIFLEX 'B'
Industrials
22
0
22
WALLENSTAM 'B'
Financials
42
0
42
WEDINS SKOR&ACCESSORIES
Consumer Discretionary
1
0
1
WEST SIBERIAN RES.SDB
Energy
17
0
17
WIHLBORGS FASTIGHETER
Financials
21
1
21
VOLVO 'B'
Industrials
111
82
111
XANO INDUSTRI 'B'
Industrials
23
0
23
XPONCARD
Information Technology
10
0
10
ZODIAK TELEVISION 'B'
Consumer Discretionary
17
0
17
Table 39 (cont’d): Sample members, assigned GICS industry sector and total number of complete observations.
64
8.4. Appendix 4: Valuation error in RIV(TVC)
The valuation bias of RIV(TVC) is calculated as the difference between
( TVC )
V0RIV
:
, UB
T*
( TVC )
= Bv (oUB ) + ∑
V0RIV
, UB
t =1
T*
( TVC )
= Bv o + ∑
V0RIV
,CB
t =1
= ( Bv
E 0 (X t − r ⋅ Bv t −1 )
=
R tE
E 0 (X (t UB ) − ∆( Cb t ) − r ⋅ ( Bv (t −UB1 ) − Cb t −1 )
− Cb 0 ) + ∑
=
R tE
t =1
T*
( UB )
o
RIV ( TVC )
0 , UB
V
E 0 (X (t UB ) − r ⋅ Bv (t −UB1 ) )
R tE
= Bv
)
E 0 (X (t UB ) − r ⋅ Bv (t UB
−1 )
+∑
R tE
t =1
T*
( UB )
o
The valuation bias of RIV(TVC):
T*
( TVC )
( TVC )
V0RIV
− V0RIV
= −Cb 0 + ∑
,CB
, UB
t =1
E 0 (− ∆( Cb t ) + r ⋅ Cb t −1 )
R tE
It can be inferred that:
( TVC )
( TVC )
V0RIV
− V0RIV
+
,CB
, UB
E 0 (Cb T* )
T*
RE
=0
And hence:
( TVC )
( TVC )
V0RIV
− V0RIV
=−
,CB
, UB
E 0 (Cb T * )
T*
RE
(Skogsvik and Juettner-Nauroth, 2007)
65
( TVC )
V0RIV
and
,CB
8.5. Appendix 5: Valuation error in RIV(PMB)
The valuation error in RIV(PMB) V0 − P0 is derived from
T
V0RIV( PMB ) = Bv 0 + ∑
t =1
E 0 ( X t − rE ⋅ Bv t −1 ) q ⋅ Bv T
+
= P0
R tE
R ET
(RIV(PMB))
Where q is the correct adjustment for business goodwill/badwill at T* (i.e. company is in
steady state):
q ⋅ Bv T E 0 ( PT − Bv T )
=
R TE
R TE
And q is estimated by PMB. The valuation error is subsequently a function of the failure in
PMB to estimate q correctly:
V0 − P0 = −
( PMB − q ) ⋅ Bv T
R ET
66
8.6. Appendix 6: Valuation error in AEG(TVC)
In order for the AEG(TVC) model to have no valuation bias with unbiased accounting
principles, the horizon point in time is here set to T=(T*+1). With this value of T, the valuation
of AEG(TVC):
( TVC )
V0AEG
=
, UB
E 0 (X (1UB ) ) T* E 0 (X (t +UB1 ) + r ⋅ Div t − X (t UB ) ⋅ R E )/ rE
+∑
rE
R tE
t =1
( TVC )
V0AEG
=
,CB
E 0 (X 1 ) T* E 0 (X t +1 + r ⋅ Div t − X t ⋅ R E )/ rE
+∑
=
rE
R tE
t =1
=
[
]
)
( UB )
E 0 (X (1UB ) − ∆( Cb 1 )) T* E 0 (X (t UB
− ∆( Cb t ))⋅ R E ) / rE
+1 − ∆( Cb t +1 )) + r ⋅ Div t − (X t
+∑
=
t
rE
RE
t =1
( TVC )
( TVC )
The difference between V0AEG
and V0AEG
:
,CB
, UB
( TVC )
( TVC )
V0AEG
− V0AEG
=
,CB
, UB
E 0 (− ∆( Cb1 )) T* E 0 [(− ∆( Cb t +1 )) + (Cb t ) ⋅ R E )]/ rE
+∑
rE
R tE
t =1
Expressed together with the assumption of zero valuation error in the unconstraint AEG
valuation model:
( TVC )
( TVC )
V0AEG
− V0AEG
=
,CB
, UB
=−
E 0 [(− ∆( Cb T* +1 )) + (Cb T* ) ⋅ R E )]/ rE
T*
RE
E 0 [∆(Cb T* +1 )]/ rE
T*
RE
(Skogsvik and Juettner-Nauroth, 2007)
67
−
E 0 [(∆Cb T * ) ⋅ R E ]/ rE
T*
RE
=
8.7. Appendix 7: Comparison Between the Valuation Error in AEG(TVC) and
RIV(TVC)
( TVC )
( TVC )
The valuation error in RIV(TVC) is V0RIV
− V0RIV
=−
,CB
, UB
E 0 (Cb T * )
T*
RE
, and given that the
valuation bias is non-positive due to conservative biased accounting regime, the sign of the
valuation error of the AEG(TVC) is indeterminate:
( TVC )
( TVC )
V0AEG
− V0AEG
=
,CB
, UB
=−
E 0 [(− ∆( Cb T* +1 )) + (Cb T* ) ⋅ R E )]/ rE
T*
RE
E 0 [∆(Cb T* +1 )]/ rE
−
E 0 [(∆Cb T * ) ⋅ R E ]/ rE
T*
RE
T*
RE
The following two conditions must both be fulfilled for the AEG(TVC) to dominate
RIV(TVC):
( TVC )
( TVC )
V0AEG
− V0AEG
>−
,CB
, UB
E 0 (Cb T* )
T*
RE
( TVC )
( TVC )
and V0AEG
− V0AEG
<
,CB
, UB
E 0 (Cb T* )
T*
RE
Solving for the two equations above:
−
E 0 [∆(Cb T * +1 )]
rE ⋅ R E
T*
>
E 0 (Cb T * )
T*
RE
⇔
E 0 [Cb T * ⋅ rE − ∆(Cb T* +1 )] > 0
and
−
E 0 [∆(Cb T * +1 )]
rE ⋅ R E
T*
<−
E 0 (Cb T * )
T*
RE
⇔
E 0 [Cb T * ⋅ rE − ∆(Cb T* +1 )] > 0
This implies that the valuation error of AEG(TVC) is smaller than the valuation error of
RIV(TVC) if the expected growth of the conservative bias in period (T*+1) is smaller
than E 0 (Cb T* ) ⋅ rE , but larger than − E0 (Cb T * ) ⋅ rE .
(Skogsvik and Juettner-Nauroth, 2007)
68
=
8.8. Appendix 8: Beta Calculations
2.50
1.80
1.60
2.00
1.40
1.20
Beta
0.80
1.00
0.60
0.40
0.50
0.20
Chart 31: Average (1998-2007) beta values per industry sector.
69
Consumer Staples
Energy
Financials
Health Care
Industrials
Information Technology
Materials
Telecommunication Services
2002
0.8589
0.0996
0.7542
0.8779
0.4046
0.6816
1.9807
0.5130
1.2016
2003
0.8786
0.2045
0.8645
1.0167
0.6593
0.8705
2.0107
0.6295
1.2447
2004
0.7507
0.2786
0.9503
0.9267
0.7169
0.9573
2.0587
0.6749
1.0413
2005
0.7104
0.3777
0.9954
0.8103
0.5603
0.9764
2.0658
0.6275
1.0100
2006
0.8150
0.5132
1.1527
0.9969
0.6733
1.1285
1.2986
0.9587
0.9124
2007
0.8852
0.5723
1.1704
1.0552
0.6488
1.1684
1.0151
1.1475
0.8280
2007-10-31
2007-04-30
Consumer Discretionary
Chart 32: Estimated beta values per industry sector historically.
GICS Sector
1998
1999
2000
2001
Consumer Discretionary
0.9272 0.9313 0.7403 0.6383
Consumer Staples
0.3979 0.2182 0.1134
Energy
0.8651 0.8464 0.3718 0.3845
Financials
0.8789 0.9144 0.6868 0.6221
Health Care
0.8365 0.7170 0.3538 0.1109
Industrials
0.8687 0.8064 0.4254 0.3752
Information Technology
1.5740 1.6932 1.8373 1.9835
Materials
0.8042 0.7479 0.4068 0.3038
Telecommunication Services
1.0981 1.1438 1.2231 1.1501
Table 40: Average estimated beta values per industry sector and year.
2006-10-31
2006-04-30
2005-10-31
2005-04-30
2004-10-31
2004-04-30
2003-10-31
2003-04-30
2002-10-31
2002-04-30
2001-10-31
2001-04-30
2000-10-31
2000-04-30
1999-10-31
1999-04-30
1998-10-31
1998-04-30
Telecommunication
Services
Materials
Information
Technology
Industrials
Health Care
Financials
Energy
Consumer Staples
Avg(Beta)
1997-10-31
0.00
0.00
Consumer
Discretionary
Beta
1.50
1.00
8.9. Appendix 9: Average Absolute Valuation errors per Sector and Year
GICS Sector
1998
1999
2000
2001
2002
2003
2004
2005
2006
Consumer Discretionary
0.5944 0.6266 0.5807 0.6177 0.6585 0.4969 0.5581 0.6626 0.6873
Consumer Staples
0.7468 0.7045 0.7868 0.8107 0.7101 0.7104 0.7593 0.7153
Energy
0.5339 0.6000 0.7171 0.5253 0.3751 0.3522 0.3397 0.5072 0.4579
Financials
0.5699 0.5407 0.5352 0.5436 0.5003 0.3655 0.4425 0.5027 0.4372
Health Care
1.1787 0.7521 0.7150 0.4923 0.8222 0.7728 0.7691 0.8281 0.8515
Industrials
0.5458 0.5945 0.5549 0.5985 0.6376 0.4153 0.4948 0.5872 0.6549
Information Technology
0.8041 0.7401 0.7781 0.9021 0.4186 0.4636 0.5941 0.6295 0.6799
Materials
0.3512 0.3151 0.3130 0.2818 0.3317 0.2613 0.2914 0.3296 0.5090
Telecommunication Services
0.8927 0.8976 0.8775 0.6986 0.4388 0.2619 0.2729 0.1933 0.3788
Table 41: Average absolute valuation error in book value of owners’ equity measured per industry sector and year.
2007
0.7364
0.7629
0.4353
0.4699
0.8483
0.7021
0.6777
0.4807
0.5695
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
0.6647 0.5916 0.5755 0.5881 0.6493 0.4457 0.4591
Consumer Staples
0.5934 0.5176 0.6038 0.6578 0.5078 0.5436
Energy
0.6033 0.5815 0.6785 0.7009 0.5377 0.2825 0.2465
Financials
0.5162 0.5025 0.4752 0.4661 0.4142 0.3061 0.3611
Health Care
1.1142 0.6260 0.5841 0.4548 0.7228 0.6439 0.6788
Industrials
0.4571 0.5250 0.4728 0.5062 0.5290 0.3343 0.3862
Information Technology
0.7517 0.6632 0.7618 0.9209 0.4319 0.4315 0.5529
Materials
0.3394 0.2538 0.2327 0.2184 0.2219 0.2163 0.2317
Telecommunication Services
0.8458 0.8456 0.8411 0.7033 0.4622 0.2611 0.2068
Table 42: Average absolute valuation error in RIV(TVC) measured per industry sector and year.
2005
0.5383
0.5964
0.3883
0.4229
0.7434
0.4717
0.5797
0.2556
0.1504
2006
0.5691
0.5877
0.4211
0.3800
0.7651
0.5494
0.5868
0.3812
0.3153
2007
0.6199
0.6455
0.3942
0.4160
0.7655
0.5946
0.5700
0.3843
0.5038
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
0.9816 0.6755 0.7341 0.8418 0.7949 0.6435 0.4550
Consumer Staples
0.3192 0.2049 0.3424 0.4120 0.2415 0.3022
Energy
2.1066 2.2956 1.8859 1.7264 1.5616 1.0536 0.2227
Financials
0.2275 0.3428 0.3875 0.2471 0.2087 0.3203 0.2239
Health Care
1.2833 0.5199 0.6919 0.3077 0.3698 0.3401 0.3410
Industrials
0.4087 0.4468 0.4538 0.4889 0.4691 0.3181 0.2837
Information Technology
0.5758 0.5965 0.7328 1.1617 0.4570 0.5082 0.4644
Materials
0.5642 0.2892 0.4053 0.2840 0.1409 0.4049 0.3205
Telecommunication Services
0.7514 0.7609 0.7541 0.5275 0.3770 0.2940 0.1871
Table 43: Average absolute valuation error in RIV(PMB) measured per industry sector and year.
2005
0.3971
0.3856
0.0752
0.2393
0.4060
0.3459
0.4703
0.3081
0.3547
2006
0.4075
0.3904
0.2510
0.2442
0.4010
0.4379
0.4505
0.2525
0.3895
2007
0.4271
0.4758
0.1799
0.3104
0.3938
0.4894
0.4035
0.2890
0.2806
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
2.0530 1.3389 1.6136 1.6198 1.5863 1.5477 1.0316
Consumer Staples
0.4510 0.6705 0.3705 0.3433 0.4969 0.3911
Energy
1.6244 1.7458 1.4986 1.3975 1.2331 0.7823 0.1163
Financials
0.1696 0.3505 0.4580 0.3334 0.2959 0.5679 0.3892
Health Care
1.7915 1.0652 1.0899 0.7795 0.7549 0.5927 0.4271
Industrials
0.6877 0.6145 0.8072 0.7382 0.6982 0.8161 0.4347
Information Technology
0.4593 0.8066 0.9584 2.7940 1.2041 1.8901 0.8969
Materials
0.5806 0.3003 0.4208 0.2959 0.1515 0.4179 0.3329
Telecommunication Services
0.5757 0.6033 0.5922 0.2115 0.7392 0.8841 0.8749
Table 44: Average absolute valuation error in RIV(Q) equity measured per industry sector and year.
2005
0.6723
0.3060
0.1551
0.3348
0.2902
0.3269
0.8977
0.3181
1.1468
2006
0.5483
0.4902
0.2219
0.3707
0.2455
0.2988
0.8313
0.2486
0.9027
2007
0.4566
0.5255
0.1976
0.4021
0.2296
0.3188
0.8181
0.2879
0.3995
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
0.9971 0.6472 0.6937 0.6632 0.5083 0.5569 0.4766
Consumer Staples
0.2269 0.3944 0.3415 0.2466 0.6297 0.3238
Energy
2.8301 3.3191 0.2991 1.8405 0.7797 0.4694 0.2254
Financials
0.2666 0.3131 0.2768 0.2251 0.1030 0.2281 0.2251
Health Care
0.3598 0.4036 0.6387 0.7114 0.3241 0.3415 0.4124
Industrials
0.3196 0.3717 0.5727 0.6098 0.2827 0.3230 0.2348
Information Technology
0.6893 0.5800 0.7474 0.7363 0.5613 0.6363 0.5895
Materials
0.4251 0.2805 1.0107 0.9390 0.2511 0.3794 0.3818
Telecommunication Services
0.8142 0.7812 0.7851 0.7327 0.6989 0.3705 0.1003
Table 45: Average absolute valuation error in PVEE(rE) measured per industry sector and year.
2005
0.3166
0.3752
0.1938
0.2757
0.4493
0.2461
0.5169
0.6690
0.1605
2006
0.2527
0.1189
0.5746
0.2698
0.4868
0.2546
0.3781
0.3590
0.3133
2007
0.2908
0.1838
0.3992
0.3021
0.5031
0.2909
0.3111
0.2445
0.3888
70
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
1.7187 0.9684 1.1777 0.9913 0.9640 1.3306 1.0003
Consumer Staples
0.5219 0.5991 0.4571 0.3383 0.9164 0.6596
Energy
5.7250 6.8951 0.2459 2.6168 1.8482 1.5989 1.3064
Financials
0.6520 0.5516 0.5131 0.6751 0.6580 0.8002 0.7769
Health Care
0.5286 0.6396 0.7587 0.6959 0.3889 0.5578 0.4287
Industrials
0.9529 0.6946 0.9172 0.9459 0.5977 0.8932 0.7846
Information Technology
0.3535 0.5319 0.8290 1.6039 0.8587 0.6320 0.5356
Materials
1.2797 0.5099 1.5096 1.4056 0.7363 0.9842 1.1472
Telecommunication Services
0.6375 0.5718 0.5824 0.4851 0.4735 0.3535 0.8080
Table 46: Average absolute valuation error in PVEE(rf) measured per industry sector and year.
2005
0.9935
1.0110
1.5975
1.0742
0.3324
1.1340
0.7990
1.6861
1.1745
2006
0.7334
0.5762
0.9707
0.7772
0.2426
0.7922
0.6276
1.1832
0.5727
2007
0.4745
0.3184
0.6108
0.6724
0.2431
0.5671
0.6445
1.0940
0.4261
GICS Sector
1998
1999
2000
2001
2002
2003
2004
Consumer Discretionary
1.0991 0.5812 0.7840 0.7610 0.5625 0.6278 0.4988
Consumer Staples
0.2845 0.7054 0.7026 0.3380 0.7326 0.4969
Energy
1.0538 0.2981 1.7813 1.4198 1.8145 0.5941 0.5867
Financials
0.2343 0.2319 0.2296 0.2461 0.1541 0.2564 0.2395
Health Care
0.1539 0.3611 0.5552 0.3186 0.2490 0.3177 0.3292
Industrials
0.3884 0.3600 0.7538 0.7590 0.4600 0.3817 0.2182
Information Technology
0.4371 0.4831 0.6682 1.0891 0.3755 0.4339 0.4245
Materials
0.5601 0.3577 1.0200 0.6544 0.3514 0.4891 0.2526
Telecommunication Services
0.5396 0.5597 0.6806 0.6359 0.3530 0.1974 0.1481
Table 47: Average absolute valuation error in AEG(TVC) measured per industry sector and year.
2005
0.4213
0.5722
0.4698
0.3016
0.3069
0.2069
0.3867
0.3643
0.2143
2006
0.2156
0.1875
0.3537
0.2449
0.2837
0.1754
0.2796
0.2155
0.1384
2007
0.2104
0.1584
0.2500
0.2812
0.2387
0.2011
0.2580
0.1487
0.1220
71
8.10. Appendix 10: Empirical Results 1998-2002
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.4254
0.0300
-0.4844 -0.3664
0.6165
0.0183
0.5804 0.6526
5
Consumer Staples
-0.7439
0.0114
-0.7666 -0.7212
0.7439
0.0114
0.7212 0.7666
7
Energy
0.5352
0.0358
0.4605 0.6100
0.5352
0.0358
0.4605 0.6100
3
Financials
-0.4911
0.0148
-0.5202 -0.4620
0.5345
0.0102
0.5145 0.5544
2
Health Care
-0.4173
0.0707
-0.5577 -0.2770
0.7681
0.0283
0.7118 0.8243
8
Industrials
-0.4599
0.0142
-0.4877 -0.4320
0.5823
0.0082
0.5662 0.5983
4
Information Technology
-0.5806
0.0413
-0.6618 -0.4995
0.7889
0.0283
0.7332 0.8446
9
Materials
-0.2807
0.0182
-0.3165 -0.2448
0.3154
0.0151
0.2856 0.3452
1
Telecommunication Services
-0.6739
0.0396
-0.7532 -0.5947
0.7034
0.0304
0.6426 0.7643
6
Table 48: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a 95 percent
confidence interval (C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.4665
0.0099
-0.4860 -0.4470
0.6003
0.0064
0.5877 0.6129
Table 49: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a
95 percent confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.3012
0.0335
Consumer Staples
-0.5696
0.0120
Energy
0.6232
0.0337
Financials
-0.4297
0.0144
Health Care
-0.3178
0.0671
Industrials
-0.3250
0.0153
Information Technology
-0.5098
0.0437
Materials
-0.1327
0.0197
Telecommunication Services
-0.6793
0.0324
Table 50: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.3670 -0.2354
-0.5934 -0.5459
0.5528 0.6935
-0.4580 -0.4014
-0.4510 -0.1846
-0.3550 -0.2951
-0.5958 -0.4239
-0.1716 -0.0938
-0.7441 -0.6144
error in RIV(TVC),
Abs(V.E.)
Mean Std. Error
0.6046
0.0185
0.5696
0.0120
0.6232
0.0337
0.4721
0.0104
0.6650
0.0326
0.4974
0.0091
0.7627
0.0299
0.2475
0.0133
0.6916
0.0280
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5683 0.6410
5
0.5459 0.5934
4
0.5528 0.6935
6
0.4517 0.4925
2
0.6004 0.7297
7
0.4794 0.5153
3
0.7039 0.8215
9
0.2213 0.2737
1
0.6356 0.7476
8
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.3556
0.0106
-0.3763 -0.3349
0.5374
0.0068
0.5241 0.5508
Table 51: Average valuation error and absolute valuation error in RIV(TVC), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.1311
0.0500
Consumer Staples
-0.2822
0.0168
Energy
1.8623
0.0724
Financials
-0.0984
0.0215
Health Care
0.4471
0.0924
Industrials
-0.1322
0.0186
Information Technology
-0.2563
0.0616
Materials
0.2045
0.0266
Telecommunication Services
-0.4718
0.0511
Table 52: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
0.0328 0.2295
-0.3156 -0.2489
1.7113 2.0133
-0.1407 -0.0561
0.2637 0.6304
-0.1687 -0.0957
-0.3774 -0.1352
0.1521 0.2570
-0.5739 -0.3697
error in RIV(PMB),
Abs(V.E.)
Mean Std. Error
0.7713
0.0294
0.2852
0.0162
1.8623
0.0724
0.3086
0.0155
0.6081
0.0826
0.4564
0.0120
0.7724
0.0460
0.3447
0.0181
0.5842
0.0269
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.7135 0.8292
7
0.2530 0.3175
1
1.7113 2.0133
9
0.2780 0.3391
2
0.4442 0.7719
6
0.4328 0.4800
4
0.6819 0.8628
8
0.3090 0.3805
3
0.5304 0.6380
5
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.0521
0.0148
-0.0811 -0.0230
0.5241
0.0105
0.5034 0.5447
Table 53: Average valuation error and absolute valuation error in RIV(PMB), with standard error and a 95 percent
confidence interval (C.I.).
72
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
1.2021
0.0944
1.0165 1.3878
1.5753
0.0773
1.4233 1.7273
9
Consumer Staples
0.4949
0.0369
0.4217 0.5681
0.5097
0.0346
0.4410 0.5784
3
Energy
1.4648
0.0551
1.3499 1.5797
1.4648
0.0551
1.3499 1.5797
8
Financials
0.1778
0.0284
0.1219 0.2337
0.3624
0.0235
0.3162 0.4085
2
Health Care
1.0232
0.1164
0.7922 1.2542
1.0642
0.1126
0.8407 1.2877
6
Industrials
0.5104
0.0310
0.4496 0.5712
0.7207
0.0262
0.6692 0.7722
5
Information Technology
0.8146
0.1377
0.5436 1.0856
1.2816
0.1260
1.0336 1.5295
7
Materials
0.2227
0.0270
0.1695 0.2759
0.3581
0.0185
0.3217 0.3945
1
Telecommunication Services
-0.0855
0.0870
-0.2594 0.0885
0.5497
0.0538
0.4422 0.6573
4
Table 54: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.5848
0.0270
0.5319 0.6378
0.8359
0.0242
0.7884 0.8833
Table 55: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence
interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.0831
0.0474
Consumer Staples
0.2885
0.0322
Energy
1.5222
0.3278
Financials
-0.0752
0.0167
Health Care
-0.2118
0.0521
Industrials
0.1691
0.0233
Information Technology
-0.4812
0.0356
Materials
0.5062
0.0669
Telecommunication Services
-0.7474
0.0162
Table 56: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.0102 0.1764
0.2245 0.3525
0.8384 2.2060
-0.1080 -0.0424
-0.3152 -0.1084
0.1235 0.2148
-0.5512 -0.4113
0.3744 0.6380
-0.7797 -0.7151
error in PVEE(rE),
Abs(V.E.)
Mean Std. Error
0.6609
0.0321
0.3234
0.0284
1.6708
0.2894
0.2452
0.0117
0.5000
0.0254
0.4708
0.0184
0.6941
0.0218
0.6536
0.0603
0.7474
0.0162
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5977 0.7241
6
0.2670 0.3798
2
1.0671 2.2744
9
0.2221 0.2683
1
0.4497 0.5504
4
0.4346 0.5069
3
0.6512 0.7370
7
0.5348 0.7724
5
0.7151 0.7797
8
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.0409
0.0153
0.0109 0.0710
0.5191
0.0113
0.497
0.5413
Table 57: Average valuation error and absolute valuation error in PVEE(rE), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Consumer Discretionary
0.7766
0.0789
0.6215 0.9318
Consumer Staples
0.5196
0.0365
0.4471 0.5922
Energy
3.0551
0.5808
1.8436 4.2666
Financials
0.4778
0.0262
0.4263 0.5293
Health Care
0.1112
0.0738
-0.0352 0.2577
Industrials
0.6783
0.0318
0.6159 0.7408
Information Technology
0.2772
0.0909
0.0985 0.4560
Materials
1.0745
0.0804
0.9160 1.2331
Telecommunication Services
-0.5092
0.0323
-0.5738 -0.4446
Table 58: Average valuation error and absolute valuation error in PVEE(rf),
interval (C.I.) per sector and ranked in ascending order.
Abs(V.E.)
Mean Std. Error
1.0894
0.0676
0.5265
0.0355
3.1297
0.5606
0.5880
0.0195
0.6260
0.0402
0.8345
0.0276
0.8853
0.0776
1.1207
0.0773
0.5279
0.0272
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.9565 1.2223
7
0.4561 0.5969
1
1.9603 4.2991
9
0.5497 0.6264
3
0.5462 0.7057
4
0.7802 0.8887
5
0.7325 1.0380
6
0.9684 1.2730
8
0.4736 0.5821
2
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.6035
0.0235
0.5574 0.6496
0.854
0.0202
0.8145 0.8936
Table 59: Average valuation error and absolute valuation error in PVEE(rf), with standard error and a 95 percent
confidence interval (C.I.).
73
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.2696
0.0499
Consumer Staples
0.5531
0.0502
Energy
1.3887
0.1634
Financials
-0.0178
0.0151
Health Care
0.0848
0.0476
Industrials
0.4205
0.0267
Information Technology
-0.1478
0.0582
Materials
0.6365
0.0543
Telecommunication Services
-0.5260
0.0258
Table 60: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Abs(V.E.)
Lower
Upper
Mean Std. Error
0.1713 0.3678
0.7069
0.0358
0.4534 0.6527
0.5621
0.0490
1.0478 1.7295
1.3887
0.1634
-0.0475 0.0120
0.2211
0.0102
-0.0096 0.1793
0.3703
0.0309
0.3682 0.4728
0.5861
0.0231
-0.2623 -0.0334 0.6879
0.0443
0.5294 0.7436
0.6588
0.0530
-0.5776 -0.4745 0.5341
0.0230
error in AEG(TVC), with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.6364 0.7773
8
0.4647 0.6595
4
1.0478 1.7295
9
0.2011 0.2411
1
0.3091 0.4315
2
0.5406 0.6315
5
0.6007 0.7750
7
0.5543 0.7632
6
0.4881 0.5800
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.2518
0.0167
0.2191 0.2844
0.5614
0.0133
0.5354 0.5875
Table 61: Average valuation error and absolute valuation error in AEG(TVC), with standard error and a 95 percent
confidence interval (C.I.).
74
8.11. Appendix 11: Empirical Results 2003-2007
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.6136
0.0097
-0.6326 -0.5946 0.6417
0.0076
0.6267 0.6567
7
Consumer Staples
-0.7338
0.0098
-0.7530 -0.7145 0.7338
0.0098
0.7145 0.7530
8
Energy
-0.3141
0.0377
-0.3890 -0.2391 0.4187
0.0233
0.3725 0.4650
3
Financials
-0.3830
0.0113
-0.4052 -0.3607 0.4457
0.0080
0.4300 0.4613
4
Health Care
-0.8150
0.0059
-0.8266 -0.8033 0.8150
0.0059
0.8033 0.8266
9
Industrials
-0.5625
0.0060
-0.5743 -0.5507 0.5874
0.0047
0.5782 0.5965
5
Information Technology
-0.5536
0.0118
-0.5767 -0.5304 0.6229
0.0074
0.6084 0.6375
6
Materials
-0.3204
0.0150
-0.3499 -0.2908 0.3848
0.0108
0.3635 0.4061
2
Telecommunication Services
-0.2842
0.0260
-0.3355 -0.2329 0.3376
0.0209
0.2964 0.3789
1
Table 62: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a 95 percent
confidence interval (C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.5407
0.0041
-0.5488 -0.5325 0.5804
0.0031
0.5743 0.5865
Table 63: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a
95 percent confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.4808
0.0105
Consumer Staples
-0.5853
0.0079
Energy
-0.2750
0.0317
Financials
-0.3306
0.0095
Health Care
-0.7215
0.0064
Industrials
-0.4525
0.0058
Information Technology
-0.5029
0.0101
Materials
-0.2221
0.0131
Telecommunication Services
-0.2379
0.0234
Table 64: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.5013 -0.4602
-0.6008 -0.5697
-0.3381 -0.2119
-0.3493 -0.3120
-0.7341 -0.7090
-0.4637 -0.4412
-0.5227 -0.4831
-0.2477 -0.1964
-0.2842 -0.1916
error in RIV(TVC),
Abs(V.E.)
Mean Std. Error
0.5364
0.0072
0.5853
0.0079
0.3642
0.0188
0.3809
0.0068
0.7215
0.0064
0.4825
0.0044
0.5536
0.0068
0.3009
0.0085
0.2883
0.0189
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5222 0.5506
6
0.5697 0.6008
8
0.3268 0.4015
3
0.3676 0.3941
4
0.7090 0.7341
9
0.4739 0.4910
5
0.5403 0.5670
7
0.2842 0.3176
2
0.2509 0.3257
1
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.4471
0.0038
-0.4545 -0.4396 0.4891
0.0028
0.4835 0.4946
Table 65: Average valuation error and absolute valuation error in RIV(TVC), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.1754
0.0165
Consumer Staples
-0.3722
0.0145
Energy
0.1836
0.0548
Financials
-0.0127
0.0132
Health Care
-0.2683
0.0176
Industrials
-0.3023
0.0073
Information Technology
-0.2372
0.0157
Materials
0.0709
0.0180
Telecommunication Services
0.1087
0.0315
Table 66: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.2077 -0.1430
-0.4008 -0.3436
0.0747 0.2926
-0.0386 0.0133
-0.3029 -0.2338
-0.3166 -0.2880
-0.2681 -0.2064
0.0355 0.1063
0.0464 0.1710
error in RIV(PMB),
Abs(V.E.)
Mean Std. Error
0.4549
0.0097
0.3755
0.0141
0.3582
0.0438
0.2691
0.0092
0.3777
0.0109
0.3854
0.0050
0.4535
0.0096
0.3082
0.0105
0.3110
0.0195
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4359 0.4739
9
0.3477 0.4034
5
0.2712 0.4453
4
0.2510 0.2872
1
0.3563 0.3990
6
0.3756 0.3951
7
0.4346 0.4724
8
0.2876 0.3288
2
0.2724 0.3496
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1900
0.0055
-0.2008 -0.1792 0.3839
0.0034
0.3772 0.3906
Table 67: Average valuation error and absolute valuation error in RIV(PMB), with standard error and a 95 percent
confidence interval (C.I.).
75
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
0.5811
0.0318
0.5188 0.6435
0.7912
0.0268
0.7387 0.8438
7
Consumer Staples
0.2038
0.0329
0.1388 0.2687
0.4478
0.0200
0.4084 0.4872
6
Energy
0.0365
0.0474
-0.0577 0.1307
0.2994
0.0351
0.2296 0.3691
1
Financials
0.2525
0.0166
0.2200 0.2851
0.4083
0.0121
0.3845 0.4321
4
Health Care
0.0730
0.0263
0.0214 0.1247
0.3499
0.0193
0.3119 0.3879
3
Industrials
0.1980
0.0127
0.1730 0.2230
0.4106
0.0099
0.3912 0.4300
5
Information Technology
0.8849
0.0403
0.8058 0.9641
0.9931
0.0377
0.9192 1.0670
9
Materials
0.0867
0.0183
0.0507 0.1226
0.3136
0.0109
0.2922 0.3350
2
Telecommunication Services
0.7540
0.0483
0.6585 0.8495
0.8519
0.0347
0.7833 0.9204
8
Table 68: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.3747
0.0106
0.3538 0.3955
0.5666
0.0091
0.5487 0.5845
Table 69: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence
interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.0149
0.0155
Consumer Staples
0.1702
0.0226
Energy
-0.0886
0.0536
Financials
-0.1186
0.0107
Health Care
-0.3890
0.0154
Industrials
-0.1316
0.0070
Information Technology
-0.4398
0.0096
Materials
0.1978
0.0272
Telecommunication Services
-0.2269
0.0214
Table 70: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.0454 0.0156
0.1256 0.2148
-0.1951 0.0179
-0.1397 -0.0975
-0.4193 -0.3588
-0.1453 -0.1178
-0.4586 -0.4210
0.1444 0.2513
-0.2693 -0.1845
error in PVEE(rE),
Abs(V.E.)
Mean Std. Error
0.3608
0.0105
0.2866
0.0168
0.4307
0.0288
0.2643
0.0068
0.4411
0.0110
0.2677
0.0047
0.4679
0.0081
0.3995
0.0213
0.2689
0.0176
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.3402 0.3814
5
0.2534 0.3198
4
0.3734 0.4880
7
0.2510 0.2775
1
0.4196 0.4627
8
0.2585 0.2769
2
0.4521 0.4837
9
0.3577 0.4414
6
0.2341 0.3037
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1432
0.0053
-0.1536 -0.1328
0.338
0.0035
0.3311 0.3449
Table 71: Average valuation error and absolute valuation error in PVEE(rE), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Consumer Discretionary
0.7926
0.0276
0.7384 0.8468
Consumer Staples
0.6482
0.0251
0.5988 0.6977
Energy
0.8316
0.1018
0.6292 1.0340
Financials
0.7436
0.0212
0.7020 0.7853
Health Care
0.0097
0.0246
-0.0386 0.0581
Industrials
0.7851
0.0139
0.7579 0.8123
Information Technology
0.4342
0.0230
0.3891 0.4794
Materials
1.1722
0.0482
1.0776 1.2669
Telecommunication Services
0.5766
0.0470
0.4837 0.6695
Table 72: Average valuation error and absolute valuation error in PVEE(rf),
interval (C.I.) per sector and ranked in ascending order.
Abs(V.E.)
Mean Std. Error
0.8641
0.0254
0.6608
0.0236
1.0125
0.0808
0.8053
0.0182
0.3552
0.0162
0.8224
0.0127
0.6417
0.0173
1.2178
0.0454
0.6729
0.0367
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.8143 0.9139
7
0.6142 0.7073
3
0.8519 1.1732
8
0.7695 0.8410
5
0.3233 0.3871
1
0.7974 0.8473
6
0.6078 0.6757
2
1.1286 1.3070
9
0.6004 0.7454
4
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.6938
0.0096
0.6750 0.7126
0.7896
0.0083
0.7734 0.8058
Table 73: Average valuation error and absolute valuation error in PVEE(rf), with standard error and a 95 percent
confidence interval (C.I.).
76
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.2180
0.0160
Consumer Staples
0.3365
0.0243
Energy
-0.0002
0.0538
Financials
-0.0881
0.0111
Health Care
-0.1144
0.0175
Industrials
0.0466
0.0071
Information Technology
-0.1927
0.0118
Materials
0.1694
0.0170
Telecommunication Services
-0.0231
0.0174
Table 74: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Abs(V.E.)
Lower
Upper
Mean Std. Error
0.1866 0.2493
0.3689
0.0129
0.2887 0.3843
0.3792
0.0214
-0.1071 0.1067
0.3891
0.0339
-0.1099 -0.0663 0.2647
0.0067
-0.1487 -0.0800 0.2960
0.0102
0.0327 0.0605
0.2259
0.0051
-0.2158 -0.1695 0.3461
0.0073
0.1359 0.2028
0.2779
0.0132
-0.0575 0.0113
0.1629
0.0108
error in AEG(TVC), with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.3437 0.3942
7
0.3371 0.4214
8
0.3216 0.4565
9
0.2514 0.2779
3
0.2760 0.3160
5
0.2160 0.2359
2
0.3316 0.3605
6
0.2520 0.3038
4
0.1416 0.1841
1
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.0257
0.0051
0.0157 0.0357
0.2889
0.0035
0.282
0.2958
Table 75: Average valuation error and absolute valuation error in AEG(TVC), with standard error and a 95 percent
confidence interval (C.I.).
77
8.12. Appendix 12: Empirical Results Five or More Consensus Estimates (1998-2007)
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.5787
0.0181
-0.6142 -0.5432 0.6238
0.0142
0.5959 0.6517
6
Consumer Staples
-0.8253
0.0090
-0.8432 -0.8073 0.8253
0.0090
0.8073 0.8432
9
Energy
-0.3747
.
.
.
0.3747
.
.
.
1
Financials
-0.4599
0.0087
-0.4769 -0.4429 0.4684
0.0075
0.4536 0.4832
4
Health Care
-0.7968
0.0068
-0.8104 -0.7833 0.7968
0.0068
0.7833 0.8104
8
Industrials
-0.5144
0.0096
-0.5333 -0.4956 0.5585
0.0067
0.5454 0.5716
5
Information Technology
-0.6713
0.0220
-0.7146 -0.6280 0.7100
0.0148
0.6808 0.7393
7
Materials
-0.3494
0.0144
-0.3779 -0.3210 0.3752
0.0122
0.3511 0.3993
2
Telecommunication Services
-0.3802
0.0250
-0.4297 -0.3306 0.3993
0.0226
0.3545 0.4441
3
Table 76: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a 95 percent
confidence interval (C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.5233
0.0059
-0.5349 -0.5117 0.5549
0.0047
0.5456 0.5641
Table 77: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a
95 percent confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.4576
0.0197
Consumer Staples
-0.6439
0.0114
Energy
-0.2837
.
Financials
-0.3699
0.0075
Health Care
-0.6858
0.0122
Industrials
-0.4023
0.0094
Information Technology
-0.6303
0.0193
Materials
-0.2351
0.0139
Telecommunication Services
-0.3413
0.0249
Table 78: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.4964 -0.4188
-0.6667 -0.6212
.
.
-0.3846 -0.3551
-0.7100 -0.6615
-0.4206 -0.3839
-0.6684 -0.5922
-0.2625 -0.2076
-0.3906 -0.2920
error in RIV(TVC),
Abs(V.E.)
Mean Std. Error
0.5583
0.0124
0.6439
0.0114
0.2837
.
0.3764
0.0067
0.6858
0.0122
0.4543
0.0065
0.6513
0.0156
0.2931
0.0099
0.3573
0.0231
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5338 0.5827
6
0.6212 0.6667
7
.
.
1
0.3632 0.3895
4
0.6615 0.7100
9
0.4415 0.4671
5
0.6206 0.6819
8
0.2736 0.3126
2
0.3116 0.4031
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.4196
0.0059
-0.4311 -0.4081
0.465
0.0044
0.4563 0.4737
Table 79: Average valuation error and absolute valuation error in RIV(TVC), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.1274
0.0327
Consumer Staples
-0.4693
0.0198
Energy
0.1185
.
Financials
-0.0626
0.0112
Health Care
-0.2075
0.0291
Industrials
-0.2421
0.0117
Information Technology
-0.4228
0.0301
Materials
0.0528
0.0188
Telecommunication Services
-0.0298
0.0354
Table 80: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.1916 -0.0632
-0.5087 -0.4300
.
.
-0.0846 -0.0407
-0.2653 -0.1497
-0.2649 -0.2192
-0.4821 -0.3635
0.0158 0.0899
-0.1000 0.0403
error in RIV(PMB),
Abs(V.E.)
Mean Std. Error
0.5930
0.0172
0.4710
0.0194
0.1185
.
0.1734
0.0080
0.3200
0.0163
0.3760
0.0072
0.5636
0.0149
0.2748
0.0112
0.3289
0.0208
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5592 0.6269
9
0.4324 0.5095
7
.
.
1
0.1577 0.1891
2
0.2877 0.3524
4
0.3619 0.3902
6
0.5342 0.5931
8
0.2528 0.2969
3
0.2878 0.3700
5
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1699
0.0084
-0.1863 -0.1534 0.3796
0.0053
0.3693
0.39
Table 81: Average valuation error and absolute valuation error in RIV(PMB), with standard error and a 95 percent
confidence interval (C.I).
78
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
0.6905
0.0652
0.5623 0.8186
1.0376
0.0536
0.9322 1.1429
9
Consumer Staples
0.0027
0.0450
-0.0866 0.0920
0.3428
0.0270
0.2892 0.3965
5
Energy
-0.0105
.
.
.
0.0105
.
.
.
1
Financials
0.1936
0.0144
0.1653 0.2218
0.2727
0.0110
0.2511 0.2943
2
Health Care
0.1527
0.0420
0.0695 0.2360
0.3091
0.0325
0.2447 0.3736
4
Industrials
0.2919
0.0204
0.2519 0.3318
0.4607
0.0169
0.4275 0.4938
6
Information Technology
0.4535
0.0765
0.3027 0.6044
0.6855
0.0675
0.5524 0.8186
7
Materials
0.0683
0.0191
0.0307 0.1059
0.2800
0.0115
0.2573 0.3027
3
Telecommunication Services
0.5500
0.0560
0.4392 0.6609
0.7342
0.0363
0.6623 0.8060
8
Table 82: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.3236
0.0154
0.2934 0.3537
0.5227
0.0132
0.4968 0.5485
Table 83: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence
interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.0220
0.0306
Consumer Staples
0.2414
0.0284
Energy
0.3429
.
Financials
-0.0085
0.0117
Health Care
-0.2450
0.0422
Industrials
-0.0457
0.0117
Information Technology
-0.5320
0.0183
Materials
0.3054
0.0458
Telecommunication Services
-0.3243
0.0285
Table 84: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.0821 0.0382
0.1851 0.2978
.
.
-0.0314 0.0144
-0.3288 -0.1613
-0.0686 -0.0228
-0.5680 -0.4960
0.2154 0.3955
-0.3807 -0.2678
error in PVEE(rE),
Abs(V.E.)
Mean Std. Error
0.4703
0.0207
0.2984
0.0216
0.3429
.
0.1847
0.0075
0.4300
0.0237
0.2904
0.0073
0.5425
0.0167
0.5086
0.0397
0.3539
0.0257
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4295 0.5110
7
0.2555 0.3413
3
.
.
4
0.1699 0.1996
1
0.3831 0.4769
6
0.2762 0.3046
2
0.5096 0.5754
9
0.4305 0.5866
8
0.3031 0.4048
5
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.0425
0.0099
-0.0619 -0.0232
0.356
0.0071
0.342
0.3701
Table 85: Average valuation error and absolute valuation error in PVEE(rE), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
0.7042
0.0510
Consumer Staples
0.6669
0.0275
Energy
1.8383
.
Financials
0.8235
0.0245
Health Care
0.1583
0.0549
Industrials
0.7368
0.0198
Information Technology
0.1938
0.0428
Materials
1.1601
0.0643
Telecommunication Services
0.3624
0.0606
Table 86: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
0.6039 0.8044
0.6122 0.7216
.
.
0.7754 0.8716
0.0495 0.2672
0.6980 0.7756
0.1095 0.2781
1.0336 1.2865
0.2425 0.4823
error in PVEE(rf),
Abs(V.E.)
Mean Std. Error
0.8675
0.0448
0.6669
0.0275
1.8383
.
0.8478
0.0225
0.4672
0.0334
0.8073
0.0168
0.5218
0.0260
1.2075
0.0615
0.6864
0.0326
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.7794 0.9556
7
0.6122 0.7216
3
.
.
9
0.8037 0.8920
6
0.4009 0.5335
1
0.7745 0.8402
5
0.4705 0.5732
2
1.0866 1.3284
8
0.6220 0.7508
4
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.7120
0.0155
0.6817 0.7424
0.8259
0.0132
0.7999 0.8518
Table 87: Average valuation error and absolute valuation error in PVEE(rf), with standard error and a 95 percent
confidence interval (C.I.).
79
V.E.
95 % C.I.
Abs(V.E.)
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error
Consumer Discretionary
0.1693
0.0321
0.1061 0.2324
0.4700
0.0243
Consumer Staples
0.4682
0.0370
0.3946 0.5417
0.4714
0.0366
Energy
-0.1474
.
.
.
0.1474
.
Financials
0.0336
0.0115
0.0111 0.0562
0.1877
0.0072
Health Care
-0.0605
0.0397
-0.1392 0.0182
0.3212
0.0245
Industrials
0.1088
0.0120
0.0854 0.1323
0.2813
0.0086
Information Technology
-0.3772
0.0213
-0.4191 -0.3352 0.4186
0.0171
Materials
0.2428
0.0320
0.1798 0.3057
0.3334
0.0293
Telecommunication Services
-0.1455
0.0287
-0.2023 -0.0887 0.2657
0.0211
Table 88: Average valuation error and absolute valuation error in AEG(TVC), with standard error
interval (C.I.) per sector and ranked in ascending order.
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4222 0.5178
8
0.3988 0.5441
9
.
.
1
0.1735 0.2020
2
0.2726 0.3697
5
0.2644 0.2983
4
0.3849 0.4522
7
0.2757 0.3911
6
0.2241 0.3074
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.0789
0.0091
0.0611 0.0967
0.3205
0.0068
0.3071 0.3339
Table 89: Average valuation error and absolute valuation error in AEG(TVC), with standard error and a 95 percent
confidence interval (C.I.).
80
8.13. Appendix 13: Empirical Results 5% Equity Risk Premium (1998-2007)
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
-0.5640
0.0109
-0.5854 -0.5426 0.6350
0.0074
0.6205 0.6496
6
Consumer Staples
-0.7367
0.0077
-0.7518 -0.7215 0.7367
0.0077
0.7215 0.7518
8
Energy
-0.1504
0.0448
-0.2393 -0.0616 0.4412
0.0204
0.4007 0.4817
2
Financials
-0.4163
0.0091
-0.4342 -0.3984 0.4729
0.0064
0.4604 0.4854
4
Health Care
-0.7305
0.0174
-0.7647 -0.6964 0.8050
0.0077
0.7900 0.8200
9
Industrials
-0.5293
0.0062
-0.5415 -0.5172 0.5857
0.0041
0.5776 0.5938
5
Information Technology
-0.5599
0.0135
-0.5864 -0.5334 0.6636
0.0092
0.6456 0.6816
7
Materials
-0.3073
0.0117
-0.3304 -0.2843 0.3620
0.0089
0.3446 0.3795
1
Telecommunication Services
-0.4065
0.0251
-0.4560 -0.3569 0.4524
0.0209
0.4112 0.4936
3
Table 90: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a 95 percent
confidence interval (C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.5186
0.0041
-0.5268 -0.5105
0.586
0.0029
0.5803 0.5917
Table 91: Average valuation error and absolute valuation error in book value of owners’ equity, with standard error and a
95 percent confidence interval (C.I).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.4461
0.0117
Consumer Staples
-0.5848
0.0065
Energy
-0.1276
0.0422
Financials
-0.3774
0.0079
Health Care
-0.6416
0.0168
Industrials
-0.4249
0.0063
Information Technology
-0.5280
0.0126
Materials
-0.2083
0.0109
Telecommunication Services
-0.3933
0.0233
Table 92: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.4690 -0.4232
-0.5977 -0.5719
-0.2113 -0.0439
-0.3928 -0.3620
-0.6746 -0.6086
-0.4373 -0.4126
-0.5526 -0.5033
-0.2297 -0.1869
-0.4393 -0.3473
error in RIV(TVC),
Abs(V.E.)
Mean Std. Error
0.5594
0.0072
0.5848
0.0065
0.4165
0.0181
0.4201
0.0057
0.7145
0.0085
0.4968
0.0041
0.6150
0.0090
0.2892
0.0074
0.4248
0.0204
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5453 0.5735
6
0.5719 0.5977
7
0.3805 0.4524
2
0.4088 0.4313
3
0.6979 0.7312
9
0.4887 0.5050
5
0.5974 0.6326
8
0.2747 0.3036
1
0.3845 0.4651
4
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.4349
0.0040
-0.4428 -0.4270 0.5113
0.0028
0.5058 0.5168
Table 93: Average valuation error and absolute valuation error in RIV(TVC), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.1135
0.0179
Consumer Staples
-0.3525
0.0115
Energy
0.4692
0.0773
Financials
-0.0624
0.0112
Health Care
-0.1295
0.0272
Industrials
-0.2642
0.0078
Information Technology
-0.2751
0.0184
Materials
0.0942
0.0149
Telecommunication Services
-0.0977
0.0321
Table 94: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.1487 -0.0784
-0.3752 -0.3298
0.3159 0.6225
-0.0843 -0.0405
-0.1830 -0.0760
-0.2795 -0.2489
-0.3111 -0.2390
0.0648 0.1235
-0.1610 -0.0345
error in RIV(PMB),
Abs(V.E.)
Mean Std. Error
0.5346
0.0109
0.3550
0.0113
0.6234
0.0665
0.2815
0.0078
0.4297
0.0196
0.4160
0.0051
0.5355
0.0132
0.3132
0.0090
0.3881
0.0183
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.5133 0.5560
7
0.3328 0.3772
3
0.4916 0.7552
9
0.2662 0.2969
1
0.3912 0.4682
6
0.4060 0.4260
5
0.5097 0.5614
8
0.2956 0.3308
2
0.3520 0.4241
4
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1700
0.0057
-0.1813 -0.1588
0.427
0.0039
0.4194 0.4345
Table 95: Average valuation error and absolute valuation error in RIV(PMB), with standard error and a 95 percent
confidence interval (C.I.).
81
Rank
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper Abs(V.E.)
Consumer Discretionary
0.7101
0.0343
0.6429 0.7773
0.9714
0.0291
0.9144 1.0285
8
Consumer Staples
0.2757
0.0266
0.2234 0.3279
0.4591
0.0171
0.4255 0.4926
3
Energy
0.2777
0.0659
0.1471 0.4084
0.5124
0.0512
0.4109 0.6140
6
Financials
0.2003
0.0143
0.1723 0.2283
0.3749
0.0109
0.3535 0.3963
2
Health Care
0.2562
0.0364
0.1846 0.3278
0.4932
0.0308
0.4327 0.5537
4
Industrials
0.2715
0.0133
0.2454 0.2976
0.4981
0.0108
0.4769 0.5194
5
Information Technology
0.7931
0.0436
0.7075 0.8786
1.0061
0.0401
0.9275 1.0846
9
Materials
0.1105
0.0152
0.0807 0.1402
0.3206
0.0092
0.3025 0.3387
1
Telecommunication Services
0.4527
0.0496
0.3549 0.5504
0.7279
0.0293
0.6701 0.7856
7
Table 96: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence interval
(C.I.) per sector and ranked in ascending order.
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.4018
0.0107
0.3809 0.4227
0.6236
0.0093
0.6053 0.6418
Table 97: Average valuation error and absolute valuation error in RIV(Q), with standard error and a 95 percent confidence
interval (C.I.).
V.E.
GICS Sector
Mean Std. Error
Consumer Discretionary
-0.0873
0.0154
Consumer Staples
0.1366
0.0187
Energy
0.0998
0.0889
Financials
-0.1949
0.0082
Health Care
-0.4052
0.0156
Industrials
-0.1262
0.0087
Information Technology
-0.5204
0.0099
Materials
0.1893
0.0275
Telecommunication Services
-0.4583
0.0204
Table 98: Average valuation error and absolute valuation
interval (C.I.) per sector and ranked in ascending order.
95 % C.I.
Lower
Upper
-0.1176 -0.0571
0.0999 0.1733
-0.0764 0.2759
-0.2111 -0.1788
-0.4358 -0.3746
-0.1433 -0.1090
-0.5399 -0.5009
0.1352 0.2433
-0.4984 -0.4182
error in PVEE(rE),
Abs(V.E.)
Mean Std. Error
0.4248
0.0105
0.2743
0.0132
0.5992
0.0683
0.2722
0.0061
0.4770
0.0104
0.3486
0.0064
0.5644
0.0079
0.4353
0.0226
0.4659
0.0195
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.4043 0.4453
4
0.2483 0.3003
2
0.4638 0.7346
9
0.2602 0.2842
1
0.4566 0.4974
7
0.3361 0.3611
3
0.5490 0.5798
8
0.3909 0.4797
5
0.4275 0.5044
6
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.1766
0.0055
-0.1874 -0.1659 0.3994
0.0039
0.3917
0.407
Table 99: Average valuation error and absolute valuation error in PVEE(rE), with standard error and a 95 percent
confidence interval (C.I.).
V.E.
95 % C.I.
GICS Sector
Mean Std. Error Lower
Upper
Consumer Discretionary
0.7884
0.0291
0.7313 0.8454
Consumer Staples
0.6116
0.0210
0.5703 0.6528
Energy
1.2600
0.1609
0.9410 1.5790
Financials
0.6570
0.0171
0.6235 0.6906
Health Care
0.0313
0.0249
-0.0177 0.0803
Industrials
0.7506
0.0140
0.7232 0.7779
Information Technology
0.3964
0.0284
0.3407 0.4521
Materials
1.1402
0.0417
1.0582 1.2222
Telecommunication Services
0.2360
0.0489
0.1395 0.3324
Table 100: Average valuation error and absolute valuation error in PVEE(rf),
interval (C.I.) per sector and ranked in ascending order.
Abs(V.E.)
Mean Std. Error
0.9235
0.0259
0.6225
0.0199
1.4204
0.1480
0.7347
0.0142
0.4127
0.0162
0.8263
0.0124
0.7018
0.0233
1.1860
0.0397
0.6274
0.0269
with standard error
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.8726 0.9744
7
0.5832 0.6617
2
1.1270 1.7139
9
0.7069 0.7625
5
0.3809 0.4445
1
0.8019 0.8506
6
0.6560 0.7476
4
1.1081 1.2638
8
0.5743 0.6805
3
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
0.6675
0.0097
0.6485 0.6864
0.8086
0.0083
0.7922 0.8249
Table 101: Average valuation error and absolute valuation error in PVEE(rf), with standard error and a 95 percent
confidence interval (C.I.).
82
V.E.
95 % C.I.
Abs(V.E.)
GICS Sector
Mean Std. Error Lower
Upper
Mean Std. Error
Consumer Discretionary
0.1018
0.0159
0.0706 0.1330
0.4080
0.0117
Consumer Staples
0.3163
0.0229
0.2712 0.3613
0.3772
0.0199
Energy
0.1314
0.0696
-0.0065 0.2692
0.5489
0.0470
Financials
-0.1654
0.0081
-0.1813 -0.1495 0.2550
0.0058
Health Care
-0.1560
0.0160
-0.1875 -0.1245 0.3235
0.0093
Industrials
0.0471
0.0098
0.0279 0.0663
0.3228
0.0078
Information Technology
-0.3007
0.0144
-0.3291 -0.2724 0.4589
0.0107
Materials
0.2024
0.0219
0.1594 0.2454
0.3419
0.0189
Telecommunication Services
-0.2801
0.0191
-0.3178 -0.2423 0.3169
0.0161
Table 102: Average valuation error and absolute valuation error in AEG(TVC), with standard error
interval (C.I.) per sector and ranked in ascending order.
Rank
95 % C.I.
Lower Upper Abs(V.E.)
0.3850 0.4309
7
0.3381 0.4163
6
0.4557 0.6420
9
0.2436 0.2664
1
0.3052 0.3418
4
0.3075 0.3382
3
0.4379 0.4800
8
0.3048 0.3791
5
0.2852 0.3486
2
and a 95 percent confidence
V.E.
95 % C.I.
Abs(V.E.)
95 % C.I.
Mean Std. Error Lower
Upper
Mean Std. Error Lower Upper
Total
-0.0229
0.0057
-0.0341 -0.0117 0.3537
0.0042
0.3454
0.362
Table 103: Average valuation error and absolute valuation error in AEG(TVC), with standard error and a 95 percent
confidence interval (C.I.).
83
8.14. Appendix 14: Statistical Testing 1998-2002
Number of
H0: RIV(TVC)-BV = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0118*
-1.4588
0.0728
0.1455
0.9272
354
Consumer Staples
-0.1743*** -26.3603
0.0000
0.0000
1.0000
93
Energy
0.0879***
2.9781
0.9963
0.0074
0.0037
21
Financials
-0.0624*** -15.3718
0.0000
0.0000
1.0000
387
Health Care
-0.1030*** -11.3111
0.0000
0.0000
1.0000
100
Industrials
-0.0849*** -17.9565
0.0000
0.0000
1.0000
953
Information Technology
-0.0262*** -4.6006
0.0000
0.0000
1.0000
318
Materials
-0.0679*** -8.5542
0.0000
0.0000
1.0000
205
Telecommunication Services
-0.0118*
-1.5106
0.0679
0.1359
0.9321
64
Table 104: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(TVC)-BV = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0629*** -24.0723
0.0000
0.0000
1.0000
2495
Table 105: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.1667***
6.3100
1.0000
0.0000
0.0000
354
Consumer Staples
-0.2844*** -34.9853
0.0000
0.0000
1.0000
93
Energy
1.2391*** 19.3690
1.0000
0.0000
0.0000
21
Financials
-0.1635*** -10.4949
0.0000
0.0000
1.0000
387
Health Care
-0.0570
-0.8232
0.2062
0.4124
0.7938
100
Industrials
-0.0410*** -5.8426
0.0000
0.0000
1.0000
953
Information Technology
0.0097
0.4281
0.6656
0.6689
0.3344
318
Materials
0.0972***
5.0412
1.0000
0.0000
0.0000
205
Telecommunication Services
-0.1074*** -4.0282
0.0001
0.0002
0.9999
64
Table 106: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-1.7759
0.0379
0.0759
0.9621
2495
Table 107: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.0134**
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.8040*** 13.8909
1.0000
0.0000
0.0000
354
Consumer Staples
0.2245***
4.5192
1.0000
0.0000
0.0000
93
Energy
-0.3975*** -19.3690
0.0000
0.0000
1.0000
21
Financials
0.0538***
3.8458
0.9999
0.0001
0.0001
387
Health Care
0.4561*** 10.4741
1.0000
0.0000
0.0000
100
Industrials
0.2643*** 12.5275
1.0000
0.0000
0.0000
953
Information Technology
0.5092***
5.6726
1.0000
0.0000
0.0000
318
Materials
0.0134*** 14.2218
1.0000
0.0000
0.0000
205
Telecommunication Services
-0.0345
-0.6666
0.2537
0.5075
0.7463
64
Table 108: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.3118*** 17.9369
1.0000
0.0000
0.0000
2495
Table 109: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
84
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.4285*** 10.2376
1.0000
0.0000
0.0000
354
Consumer Staples
0.2031*** 12.4607
1.0000
0.0000
0.0000
93
Energy
1.4589***
5.0410
1.0000
0.0001
0.0000
21
Financials
0.3428*** 17.0863
1.0000
0.0000
0.0000
387
Health Care
0.1259***
3.2223
0.9991
0.0017
0.0009
100
Industrials
0.3637*** 24.5224
1.0000
0.0000
0.0000
953
Information Technology
0.1912***
2.8896
0.9979
0.0041
0.0021
318
Materials
0.4671*** 16.8000
1.0000
0.0000
0.0000
205
Telecommunication Services
-0.2196*** -16.2623
0.0000
0.0000
1.0000
64
Table 110: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.3349*** 25.5190
1.0000
0.0000
0.0000
2495
Table 111: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.0459***
3.1609
0.9991
0.0017
0.0009
354
Consumer Staples
0.2388***
7.6771
1.0000
0.0000
0.0000
93
Energy
-0.2821
-0.7102
0.2429
0.4858
0.7571
21
Financials
-0.0241*** -3.0587
0.0012
0.0024
0.9988
387
Health Care
-0.1297*** -4.3879
0.0000
0.0000
1.0000
100
Industrials
0.1153*** 10.6101
1.0000
0.0000
0.0000
953
Information Technology
-0.0062
-0.2026
0.4198
0.8396
0.5802
318
Materials
0.0052
0.2091
0.5827
0.8346
0.4173
205
Telecommunication Services
-0.2134*** -8.9115
0.0000
0.0000
1.0000
64
Table 112: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
5.4876
1.0000
0.0000
0.0000
2495
Table 113: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
0.0423***
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.1022***
2.6139
0.9953
0.0093
0.0047
354
Consumer Staples
-0.0075
-0.1331
0.4472
0.8944
0.5528
93
Energy
0.7655***
4.8934
1.0000
0.0001
0.0000
21
Financials
-0.2510*** -20.4998
0.0000
0.0000
1.0000
387
Health Care
-0.2948*** -5.6034
0.0000
0.0000
1.0000
100
Industrials
0.0887***
3.7825
0.9999
0.0002
0.0001
953
Information Technology
-0.0748*** -3.0502
0.0012
0.0025
0.9988
318
Materials
0.4113***
7.5619
1.0000
0.0000
0.0000
205
Telecommunication Services
-0.1575*** -7.9474
0.0000
0.0000
1.0000
64
Table 114: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
1.8431
0.9673
0.0654
0.0327
2495
Table 115: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
0.0240**
85
8.15. Appendix 15: Statistical Testing 2003-2007
Number of
H0: RIV(TVC)-BV = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.1053*** -33.6117
0.0000
0.0000
1.0000
989
Consumer Staples
-0.1485*** -41.4799
0.0000
0.0000
1.0000
233
Energy
-0.0546*** -5.0747
0.0000
0.0000
1.0000
88
Financials
-0.0648*** -23.8763
0.0000
0.0000
1.0000
803
Health Care
-0.0934*** -40.4030
0.0000
0.0000
1.0000
371
Industrials
-0.1049*** -83.0224
0.0000
0.0000
1.0000
1994
Information Technology
-0.0693*** -28.6097
0.0000
0.0000
1.0000
971
Materials
-0.0839*** -17.5938
0.0000
0.0000
1.0000
420
Telecommunication Services
-0.0494*** -12.5867
0.0000
0.0000
1.0000
140
Table 116: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(TVC)-BV = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0913*** -92.0224
0.0000
0.0000
1.0000
6009
Table 117: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0815*** -8.5473
0.0000
0.0000
1.0000
989
Consumer Staples
-0.2097*** -31.3732
0.0000
0.0000
1.0000
233
Energy
-0.0059
-0.1321
0.4476
0.8952
0.5524
88
Financials
-0.1117*** -11.8051
0.0000
0.0000
1.0000
803
Health Care
-0.3439*** -30.2345
0.0000
0.0000
1.0000
371
Industrials
-0.0971*** -34.9252
0.0000
0.0000
1.0000
1994
Information Technology
-0.1001*** -10.7677
0.0000
0.0000
1.0000
971
Materials
0.0073
0.5465
0.7075
0.5850
0.2925
420
Telecommunication Services
0.0228
0.9492
0.8279
0.3442
0.1721
140
Table 118: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-32.8537
0.0000
0.0000
1.0000
6009
Table 119: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.1052***
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
GICS Sector
Mean
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.3363*** 13.9354
1.0000
0.0000
0.0000
989
Consumer Staples
0.0722***
2.3649
0.9906
0.0189
0.0094
233
Energy
-0.0589*** -3.8313
0.0001
0.0002
0.9999
88
Financials
0.1392*** 18.0246
1.0000
0.0000
0.0000
803
Health Care
-0.0278*
-1.6352
0.0514
0.1029
0.9486
371
Industrials
0.0252***
2.3626
0.9909
0.0182
0.0091
1994
Information Technology
0.5396*** 15.3249
1.0000
0.0000
0.0000
971
Materials
0.0054***
6.9477
1.0000
0.0000
0.0000
420
Telecommunication Services
0.5408*** 17.6213
1.0000
0.0000
0.0000
140
Table 120: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.1827*** 21.5655
1.0000
0.0000
0.0000
6009
Table 121: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
86
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.5033*** 24.1288
1.0000
0.0000
0.0000
989
Consumer Staples
0.3742*** 21.9433
1.0000
0.0000
0.0000
233
Energy
0.5818***
6.5427
1.0000
0.0000
0.0000
88
Financials
0.5410*** 25.3087
1.0000
0.0000
0.0000
803
Health Care
-0.0860*** -4.3314
0.0000
0.0000
1.0000
371
Industrials
0.5547*** 41.4940
1.0000
0.0000
0.0000
1994
Information Technology
0.1738***
7.6697
1.0000
0.0000
0.0000
971
Materials
0.8183*** 26.8837
1.0000
0.0000
0.0000
420
Telecommunication Services
0.4040***
7.9734
1.0000
0.0000
0.0000
140
Table 122: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.4516*** 53.9609
1.0000
0.0000
0.0000
6009
Table 123: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.0082
0.9134
0.8194
0.3613
0.1806
989
Consumer Staples
0.0926***
8.3359
1.0000
0.0000
0.0000
233
Energy
-0.0416
-0.9590
0.1701
0.3402
0.8299
88
Financials
0.0004
0.0780
0.5311
0.9379
0.4689
803
Health Care
-0.1451*** -11.7870
0.0000
0.0000
1.0000
371
Industrials
-0.0417*** -8.7734
0.0000
0.0000
1.0000
1994
Information Technology
-0.1218*** -15.2599
0.0000
0.0000
1.0000
971
Materials
-0.1216*** -5.7525
0.0000
0.0000
1.0000
420
Telecommunication Services
-0.1061*** -5.5433
0.0000
0.0000
1.0000
140
Table 124: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-14.8844
0.0000
0.0000
1.0000
6009
Table 125: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.0491***
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.1674*** -10.0932
0.0000
0.0000
1.0000
989
Consumer Staples
-0.2060*** -8.7016
0.0000
0.0000
1.0000
233
Energy
0.0249
0.6393
0.7378
0.5243
0.2622
88
Financials
-0.1162*** -11.6987
0.0000
0.0000
1.0000
803
Health Care
-0.4255*** -36.0078
0.0000
0.0000
1.0000
371
Industrials
-0.2565*** -35.1587
0.0000
0.0000
1.0000
1994
Information Technology
-0.2076*** -25.5550
0.0000
0.0000
1.0000
971
Materials
-0.0230*
-1.2920
0.0985
0.1971
0.9015
420
Telecommunication Services
-0.1254*** -5.2318
0.0000
0.0000
1.0000
140
Table 126: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-42.9440
0.0000
0.0000
1.0000
6009
Table 127: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.2002***
87
8.16. Appendix 16: Statistical Testing Five or More Consensus Estimates (1998-2007)
Number of
H0: RIV(TVC)-BV = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0655*** -10.6284
0.0000
0.0000
1.0000
436
Consumer Staples
-0.1814*** -53.2327
0.0000
0.0000
1.0000
92
Energy
-0.0911
.
.
.
.
1
Financials
-0.0920*** -35.7616
0.0000
0.0000
1.0000
432
Health Care
-0.1111*** -17.7197
0.0000
0.0000
1.0000
103
Industrials
-0.1042*** -48.0825
0.0000
0.0000
1.0000
986
Information Technology
-0.0587*** -15.5313
0.0000
0.0000
1.0000
205
Materials
-0.0821*** -14.8398
0.0000
0.0000
1.0000
319
Telecommunication Services
-0.0419*** -11.2411
0.0000
0.0000
1.0000
131
Table 128: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(TVC)-BV = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0898*** -55.3749
0.0000
0.0000
1.0000
2705
Table 129: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.0347**
1.8294
0.9660
0.0680
0.0340
436
Consumer Staples
-0.1730*** -18.6286
0.0000
0.0000
1.0000
92
Energy
-0.1652
.
.
.
.
1
Financials
-0.2029*** -23.9396
0.0000
0.0000
1.0000
432
Health Care
-0.3657*** -18.9748
0.0000
0.0000
1.0000
103
Industrials
-0.0783*** -16.0006
0.0000
0.0000
1.0000
986
Information Technology
-0.0876*** -5.2725
0.0000
0.0000
1.0000
205
Materials
-0.0183*
-1.2972
0.0977
0.1955
0.9023
319
Telecommunication Services
-0.0285
-1.2845
0.1006
0.2013
0.8994
131
Table 130: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-17.5771
0.0000
0.0000
1.0000
2705
Table 131: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.0854***
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.4445***
9.9525
1.0000
0.0000
0.0000
436
Consumer Staples
-0.1281*** -3.4446
0.0004
0.0009
0.9996
92
Energy
-0.1080
.
.
.
.
1
Financials
0.0993*** 10.1124
1.0000
0.0000
0.0000
432
Health Care
-0.0109
-0.3579
0.3606
0.7211
0.6394
103
Industrials
0.0846***
5.0515
1.0000
0.0000
0.0000
986
Information Technology
0.1219**
1.7741
0.9612
0.0775
0.0388
205
Materials
0.0052***
6.0103
1.0000
0.0000
0.0000
319
Telecommunication Services
0.4053*** 10.5109
1.0000
0.0000
0.0000
131
Table 132: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.1430*** 12.3474
1.0000
0.0000
0.0000
2705
Table 133: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
88
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.3973*** 12.0542
1.0000
0.0000
0.0000
436
Consumer Staples
0.3685*** 15.8863
1.0000
0.0000
0.0000
92
Energy
1.4954
.
.
.
.
1
Financials
0.6631*** 27.5438
1.0000
0.0000
0.0000
432
Health Care
0.0372
1.0209
0.8451
0.3097
0.1549
103
Industrials
0.5169*** 29.0727
1.0000
0.0000
0.0000
986
Information Technology
-0.0207
-0.5749
0.2830
0.5660
0.7170
205
Materials
0.6989*** 20.1642
1.0000
0.0000
0.0000
319
Telecommunication Services
0.3325***
6.4349
1.0000
0.0000
0.0000
131
Table 134: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.4698*** 40.7689
1.0000
0.0000
0.0000
2705
Table 135: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0003
-0.0244
0.4903
0.9806
0.5097
436
Consumer Staples
0.1731***
7.9423
1.0000
0.0000
0.0000
92
Energy
-0.1955
.
.
.
.
1
Financials
0.0030
0.6336
0.7367
0.5266
0.2633
432
Health Care
-0.1088*** -6.8941
0.0000
0.0000
1.0000
103
Industrials
-0.0091*
-1.4954
0.0676
0.1351
0.9324
986
Information Technology
-0.1240*** -10.3940
0.0000
0.0000
1.0000
205
Materials
-0.1752*** -7.6363
0.0000
0.0000
1.0000
319
Telecommunication Services
-0.0882*** -5.3698
0.0000
0.0000
1.0000
131
Table 136: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-7.8592
0.0000
0.0000
1.0000
2705
Table 137: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level
Mean
-0.0355***
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0883*** -3.0447
0.0012
0.0025
0.9988
436
Consumer Staples
-0.1725*** -3.7207
0.0002
0.0003
0.9998
92
Energy
-0.1363
.
.
.
.
1
Financials
-0.1886*** -18.3399
0.0000
0.0000
1.0000
432
Health Care
-0.3646*** -11.3731
0.0000
0.0000
1.0000
103
Industrials
-0.1730*** -14.6954
0.0000
0.0000
1.0000
986
Information Technology
-0.2327*** -17.2042
0.0000
0.0000
1.0000
205
Materials
0.0403*
1.2878
0.9006
0.1987
0.0994
319
Telecommunication Services
-0.0916*** -5.6474
0.0000
0.0000
1.0000
131
Table 138: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-17.9375
0.0000
0.0000
1.0000
2705
Table 139: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.1445***
89
8.17. Appendix 17: Statistical Testing 5% Equity Risk Premium (1998-2007)
Number of
H0: RIV(TVC)-BV = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0757*** -24.8458
0.0000
0.0000
1.0000
1343
Consumer Staples
-0.1519*** -45.8245
0.0000
0.0000
1.0000
326
Energy
-0.0247**
-2.1956
0.0151
0.0303
0.9849
109
Financials
-0.0528*** -22.4303
0.0000
0.0000
1.0000
1186
Health Care
-0.0905*** -35.2186
0.0000
0.0000
1.0000
471
Industrials
-0.0889*** -53.5515
0.0000
0.0000
1.0000
2947
Information Technology
-0.0486*** -20.2802
0.0000
0.0000
1.0000
1288
Materials
-0.0729*** -18.8871
0.0000
0.0000
1.0000
625
Telecommunication Services
-0.0276*** -6.7700
0.0000
0.0000
1.0000
204
Table 140: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(TVC)-BV = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
-0.0747*** -74.0984
0.0000
0.0000
1.0000
8499
Table 141: Paired t-test of DiffRIV(TVC)-Bv. *** Significant at the 1 percent level, ** Significant at the 5 percent level,
* Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0247*** -2.4500
0.0072
0.0144
0.9928
1343
Consumer Staples
-0.2298*** -40.9211
0.0000
0.0000
1.0000
326
Energy
0.2069***
3.4011
0.9995
0.0009
0.0005
109
Financials
-0.1385*** -17.4318
0.0000
0.0000
1.0000
1186
Health Care
-0.2848*** -16.1445
0.0000
0.0000
1.0000
471
Industrials
-0.0808*** -27.7473
0.0000
0.0000
1.0000
2947
Information Technology
-0.0794*** -9.2601
0.0000
0.0000
1.0000
1288
Materials
0.0240**
2.1915
0.9856
0.0288
0.0144
625
Telecommunication Services
-0.0367**
-2.0222
0.0222
0.0445
0.9778
204
Table 142: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(PMB)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-27.1871
0.0000
0.0000
1.0000
8499
Table 143: Paired t-test of DiffRIV(PMB)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.0844***
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.4368*** 18.3707
1.0000
0.0000
0.0000
1343
Consumer Staples
0.1041***
4.0339
1.0000
0.0001
0.0000
326
Energy
-0.1110*** -5.9817
0.0000
0.0000
1.0000
109
Financials
0.0934*** 13.4170
1.0000
0.0000
0.0000
1186
Health Care
0.0634***
3.4400
0.9997
0.0006
0.0003
471
Industrials
0.0821***
8.2434
1.0000
0.0000
0.0000
2947
Information Technology
0.4705*** 14.1109
1.0000
0.0000
0.0000
1288
Materials
0.0075*** 11.9719
1.0000
0.0000
0.0000
625
Telecommunication Services
0.3398*** 10.6145
1.0000
0.0000
0.0000
204
Table 144: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: RIV(Q )-RIV(PMB) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.1966*** 25.6090
1.0000
0.0000
0.0000
8499
Table 145: Paired t-test of DiffRIV(Q)-RIV(PMB). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
90
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
0.4987*** 23.2431
1.0000
0.0000
0.0000
1343
Consumer Staples
0.3482*** 21.9490
1.0000
0.0000
0.0000
326
Energy
0.8212***
7.6262
1.0000
0.0000
0.0000
109
Financials
0.4625*** 25.9744
1.0000
0.0000
0.0000
1186
Health Care
-0.0643*** -3.2311
0.0007
0.0013
0.9993
471
Industrials
0.4777*** 42.0115
1.0000
0.0000
0.0000
2947
Information Technology
0.1374***
5.5630
1.0000
0.0000
0.0000
1288
Materials
0.7507*** 28.1609
1.0000
0.0000
0.0000
625
Telecommunication Services
0.1615***
3.9437
0.9999
0.0001
0.0001
204
Table 146: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: PVEE(rf)-PVEE(rE) = 0
Observations
Mean
t
p (<0)
p (≠0)
p(>0)
Total
0.4092*** 52.7881
1.0000
0.0000
0.0000
8499
Table 147: Paired t-test of DiffPVEE(rf)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.0169*** -2.5673
0.0052
0.0104
0.9948
1343
Consumer Staples
0.1030***
8.2610
1.0000
0.0000
0.0000
326
Energy
-0.0503
-0.6684
0.2527
0.5053
0.7473
109
Financials
-0.0172*** -4.6781
0.0000
0.0000
1.0000
1186
Health Care
-0.1535*** -15.1898
0.0000
0.0000
1.0000
471
Industrials
-0.0258*** -5.7477
0.0000
0.0000
1.0000
2947
Information Technology
-0.1054*** -13.3586
0.0000
0.0000
1.0000
1288
Materials
-0.0933*** -6.4581
0.0000
0.0000
1.0000
625
Telecommunication Services
-0.1491*** -11.3010
0.0000
0.0000
1.0000
204
Table 148: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-PVEE(rE) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-15.9211
0.0000
0.0000
1.0000
8499
Table 149: Paired t-test of DiffAEG(TVC)-PVEE(rE). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.0456***
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
GICS Sector
Mean
t
p (<0)
p (≠0)
p(>0)
Consumer Discretionary
-0.1514*** -11.0280
0.0000
0.0000
1.0000
1343
Consumer Staples
-0.2076*** -9.1720
0.0000
0.0000
1.0000
326
Energy
0.1324***
3.0894
0.9987
0.0026
0.0013
109
Financials
-0.1651*** -21.7453
0.0000
0.0000
1.0000
1186
Health Care
-0.3910*** -30.3629
0.0000
0.0000
1.0000
471
Industrials
-0.1740*** -21.1329
0.0000
0.0000
1.0000
2947
Information Technology
-0.1561*** -22.7121
0.0000
0.0000
1.0000
1288
Materials
0.0528***
2.5071
0.9938
0.0124
0.0062
625
Telecommunication Services
-0.1079*** -6.8739
0.0000
0.0000
1.0000
204
Table 150: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Number of
H0: AEG(TVC)-RIV(TVC) = 0
Observations
t
p (<0)
p (≠0)
p(>0)
Total
-35.1956
0.0000
0.0000
1.0000
8499
Table 151: Paired t-test of DiffAEG(TVC)-RIV(TVC). *** Significant at the 1 percent level, ** Significant at the 5 percent
level, * Significant at the 10 percent level.
Mean
-0.1576***
91
8.18. Appendix 18: Summary of Empirical Results and Statistical Testing: 1998-2002
4.00
3.20
2.40
V.E.
1.60
0.80
0.00
RIV(PMB)
RIV(Q)
PVEE(rf)
AEG(TVC)
Chart 33: Average valuation error for each GICS industry sector and model over the period 1998-2002.
92
Materials
Industrials
Health Care
PVEE(rE)
Telecommunication Services
RIV(TVC)
Information Technology
BV
Financials
Energy
Consumer Staples
-1.60
Consumer Discretionary
-0.80
4.00
3.20
V.E.
2.40
1.60
RIV(PMB)
RIV(Q)
PVEE(rf)
AEG(TVC)
Chart 34: Average absolute valuation error for each GICS industry sector and model over the period 1998-2002.
93
Materials
Industrials
Health Care
PVEE(rE)
Telecommunication Services
RIV(TVC)
Information Technology
BV
Financials
Energy
Consumer Staples
0.00
Consumer Discretionary
0.80
0.80
0.60
0.40
V.E.
0.20
0.00
-0.20
-0.40
-0.60
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
PVEE(rf)
AEG(TVC)
Chart 35: Average valuation error for each model over the period (1998-2002).
0.90
0.80
0.70
0.60
V.E.
0.50
0.40
0.30
0.20
0.10
0.00
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
Chart 36: Average absolute valuation error for each model over the period (1998-2002).
94
The empirical modelling in this section implies that:
Average
Valuation error
Valuation
Model
Book Value
Over/underestimation
Underestimates for
8/9 sectors.
RIV(TVC)
Average
Absolute Valuation error
Largest Error
Consumer Staples
(-),
Telecommunication
Services (-)
Smallest Error
Materials (-),
Health Care (-)
Largest Error
Information
Technology,
Health Care
Smallest Error
Materials,
Financials
Underestimates for
8/9 sectors.
Telecommunication
Services (-),
Energy (+)
Industrials (-),
Consumer
Discretionary (-)
Information
Technology,
Telecommunication
Services
Materials,
Financials
RIV(PMB)
Underestimates for
5/9 sectors.
Energy (+),
Telecommunication
Services (-)
Financials (-),
Consumer
Discretionary (+)
Energy,
Information
Technology
Consumer Staples,
Financials
RIV(Q)
Overestimates
8/9 sectors.
for
Energy (+),
Consumer
Discretionary (+)
Telecommunication
Services (-),
Financials (+)
Consumer
Discretionary,
Energy
Materials,
Financials
PVEE(rE)
Overestimates
5/9 sectors.
for
Energy (+),
Telecommunication
Services (-)
Financials (-),
Consumer
Discretionary (+)
Energy,
Telecommunication
Services
Financials,
Consumer Staples
PVEE(rf)
Overestimates
8/9 sectors.
for
Energy (+),
Material (+)
Health Care (+),
Information
Technology (+)
Energy,
Materials
Consumer Staples,
Telecommunication
Services
AEG(TVC)
Overestimates
6/9 sectors.
for
Energy (+),
Material (+)
Financials (-),
Health Care (+)
Energy,
Consumer
Discretionary
Financials,
Health Care
Table 152: Overview of results from empirical modelling.
Summarised results from the statistical testing of hypotheses:
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
GICS Sector
Consumer Discretionary
*
(***)
(***)
(***)
(***)
(***)
Consumer Staples
***
***
(***)
(***)
(***)
Energy
(***)
(***)
***
(***)
(***)
Financials
***
***
(***)
(***)
***
***
Health Care
***
(***)
(***)
***
***
Industrials
***
***
(***)
(***)
(***)
(***)
Information Technology
***
(***)
(***)
***
Materials
***
(***)
(***)
(***)
(***)
Telecommunication Services
*
***
***
***
***
Table 153: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
Total
***
***
(***)
(***)
(***)
(**)
Table 154: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
95
8.19. Appendix 19: Summary of Empirical Results and Statistical Testing: 2003-2007
1.60
1.20
0.80
V.E.
0.40
0.00
-0.40
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 37: Average valuation error for each GICS industry sector and model over the period 2003-2007.
96
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
Consumer Staples
-1.20
Consumer Discretionary
-0.80
1.60
0.80
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 38: Average absolute valuation error for each GICS industry sector and model over the period 2003-2007.
97
Materials
Telecommunication Services
RIV(TVC)
Information Technology
BV
Industrials
Health Care
Financials
Energy
0.00
Consumer Staples
0.40
Consumer Discretionary
V.E.
1.20
0.80
0.60
0.40
V.E.
0.20
0.00
-0.20
-0.40
-0.60
-0.80
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 39: Average valuation error for each model over the period (2003-2007).
0.90
0.80
0.70
0.60
V.E.
0.50
0.40
0.30
0.20
0.10
0.00
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
Chart 40: Average absolute valuation error for each model over the period (2003-2007).
98
AEG(TVC)
The empirical modelling in this section implies that:
Average
Valuation error
Valuation
Model
Book Value
Over/underestimation
Underestimates for
all sectors.
RIV(TVC)
Average
Absolute Valuation error
Largest Error
Health Care (-),
Consumer Staples
(-)
Smallest Error
Telecommunication
Services (-),
Energy (-)
Largest Error
Health Care,
Consumer Staples
Smallest Error
Telecommunication
Services,
Materials
Underestimates for
all sectors.
Health Care (-),
Consumer Staples
(-)
Materials (-),
Telecommunication
Services (-),
Health Care,
Consumer Staples
Telecommunication
Services,
Materials
RIV(PMB)
Underestimates for
6/9 sectors.
Consumer Staples
(-),
Industrials (-)
Financials (-),
Materials (+)
Consumer
Discretionary,
Information
Technology
Financials,
Materials
RIV(Q)
Overestimates
alls sectors.
for
Information
Technology (+),
Telecommunication
Services (+)
Energy (+),
Health Care (+)
Information
Technology,
Telecommunication
Services
Energy,
Materials
PVEE(rE)
Overestimates
7/9 sectors.
for
Information
Technology (-),
Health Care (-)
Consumer
Discretionary (-),
Energy (-)
Information
Technology,
Health Care
Financials,
Industrials
PVEE(rf)
Overestimates
all sectors.
for
Materials (+),
Energy (+)
Health Care (+),
Information
Technology (+)
Materials,
Energy
Health Care,
Information
Technology
AEG(TVC)
Underestimates for
5/9 sectors.
Energy (-),
Telecommunication
Services (-)
Energy,
Consumer Staples
Telecommunication
Services,
Industrials
Consumer Staples
(+),
Consumer
Discretionary (+)
Table 155: Overview of results from empirical modelling.
Summarised results from the statistical testing of hypotheses:
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
GICS Sector
Consumer Discretionary
***
***
(***)
(***)
***
Consumer Staples
***
***
(***)
(***)
(***)
***
Energy
**
***
(***)
Financials
***
***
(***)
(***)
***
Health Care
***
***
*
***
***
***
Industrials
***
***
(***)
(***)
***
***
Information Technology
***
***
(***)
(***)
***
***
Materials
***
(***)
(***)
***
*
Telecommunication Services
***
(***)
(***)
***
***
Table 156: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
Total
***
***
(***)
(***)
***
***
Table 157: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
99
8.20. Appendix 20: Summary of Empirical Results and Statistical Testing: 5 or More Consensus Estimates (1998-2007)
2.00
1.60
1.20
0.40
0.00
-0.40
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 41: Average valuation error for each GICS industry sector and model over the whole period (1998-2007).
100
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
-1.20
Consumer Staples
-0.80
Consumer Discretionary
V.E.
0.80
2.00
1.80
1.60
1.40
1.00
0.80
0.60
0.40
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 42: Average absolute valuation error for each GICS industry sector and model over the whole period (1998-2007).
101
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
0.00
Consumer Staples
0.20
Consumer Discretionary
V.E.
1.20
0.80
0.60
0.40
V.E.
0.20
0.00
-0.20
-0.40
-0.60
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 43: Average valuation error for each model over the whole period (1998-2007).
0.90
0.80
0.70
0.60
V.E.
0.50
0.40
0.30
0.20
0.10
0.00
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 44: Average absolute valuation error for each model over the whole period (1998-2007).
102
The empirical modelling in this section implies that:
Average
Valuation error
Average
Absolute Valuation error
Valuation
Model
Book Value
Over/underestimation
Underestimates
for all sectors.
Largest Error
Consumer Staples (-),
Health Care (-)
Smallest Error
Materials (-),
Energy (-)
Largest Error
Consumer Staples,
Health Care
Smallest Error
Energy,
Materials
RIV(TVC)
Underestimates
for all sectors.
Health Care (-),
Consumer Staples (-)
Energy (-),
Materials (-)
Health Care,
Information
Technology
Energy,
Materials
RIV(PMB)
Underestimates
for 7/9 sectors.
Consumer Staples (-),
Information
Technology (-)
Telecommunication
Services (-),
Material (+)
Consumer
Discretionary,
Information
Technology
Energy,
Financials
RIV(Q)
Overestimates
for 8/9 sectors.
Consumer
Discretionary (+),
Telecommunication
Services (+)
Consumer Staples (+),
Energy (-)
Consumer
Discretionary,
Telecommunication
Services
Energy,
Financials
PVEE(rE)
Underestimates
for 6/9 sectors.
Information
Technology (-),
Energy (+)
Financials (-),
Consumer
Discretionary (-)
Information
Technology,
Materials
Financials,
Industrials
PVEE(rf)
Overestimates
for 7/9 sectors.
Energy (+),
Materials (+)
Health Care (+),
Information
Technology (+)
Energy,
Materials
Health Care,
Information
Technology
AEG(TVC)
Overestimates
for 5/9 sectors.
Financials (+),
Health Care (-)
Consumer Staples,
Consumer
Discretionary
Energy,
Financials
Consumer Staples (+),
Information
Technology (-)
Table 158: Overview of results from empirical modelling.
Summarised results from the statistical testing of hypotheses:
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
GICS Sector
Consumer Discretionary
***
(**)
(***)
(***)
***
Consumer Staples
***
***
***
(***)
(***)
***
Energy
Financials
***
***
(***)
(***)
***
Health Care
***
***
***
***
Industrials
***
***
(***)
(***)
*
***
Information Technology
***
***
(**)
***
***
Materials
***
*
(***)
(***)
***
(*)
Telecommunication Services
***
(***)
(***)
***
***
Table 159: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
Total
***
***
(***)
(***)
***
***
Table 160: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
103
8.21. Appendix 21: Summary of Empirical Results and Statistical Testing: 5% Equity Risk Premium (1998-2007)
1.60
1.20
0.80
V.E.
0.40
0.00
-0.40
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 45: Average valuation error for each GICS industry sector and model over the whole period (1998-2007).
104
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
Consumer Staples
-1.20
Consumer Discretionary
-0.80
1.60
1.40
1.20
0.80
0.60
0.40
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 46: Average absolute valuation error for each GICS industry sector and model over the whole period (1998-2007).
105
Materials
Information Technology
Telecommunication Services
BV
Industrials
Health Care
Financials
Energy
0.00
Consumer Staples
0.20
Consumer Discretionary
V.E.
1.00
0.80
0.60
0.40
V.E.
0.20
0.00
-0.20
-0.40
-0.60
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 47: Average valuation error for each model over the whole period (1998-2007).
0.90
0.80
0.70
0.60
V.E.
0.50
0.40
0.30
0.20
0.10
0.00
BV
RIV(TVC)
RIV(PMB)
RIV(Q)
PVEE(rE)
PVEE(rf)
AEG(TVC)
Chart 48: Average absolute valuation error for each model over the whole period (1998-2007).
106
The empirical modelling in this section implies that:
Average
Valuation error
Average
Absolute Valuation error
Valuation
Model
Book Value
Over/underestimation
Underestimates
for all sectors.
Largest Error
Consumer Staples (-),
Health Care (-)
Smallest Error
Energy (-),
Materials (-)
Largest Error
Health Care,
Consumer
Staples
Smallest Error
Materials,
Energy
RIV(TVC)
Underestimates
for all sectors.
Health Care (-),
Consumer Staples (-)
Energy (-),
Materials (-)
Health Care,
Information
Technology
Materials,
Energy
RIV(PMB)
Underestimates
for 7/9 sectors.
Energy (+),
Consumer Staples (-)
Materials (+),
Telecommunication
Services (-)
Energy,
Information
Technology
Financials,
Materials
RIV(Q)
Overestimates
for all sectors.
Information
Technology (+),
Consumer
Discretionary (+)
Materials (+),
Financials (+)
Information
Technology,
Consumer
Discretionary
Materials,
Financials
PVEE(rE)
Underestimates
for 6/9 sectors.
Information
Technology (-),
Telecommunication
Services (-)
Consumer
Discretionary (-),
Energy (+)
Energy,
Information
Technology
Health Care,
Consumer Staples
PVEE(rf)
Overestimates
for all sectors.
Energy (+),
Materials (+)
Energy,
Materials
Health Care,
Consumer Staples
AEG(TVC)
Overestimates
for 5/9 sectors.
Health Care (+),
Telecommunication
Services (+)
Industrials (+),
Consumer
Discretionary (+)
Energy,
Information
Technology
Financials,
Telecommunication
Services
Consumer Staples (+),
Information
Technology (-)
Table 161: Overview of results from empirical modelling.
Summarised results from the statistical testing of hypotheses:
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
GICS Sector
Consumer Discretionary
***
*
(***)
(***)
***
***
Consumer Staples
***
***
(***)
(***)
(***)
***
Energy
**
(***)
***
(***)
(***)
Financials
***
***
(***)
(***)
***
***
Health Care
***
***
(***)
***
***
***
Industrials
***
***
(***)
(***)
***
***
Information Technology
***
***
(***)
(***)
***
***
Materials
***
(**)
(***)
(***)
***
(***)
Telecommunication Services
***
**
(***)
(***)
***
***
Table 162: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
H0: RIV(TVC)- H0: RIV(PMB)- H0: RIV(Q )- H0: PVEE(rf)- H0: AEG(TVC)- H0: AEG(TVC)BV = 0
RIV(TVC) = 0 RIV(PMB) = 0 PVEE(rE) = 0 PVEE(rE) = 0 RIV(TVC) = 0
Total
***
***
(***)
(***)
***
***
Table 163: Summary of performed t-tests of hypotheses 1-5 and sub-hypothesis. p (<0): *** Significant at the 1 percent level, **
Significant at the 5 percent level, * Significant at the 10 percent level. p (>0): (***) Significant at the 1 percent level, (**) Significant at
the 5 percent level, (*) Significant at the 10 percent level.
107

1. E-mail Addicts

The Global Process Oil Market

Process Oil Market

Hearing Protection Market

Animal Wound Care Market Research Report 2017-2025

Auto Parts Manufacturing Market

0606Round_Robin calibration test for High resistance（1GΩ,10GΩ）

当社連結子会社 Guest-Tek の株式取引停止解除に関するお知らせ

Global Polymer Modified Bitumen (PMB) Market Size, PDF Report 2025