Estimating beta and Cost of Equity Capital for Non-traded Transportation Companies
©2010
Diplomarbeit
67 Seiten
Zusammenfassung
Inhaltsangabe:Introduction:
Estimating the cost of equity capital has two major implications. First, it reflects the return to a companys stock which an equity investor expects to receive from his investment. He makes his decision upon whether he could earn a higher rate of return in an alternative investment of equivalent risk. Second, a company must earn the cost of capital (both debt and equity) through its undertaken projects. It is hence relevant for decisions on undertaking positive net present value projects which are of similar risk as the companys average business activities. It also substantially influences the pricing of an entire firm as far as the valuation is based on a discounted cash flow model.
A lot of effort has been done in the past to achieve accurate models which precisely determine this cost. Building on the modern portfolio theory of Harry Markowitz, a widely used and commonly known model in this context is the Capital Asset Pricing Model (CAPM). Introduced by several researchers in the 1960s, it is still one of the most applied methods for practitioners. However, it suffers from several shortcomings, including statistical caveats, economic assumptions, the absence of market frictions and the behaviour of market participants. An upgrade to this model was provided by Stephen Ross which has resulted in the Arbitrage Pricing Theory (APT). It combines several risk factors in addition to one market proxy, as it is the case in the CAPM, and is less restrictive in its assumptions.
But both CAPM and APT require observable market data, i.e. stock prices, of the analysed companies. These models thus only work for publicly listed firms. If research should be done on non-traded companies, however, an alternative methodology must be applied. In general, data from the balance sheet, the income statement and the cash flow statement are available for both listed and non-listed companies. While accounting data have widely been used in the past as well and have been assumed to provide valuable information in explaining stock returns, this line of research has dissipated over time. Only a few key figures, such as size and financial leverage, are still considered to be relevant. However, they can be used to indirectly estimate a firms beta by assessing their explanatory power in a CAPM or APT framework. This methodology is particularly beneficial for firms which are not listed because there cannot be observed any stock price movements. […]
Estimating the cost of equity capital has two major implications. First, it reflects the return to a companys stock which an equity investor expects to receive from his investment. He makes his decision upon whether he could earn a higher rate of return in an alternative investment of equivalent risk. Second, a company must earn the cost of capital (both debt and equity) through its undertaken projects. It is hence relevant for decisions on undertaking positive net present value projects which are of similar risk as the companys average business activities. It also substantially influences the pricing of an entire firm as far as the valuation is based on a discounted cash flow model.
A lot of effort has been done in the past to achieve accurate models which precisely determine this cost. Building on the modern portfolio theory of Harry Markowitz, a widely used and commonly known model in this context is the Capital Asset Pricing Model (CAPM). Introduced by several researchers in the 1960s, it is still one of the most applied methods for practitioners. However, it suffers from several shortcomings, including statistical caveats, economic assumptions, the absence of market frictions and the behaviour of market participants. An upgrade to this model was provided by Stephen Ross which has resulted in the Arbitrage Pricing Theory (APT). It combines several risk factors in addition to one market proxy, as it is the case in the CAPM, and is less restrictive in its assumptions.
But both CAPM and APT require observable market data, i.e. stock prices, of the analysed companies. These models thus only work for publicly listed firms. If research should be done on non-traded companies, however, an alternative methodology must be applied. In general, data from the balance sheet, the income statement and the cash flow statement are available for both listed and non-listed companies. While accounting data have widely been used in the past as well and have been assumed to provide valuable information in explaining stock returns, this line of research has dissipated over time. Only a few key figures, such as size and financial leverage, are still considered to be relevant. However, they can be used to indirectly estimate a firms beta by assessing their explanatory power in a CAPM or APT framework. This methodology is particularly beneficial for firms which are not listed because there cannot be observed any stock price movements. […]
Leseprobe
Inhaltsverzeichnis
Sascha Heller
Estimating beta and Cost of Equity Capital for Non-traded Transportation Companies
ISBN: 978-3-8428-1280-2
Herstellung: Diplomica® Verlag GmbH, Hamburg, 2011
Zugl. Technische Universität Hamburg-Harburg, Hamburg-Harburg, Deutschland,
Diplomarbeit, 2010
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© Diplomica Verlag GmbH
http://www.diplomica.de, Hamburg 2011
Estimating beta and Cost of Equity Capital for Non-traded
Transportation Companies
Sascha Heller
*
March 2010
Diplomarbeit
Supervisor: Prof. Wolfgang Drobetz (University of Hamburg)
Second Supervisor: Prof. Martin Nell (University of Hamburg)
Abstract
This thesis examines the relationship between systematic risk and accounting variables
for non-traded transportation companies and provides an applicable CAPM framework
for estimating the cost of equity capital. I extend previous research by assessing the risk
relevance of accounting measures in an international multi-beta asset pricing model.
The findings indicate that accounting variables can significantly explain systematic risk
in this context. However, the non-significance and the signs of certain variables are
contradictory to either theoretical assumptions or previous results. Firm size appears to
be a key variable in explaining market betas, though positively correlated to systematic
risk. A CAPM-linked framework is used to estimate the cost of equity capital which on
average range between 5.5% and 8.7% per annum. It can be shown that they
substantially vary across divisions and subsidiaries when broken down to single groups
of companies.
*
Sascha Heller, Email: sascha.heller@wiso.uni-hamburg.de, Hochschulübergreifender Studiengang
Wirtschaftsingenieurwesen Hamburg, University of Hamburg, Hamburg-Harburg University of
Technology and Hamburg University of Applied Sciences
Contents
I. Introduction
II. Background
A.
CAPM and APT A Review...
B.
The Risk Relevance of Accounting Variables...
C.
The Transportation Sector...
III. Empirical
Methodology
A.
The Relevant Global Risk Factors...
B.
Estimating beta for Listed Companies...
C.
Relating Accounting Measures to Systematic Risk...
D.
beta and the Cost of Equity Capital of Non-traded Companies...
IV. Data
A.
The Sample...
B.
Global Risk Factors...
C.
Accounting Variables...
V. Empirical
Results
A.
The Common Risk Factors...
B.
The Significance of Accounting Variables...
C.
The Estimated betas...
D.
The Expected Cost of Equity Capital...
E.
Evidence from the Field...
F.
Robustness
Tests...
VI. Conclusions
References
1
3
3
4
6
7
7
8
9
10
12
12
13
17
24
24
26
30
37
39
42
55
57
1
I. Introduction
Estimating the cost of equity capital has two major implications. First, it reflects the
return to a company's stock which an equity investor expects to receive from his
investment. He makes his decision upon whether he could earn a higher rate of return in
an alternative investment of equivalent risk. Second, a company must earn the cost of
capital (both debt and equity) through its undertaken projects. It is hence relevant for
decisions on undertaking positive net present value projects which are of similar risk as
the company's average business activities. It also substantially influences the pricing of
an entire firm as far as the valuation is based on a discounted cash flow model.
A lot of effort has been done in the past to achieve accurate models which precisely
determine this cost. Building on the modern portfolio theory of Harry Markowitz
(1952), a widely used and commonly known model in this context is the Capital Asset
Pricing Model (CAPM). Introduced by several researchers (Sharpe (1964), Lintner
(1965) and Mossin (1966)) in the 1960s, it is still one of the most applied methods for
practitioners (Graham and Harvey (2001)). However, it suffers from several
shortcomings, including statistical caveats, economic assumptions, the absence of
market frictions and the behaviour of market participants (Fama and French (2004) and
King (2009)). An upgrade to this model was provided by Stephen Ross (1976) which
has resulted in the Arbitrage Pricing Theory (APT). It combines several risk factors in
addition to one market proxy, as it is the case in the CAPM, and is less restrictive in its
assumptions (Reinganum (1980)).
But both CAPM and APT require observable market data, i.e. stock prices, of the
analysed companies. These models thus only work for publicly listed firms. If research
should be done on non-traded companies, however, an alternative methodology must be
applied. In general, data from the balance sheet, the income statement and the cash flow
statement are available for both listed and non-listed companies. While accounting data
have widely been used in the past as well (Beaver et al. (1970), Thompson (1976) and
Bowman (1979)) and have been assumed to provide valuable information in explaining
stock returns, this line of research has dissipated over time. Only a few key figures, such
as size and financial leverage, are still considered to be relevant. However, they can be
used to indirectly estimate a firm's beta by assessing their explanatory power in a
CAPM or APT framework. This methodology is particularly beneficial for firms which
are not listed because there cannot be observed any stock price movements. According
to Ryan (1997), further motivations for using accounting data are: i) to make ex post
2
risk measures more efficient, ii) to determine actual risk determinants, iii) to reduce the
noise when estimating beta through stock returns and iv) to develop trading strategies.
In this thesis, I apply a methodology proposed by Brimble and Hodgson (2007) and
Bowman and Bush (2006) to a sample of listed and non-listed European transportation
companies.
Transportation has a substantial economic importance because it undertakes a
spatiotemporal transformation where transport serves as the spatial bridging function
and warehousing is the temporal bridging function (Pfohl (2010)). As it plays an
important part in economic growth and globalization, the transportation sector is
suggested to be highly cyclical and its performance should mainly depend on
fundamental factors (Stopford (2009)) what implies that global economic trends are
superior to firm-individual business risk. It can be subclassified into air transport, water
transport, rail transport, road transport, transport via pipelines, warehousing and postal
activities. Additionally, one can distinguish between passenger and freight transport
(European Commission (2010)). It is surprising that little research has yet been done on
examining the determinants of transportation stock movements in previous studies,
while asset pricing literature provides a widely accepted methodology.
The rest of this thesis is organised as follows. The next section reviews previous results
on both global risk factors and fundamental accounting variables. Section III describes
the empirical methodology used to estimate beta and to relate accounting variables to
systematic risk. Section IV presents the data and in section V, I discuss the empirical
results. Section VI concludes.
3
II. Background
A.
CAPM and APT A Review
In a CAPM or APT framework, systematic risk refers to a firm's stock price movement,
i.e. its return, which depends on a set of risk factors. This type of risk cannot be
diversified away. It must be taken into account by both investor and company when
deciding on an optimal asset allocation or the true value of either a business project or
the entire firm. Unsystematic risk, however, is firm-individual and can thus be
eliminated when a broadly diversified portfolio is built up (Brealey and Myers (2008)).
It is not pricing relevant in this context (Fu (2009)).
Hence, literature has focused on estimating systematic risk which is measured by beta in
the CAPM. This model proposes that a firm's expected stock return can be explained as
a one-dimensional linear combination of a market proxy's return in excess of a risk-free
rate (i.e. the market risk premium) plus the risk-free rate. It makes the following
restrictive assumptions (Black et al. (1972) and Bowman (1979)): i) investors are
single-period, risk-averse maximisers of the expected utility of terminal wealth, ii) they
can make their optimal portfolio decisions solely on the basis of mean and standard
deviation of the probability distributions of terminal wealth, iii) they have homogeneous
expectations about the mean and standard deviation of the probability distributions, iv)
they have the same decision horizon and can lend and borrow at the same risk-free rate
and v) there are perfect capital markets.
In addition to this single-factor model, a set of macroeconomic risk factors has been
added over time and found to contain valuable information to assess stock price
movements (King (1966), Chen et al. (1986) and Ferson and Harvey (1993)).
1
The risk
factors refer to macroeconomic shocks which may affect required excess returns by
expectations about either future dividend payments or future real interest rates or future
risk premia (Campbell and Mei (1993)). The APT essentially requires three less
restrictive assumptions (Reinganum (1981)): i) there are perfect capital markets, ii)
investors prefer more wealth to less wealth with certainty and iii) the process generating
stock returns can be expressed as a K-factor model. However, additional assumptions
are needed in an international context, i.e. perfect integration of national equity markets
and the absence of distorting taxes and transaction costs (Drobetz et al. (2009)).
1
Instead of adding macroeconomic factors, portfolio returns derived from mimicking portfolios for firm
size and market-to-book ratio can also serve as risk proxies (Fama and French (1993)).
4
But research solely relates to publicly listed firms for which movements in stock prices
are observable. Then exposures to a set of risk factors can be estimated. If stock prices
are not available, one has to implement a more sophisticated empirical methodology to
estimate the cost of equity capital. It was some 40 years ago when asset pricing
literature was in the fledgling stages and much research was done on determining the
drivers of stock prices. Researchers developed different methods in estimating beta
which included both market measures of risk (i.e. stock returns and macroeconomic
factors) and key figures derived from accounting data (i.e. balance sheet, income
statement and cash flow statement). While the latter approach has disappeared for
several years, some key variables are still assumed to have a substantial influence in
explaining stock price movements. Essentially, these are, among others, firm size, price-
earnings ratio and market-to-book ratio (Fama and French (1995) and Penman (1996)).
They have turned out to provide good explanatory power and are used in several ways.
B.
The Risk Relevance of Accounting Variables
The models always require data which are observable on the market. Thus, one cannot
relate them to estimations focused on non-traded companies. Another methodology first
provided by Beaver et al. (1970) and Rosenberg and McKibben (1973), among others, is
based on indirect measures of systematic risk. In this framework, a set of variables
derived from accounting data is used to explain a previously estimated beta using a
CAPM or APT model, respectively. In early studies, empirical work examined multiple
accounting variables. While most researchers applied a set of three to seven accounting
variables (Logue and Merville (1972), Breen and Lerner (1973), Ben-Zion and Shalit
(1975) and Patel and Olsen (1984)), others used up to one hundred and one variables
(Rosenberg and Marathe, 1975). Several studies focused on specific variables such as
operating leverage (Lev (1974)), turnover and coverage ratio (Bildersee (1975)) and
variability in sales and financial leverage (Lev and Kunitzky (1974)). In Figure I,
Penman (2001) presents a model which illustrates the theoretical relationship between
systematic risk and accounting variables. This model divides systematic risk into two
fundamental risk measures, growth risk and return on common equity risk. The latter is
then broken down into operating risk and financial risk. Operating risk is measured by
profit margin risk which is determined by expense risk and operating leverage risk, asset
turnover risk and operating liability leverage risk. Financing risk is further subdivided
into financial leverage risk and borrowing cost risk.
5
Figure I
The Relationship between Systematic Riks and Accounting Variables
Systematic risk is divided in both ROCE risk and Growth Risk, where ROCE is rate of return on common
equity, RNOA is rate of return on net operating assets, FLEV is financial leverage, NBC is net borrowing
cost. NOA is net operating assets and ATO is asset turnover. ROCE Risk is then subdivided into
Operating Risk and Financing Risk. OI is defined as operating income and OL is operating liabilities.
NFO is net financial obligations, CSE is common shareholder equity and NFE is net financial expense.
Source: Penman (2001)
A number of studies has attempted to relate accounting measures of the aforementioned
types of risk to a firm's systematic risk (Lakonishok et al. (1994), Laveren et al. (1997),
Kim et al. (2002) and Lee and Jang (2007)). The seminal empirical work used a set of
seven accounting variables (i.e. dividend payout ratio, growth in assets, financial
leverage, asset size, liquidity, earnings variability and accounting beta) where only
dividend payout ratio, asset growth and variability in earnings turned out to be
significantly correlated with systematic risk (Beaver et al. (1970)). While other studies
determined different sets of relevant accounting measures, there is still little agreement
over which variables are most relevant, and even less evidence whether there are
substantial differences across industries and countries. In addition, coefficient signs, i.e.
the direction of contribution to systematic risk, are somewhat different to what is
theoretically expected.
6
C.
The Transportation Sector
From a financial research perspective, transportation companies are somewhat curious.
Gong et al. (2002) ask "A High Risk Low Beta Business?" what best describes the
intuition behind a substantial and ongoing examination. This industry sector is assumed
to be highly cyclical and, hence, should bear a remarkably high amount of systematic
risk. Its performance should depend on stock market-related factors and the industrial
and economy-wide development. Previous findings, however, report relatively low
market betas (Alexander et al. (1999), Kavussanos and Marcoulis (2000), Gong et al.
(2002), Morrell and Turner (2003) and Yamada (2005)) which stand in contrast to
theoretical expectations.
2
The studies suggest that betas may differ across transportation
sectors and may be time-variant. Kavussanos and Marcoulis (1997) report betas which
are on average higher for the subperiod January 1990 to June 1995 as compared to the
subperiod July 1984 to December 1989, where water and rail transportation industries
betas significantly differ in the entire period and the second subperiod. Allen et al.
(1990) document the time-dependent character of airline, motor carrier and railroad
industries betas in the period from January 1963 to June 1987, while betas remained
relatively stable for different 5-year to 10-year subperiods. betas also substantially
differed across industries.
In this thesis, I focus on European transportation companies, both traded and non-
traded. While even some big players, measured by sales, in this sector are not listed on
any stock exchange (e.g. Deutsche Bahn AG, Condor Flugdienst GmbH, Hapag-Lloyd
AG, La Poste), issuing stock is attractive mainly for well-established firms. Most firms
in this industry stay privately held and, thus, market data are not observable. They are,
however, expected to face the same risky environment, as do big companies. Hence,
practitioners must apply a precise valuation method including estimations on the cost of
capital.
2
Some studies find betas equal to or higher than market average (Allen et al. (1990) and Lee and Jang
(2007).
7
III. Empirical
Methodology
In order to finally estimate the cost of equity capital for non-traded companies, I need
several steps including estimations based on listed and non-listed companies as well as
macroeconomic data and accounting data. My empirical analysis is based on
transportation-related companies where all models are estimated for both transportation
and transportation service companies, and for each of those subsectors individually.
First, exposures to a set of global macroeconomic factors are estimated using a market
model regression with one market proxy and a methodology proposed by Ferson and
Harvey (1994) for several global risk factors, respectively. This framework is also used
in Chen at al. (1986) and in Drobetz et al. (2009) who focus on shipping companies. In a
second step, I apply a methodology provided by Bowman and Bush (2006) and Brimble
and Hodgson (2007) to assess an applicable set of accounting variables which can
explain systematic risk for traded companies. Afterwards, I estimate betas for non-
traded companies using the previous results. Fourth, I use a CAPM-linked model to
determine the expected cost of equity capital for non-listed firms. Econometric
assumptions and guidelines for the regression models are provided in Campbell et al.
(1996) and Wooldridge (2002).
A.
The Relevant Global Risk Factors
According to Ferson and Harvey (1994) and Drobetz et al. (2009), among others, I
apply a multi-factor model which includes K-1 risk factors in addition to one market
proxy. In this context, I first estimate a linear fixed-effects (within) cross-sectional time-
series regression model
3
to determine which factors have a significant impact on
predicting returns on transportation stocks:
r
it
r
ft
=
i
+
k
F
kt
k
=1
K
+
it
,
(1)
where r
it
is the continuously compounded return for firm i in period t-1 to t and r
ft
is the
risk-free rate.
i
denotes the intercept term
4
and
k
is the exposure against the k-th
macroeconomic risk factor F
kt
. beta is a measure of systematic risk and can be
3
xtreg command in Stata with robust standard errors allowing for intragroup correlation (vce(cluster)
command in Stata)
4
Economically, a positive alpha indicates a stock's underpricing where the return is lower than expected
by the CAPM. A negative alpha indicates that the stock is overpriced (Kavussanos et al. (2003).
8
expressed by the covariance between a stock's return and the market return,
standardised with the variance of the stock's return.
it
is an error term and indicates the
unsystematic risk which is not priced in an asset pricing context (Fu (2009)). A fixed-
effects model takes into account a firm-specific constant term. This estimation method
results in one pooled beta for each risk factor. The model is estimated in a step-wise
procedure, i.e. risk factors which are not significant in at least one subsample (all
companies, transportation companies and transportation service companies) are
excluded and the reduced model is then re-estimated. The estimation process is repeated
successively until all coefficients are significant.
B.
Estimating beta for Listed Companies
The market model regression is an OLS regression
5
with one market proxy. This single
beta model separately estimates one risk exposure, i.e. market beta, for each company:
r
it
r
ft
=
i
+
i
r
mt
r
ft
(
)
+
it
i, (2)
where r
it
and r
ft
are the same as in model (1). r
mt
is the return on the market proxy.
i
is
a firm-individual intercept term and
i
is a firm's sensitivity against a market proxy's
return.
it
is an error term. alpha, beta and epsilon have the same economic
interpretation as in model (1). Consequently, this model provides one beta for each
company and is applied exclusively to traded companies.
In a next step, a multi-factor model (OLS)
6
is estimated which includes solely K'
significant risk factors:
r
it
r
ft
=
i
+
ik
F
kt
k
=1
K '
+
it
i ,
(3)
where
ik
is the sensitivity against the k-th macroeconomic risk factor F
kt
for firm i,
while the remaining variables and coefficients are the same as in model (2). This model
is separately estimated for each listed firm and results in an array of N betas for each
risk factor.
5
reg command in Stata
6
reg command in Stata
9
C.
Relating Accounting Measures to Systematic Risk
The next section assesses the contribution to risk of several accounting variables. The
model in Bowman and Bush (2006) differs slightly from that applied in Brimble and
Hodgson (2007), in that Bowman and Bush estimate their results for one point in time,
while the estimations in Brimble and Hodgson are based on accounting variables
averaged over a specific time period. I use the latter in order to take into account
changes in the economic environment. However, I do not use time-series betas what
implicitly assumes stationarity throughout the whole period (Beaver et al. (1970)). This
model (OLS)
7
proposes that market beta can be explained by a set of L accounting
variables:
^
i
=
l
V
li
+
i
l
=1
L
,
(4)
where ^
i
is the market beta for traded firm i estimated by (2).
l
is the exposure against
the l-th accounting variable V
li
for firm i, averaged over the time period , and
i
is the
error term. In my analysis, I exclude the intercept because a firm without any business
activities and thus with accounting variables equal to zero has no exposure to a certain
risk factor, i.e. beta is zero. A positive gamma indicates a positive relationship between
systematic risk and the respective accounting measure, and vice versa. This results in
one pooled gamma for each accounting variable. The model is estimated in a step-wise
procedure, i.e. non-significant accounting variables are excluded and the reduced model
is then re-estimated. The estimation process is repeated successively until all
coefficients are significant. The model (OLS)
8
finally delivers L' significant accounting
variables:
^
i
=
l
V
li
l
=1
L'
+
i
.
(5)
This allows for an applicable model to calculate the expected cost of equity capital.
7
reg command in Stata with robust standard errors (vce(robust) command in Stata)
8
reg command in Stata with robust standard errors (vce(robust) command in Stata)
10
The model (OLS)
9
is also estimated for each significant beta derived from the multi-
factor model in (3):
^
ik
=
kl
V
li
+
ik
l
=1
L
,
(6)
where
ik
is the exposure against the k-th global risk factor for firm i and
kl
is the
sensitivity against the l-th averaged accounting variable V
li
for firm i for
k
.
ik
is the
error term. As in (4), a step-wise estimation procedure (OLS)
10
is applied and delivers
L' significant -coefficients:
^
ik
=
kl
V
li
+
ik
l
=1
L'
.
(7)
D.
beta and the Cost of Equity Capital of Non-traded Companies
I then estimate market betas and multi-factor betas, respectively, for a sample of non-
traded companies using the estimated gammas from (5) and (7) and the appropriate
accounting variables:
j
=
^
l
V '
lj
l
=1
L'
(8)
for a market beta estimation where
j
is the exposure against a market proxy for the j-
th non-traded company and ^
l
is the l-th estimated coefficient for the market beta. V '
lj
is accounting variable l for non-traded firm j, averaged over the time period .
jk
=
^
kl
V '
lj
l
=1
L'
(9)
is utilised for estimating multi-factor betas where
jk
is the exposure against the k-th
global risk factor for non-traded firm j. ^
kl
is the l-th estimated coefficient for the k-th
beta from (5) and (7), respectively. V '
lj
is defined as above. To compare results,
9
reg command in Stata with robust standard errors (vce(robust) command in Stata)
10
reg command in Stata with robust standard errors (vce(robust) command in Stata)
11
models (8) and (9) are also estimated for traded companies where index j changes to
index i.
Using a CAPM-linked methodology and the estimated market beta from (8), I calculate
the expected cost of equity capital for non-listed companies. In addition to a risk-free
rate and a market risk premium, this model takes into account a liquidity risk premium
which corrects for the risk of a stock's thin trading. This concept is provided by
Acharya and Pedersen (2005) and Amihud et al. (2005), among others. While Amihud
et al. give four possible explanations for illiquidity
11
, Acharya and Pedersen estimate a
risk premium when correcting for the level of liquidity. The expected cost of equity
capital is determined as follows:
R
j
( )
= R
f
+ ^
j
R
m
( )
R
f
[
]
+ ,
(10)
where R
j
is the annual return for non-traded firm j, R
f
is the annual risk-free rate and R
m
is the annual market return. ^
j
is the estimated systematic risk from (8) for firm j and
is the annual liquidity risk premium. E is the expectation operator and E R
m
( )
R
f
is the
expected market risk premium.
11
These are: i) exogenous transaction costs, ii) demand pressure and inventory risk, iii) private
information about fundamentals of the security and order flow, and iv) search friction.
Details
- Seiten
- Erscheinungsform
- Originalausgabe
- Jahr
- 2010
- ISBN (eBook)
- 9783842812802
- Dateigröße
- 3.6 MB
- Sprache
- Englisch
- Institution / Hochschule
- Technische Universität Hamburg-Harburg – Wirtschafts- und Sozialwissenschaften, Wirtschaftsingenieurswesen
- Erscheinungsdatum
- 2014 (April)
- Note
- 1,3
- Schlagworte
- equity capital capm accounting
