The effect of asymmetric information and transaction costs on asset pricing: theory and tests.
Bellalah, Makram ; Aboura, Sofiane
ABSTRACT
This paper presents a capital asset pricing model in the presence
of asymmetric information and transaction costs. The model is a
generalized version of Merton's (1987) model and Black's
(1974) model. Empirical tests show a negative relation between the
expected rate of return and the shadow costs of incomplete information.
The results in this paper have the potential to explain the home bias
equity in a domestic and an international context.
JEL Classification: G11, G12, G14
Keywords: Asset pricing; Asymmetric information; Home bias
I. INTRODUCTION
Market imperfections are important elements in capital asset
pricing models in a domestic setting (Mayshar (1979, 1980)) and in an
international setting (Black (1974), Stulz (1981)).
Transaction costs and asymmetric information are potential factors
that explain the home bias equity in domestic and international
financial markets. Using the model in Black (1974), Lewis (1999) shows
the effect of transaction costs on portfolio choice in the case of
two-country model. Cooper and Kaplanis (1994) extend the model of Adler
and Dumas (1983) by incorporating a tax similar to that in Black (1974).
Cooper and Kaplanis (1994) show that the home bias can be explained by
deadweight costs (transaction costs or tax) and not by the inflation
risk as suggested by Adler and Dumas (1983). Cooper and Kaplanis (2000)
extend the model of Stulz (1981) to the case of N countries and show how
deadweight costs affect the portfolio choice and the capital budgeting
decisions. The effect of market imperfections is used as an argument to
explain the market segmentation or/and integration. Market imperfections
such as transaction costs and taxes suggest that financial markets are
not efficient and explain some observed anomalies.
This paper develops an asset-pricing model that accounts for the
effect of asymmetric information and transaction costs. The model
explains the effect of market imperfections on the expected return and
shows how these frictions explain the home bias equity. We develop an
empirical test in order to explain the relationship between the expected
rate of return, the transaction costs and the information costs.
This paper is organized as follows. Section 2 presents the
importance of transaction costs, taxes and asymmetric information in
portfolio choice. Section 3 develops a model that incorporates the
effects of asymmetric information about assets and the transaction
costs. Section 4 provides some empirical evidence. Finally, we conclude
and provide some suggestions for future research.
II. THE EFFECT ON PORTFOLIO CHOICE OF ASYMMETRIC INFORMATION AND
TRANSACTION COSTS
The gain from international diversification were documented by
Grubel (1968), Levy and Sarnat (1970), Solnik (1974a), Gerard and De
Santis (1997) and others. Tesar and Werner (1995) find a strong evidence
of a home bias in national investment portfolios. They explain the home
bias by transactions costs. They suggest that the best explanation of
this bias should be based on asymmetric information. Hasan and Simaan
(2000) develop a model that incorporates both the forgone gains from
diversification and the informational constraints of international
investments. This model is a generalization of French and Poterba
(1991). These authors show that the lack of diversification appears to
be the result of investor choices rather than institutional constraints.
Kadalec and Mcconnell (1994) show that the change in share value is
attributed to investor recognition factor as suggested by Merton (1987).
Forester and Karolyi (1999) show that the abnormal returns can be
explained by the asymmetric information. In this model the empirical
tests provide support for market segmentation hypothesis and
Merton's (1987) investor recognition hypothesis. Forester and
Karolyi (1999) and Kadalec and Mcconnell (1994) use a sample from US
exchanges for an investor who trade in local market by constructing a
diversified portfolio from securities of foreign firms listed in US
exchange. Asymmetric information is very important in a national and an
international setting. Brennan and Cao (1997) develop a model of
international equity portfolio investment flows based on informational
endowments between foreign and domestic investors. They show that when
domestic investors hold an information advantage over foreign investors
about their domestic market, investors tend to purchase foreign assets
in periods when the return in foreign assets is high. The effects of
taxes and transaction costs on asset pricing are presented the first
time by Black (1974) on a model where the investor is imposed on his
holding. Black (1974) shows that the taxes discourage some investors to
invest in some assets and in other countries. Stulz (1981) proposes a
model in which it is costly for the domestic investors to hold foreign
assets. He shows that due to the existence of these costs some assets
are not traded and the domestic investors tend to hold more in their
domestic securities that explain the home bias equity. Whatley (1988)
develops a consumption-based asset pricing model that incorporates a tax
as Black (1974) and Stulz (1981). He shows that there is a little
evidence about market integration due to these costs.
Falkenstein (1996) explains that the preference for some assets is
explained by the low transaction costs and low volatility. He shows that
the investors tend to trade on the assets about which they are informed.
In his model, the information is detected by the investors through the
publication of the new stories and the age of these assets.
We develop in the next section a model of asset pricing in the
presence of transaction costs and information costs. We show that the
two market imperfections in the asset pricing have the same rule and
they are very important in theoretical and practical activity on the
market.
This paper shows that the two imperfections are not the same as
suggested in the literature, which considers the transaction costs as
information costs. We consider that the information costs as indirect
costs but the transaction costs as direct costs. The presence of these
costs shows that in equilibrium, the market portfolio is not efficient,
and that the portfolio choice of an investor depends on these variables.
III. THE MODEL
We develop a two-period model of asset pricing in an environment
where each investor knows only about a subset of the available
securities. The equilibrium return of security k follows the equation:
[[??].sub.k] = [[bar.R].sub.k] + [b.sub.k] [??] + [[sigma].sub.k]
[[??].sub.k] (1)
with [[bar.R].sub.k] = the expected rate of return of security k;
[??] = denotes a random variable common factor with ; E([??])=0,
Var([??]) = 1; and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
By inspectation of (1), the structure of return is like the Sharpe
(1964) diagonal model or the one factor version of the Ross (1976)
Arbitrage pricing theory and Merton's (1987) model. In addition to
the n risky securities, we consider two other traded securities, a
riskless security with sure return and a security that combines the
riskless security and forward contract on the observed factor. We assume
that the forward price of the contract is that the standard deviation of
the equilibrium return on the security is unity. The rate of return on
this security is given by:
[[??].sub.n+1] = [[bar.R].sub.k] + Y (2)
We assume that investors' aggregate demand for this security
as well as the riskless security must be zero in equilibrium. The model
assumes the existence of transaction costs or taxes as Black (1974) and
Lewis (1999) when we trade on security k.
Borrowing and short selling are assumed without restrictions.
Investors are risk averse and select an optimal portfolio according to the Markowitz - Tobin (1959) mean-variance criterion applied to the end
of period wealth. The preference of investor j is represented as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)
where [W.sup.j] = the Wealth of investor j ; [[??].sup.j.sub.k] =
the return on his portfolio of investor j ; and [[delta].sup.j] [grater
than or equal to] 0, for j=1,2,3..., N.
We call [J.sup.j] a collection of integers such that the security k
is an element of [J.sup.j] if investor j is informed about this asset,
with k =1,2,3..., n. We assume that the security (n+2) is the riskless
security and the (n+1) security is contained in . With the structure of
the model established, we turn now to the solution of the portfolio
selection problem for investor j.
Let [w.sup.j.sub.k] be the fraction of initial wealth allocated to
security k by investor j. The return on portfolio for an investor j in
the presence of transaction costs can be written as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)
Inserting (1) and (2) in (4) we get:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)
where [[tau].sub.k] the transaction costs paid by investor j on
asset k.
Equation (5) can be written as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)
Let:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)
and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)
From (7) and (8), we can write (6) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)
With the properties of [??] and [[??].sub.k], we can write the
variance of the portfolio of investor j as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)
If we look to equation (10), we see that the variance of the
portfolio of investor j is characterized by the common factor risk
[b.sup.[j.sup.2]] and the risk of all assets contained in the portfolio.
Let us derive the expected rate of return on portfolio of investor j.
This can be done by using equation (9):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)
Using (11) the expected rate of return on a portfolio for investor
j is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)
This expression shows that the transaction costs decrease the
expected rate of return of the portfolio of investor j. We can write the
expression (12) as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
with
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
From equation (3), the optimal portfolio choice for the investor
can be formulated as a solution to the constrained maximization problem:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)
where [[lambda].sup.j.sub.k] is Lagrange multiplier that reflects
the constraint that investor j can not invest in security k if he does
not have an information about this security. From this interpretation,
we have
[[lambda].sup.j.sub.k] = 0 if k [member of] [J.sup.j] (14)
This condition means that the investor is informed about security
k:
[w.sup.j.sub.k] = 0 if k [member of] [J.sup.[j.sup.c]] (15)
From the optimization problem given by relation (13) and from
relation (12) and (10) we obtain the first-order conditions that give
the optimal common factor and portfolio weights for investor j:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)
From (16), we can write
[[bar.R].sub.n+1] - R / [[delta].sup.j] = [b.sup.j] (18)
Equation (18) represents the common factor exposure (political risk
for example) that affects the portfolio of investor j. Using relation
(17), we have:
[[DELTA].sub.k] - [[lambda].sub.k] /
[[delta].sup.j][[sigma].sup.2.sub.k] = [w.sup.j.sub.k] (19)
Using (14) equation (19) becomes for an informed investor:
[[DELTA].sub.k] / [[delta].sup.j][[sigma].sup.2.sub.k] =
[w.sup.j.sub.k] (20)
Equation (20) shows that investor j invests only in securities he
knows about and that the fraction allocated to security k depends on the
required return, the risk and the transaction costs. If the investor
does not have any information about security k, then his proportion
invested in this security is equal to zero. From equation (19) we get:
[[DELTA].sub.k] = [[lambda].sup.j.sub.k] if k [member of]
[J.sup.[j.sub.c]] (21)
Up to now we have solved for individual optimal demands. We now
aggregate to determine equilibrium asset prices and expected returns. We
simplify the analysis and focus on the effect of transaction costs and
incomplete information on equilibrium prices. Assuming that the
representative investors have identical preferences and the same initial
wealth, then we can write:
[[delta].sup.j] = [delta] [for all] j and [W.sup.j] = W j = 1,2,3,
..., N
Under these assumptions it follows that all investors choose the
same exposure to the common factor, [b.sup.j] = b for j=1,2,3 ....., N.
Equation (16) becomes:
[[bar.R].sub.n+1] - R = [delta]b + (22)
Let [D.sub.k] be the aggregate demand for security k by investors:
[D.sub.k] = [N.summation over (j=1)] [w.sup.j.sub.k][W.sup.j] (23)
With our assumptions that investor j, invests only in the
securities that he has information about, equation (23) becomes with
reference to (15) and (20):
[D.sub.k] = [N.sub.k] W[[DELTA].sub.k] /
[delta][[sigma].sup.2.sub.k] (24)
wth [N.sub.k] the number of investors who have information about
security k. When all investors know about the security k, then [N.sub.k]
= N. Let [x.sub.k] be the fraction of the market portfolio invested in
security k, then we write:
[x.sub.k] = [D.sub.k]/M (25)
where M denotes the equilibrium national wealth:
M = [N.summation over (j)] [W.sup.j] (26)
In reality, not all investors know about the security k. That is
why we can give the fraction of all investors who have information about
security k as:
[q.sub.k] = [N.sub.k]/N (27)
The value [q.sub.k] of varies between zero and one, 0 <
[q.sub.k] [less than or equal to] 1. This fraction is greater than zero
because there is an investor who is informed about security k. When this
fraction is equal to one, then all investors have the same information
about security k. From equations (24), (26), (27), equation (25) allows
to write:
[x.sub.k] = [q.sub.k][[DELTA].sub.k]/[delta][[sigma].sup.2.sub.k]
(28)
Because the market portfolio is a weighted average of optimal
portfolios and because all investors choose the same common factor
exposure [b.sup.j], it follows that [b.sup.j] = b. We assume that assets
(n+1) and (n+2) are inside securities. We can write b = [n.summation
over (k)][b.sub.k]. In addition, we have [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII.]. Inserting (18) in the expression of
[[DELTA].sub.k], we obtain:
[[DELTA].sub.k] = [[bar.R].sub.k] - [[tau].sub.k] - R -
[b.sub.k][delta] [sup.j][b.sup.j] (29)
Since [b.sup.j] = b and [[delta].sup.j] = [delta], equation (29)
becomes:
[[DELTA].sub.k] = [[bar.R].sub.k] - [[tau].sub.k] - R -
[b.sub.k][delta]b) (30)
From (30), we have:
[[bar.R].sub.k] = R + [[tau].sub.k] + [b.sub.k][delta]b +
[[DELTA].sub.k] (31)
From (28) the expression of [[DELTA].sub.k] is given by:
[[DELTA].sub.k] = [x.sub.k] / [q.sub.k]
[delta][[sigma].sup.2.sub.k] (32)
Inserting (32) in (31) we obtain:
[[bar.R].sub.k] = R + [[tau].sub.k] + [b.sub.k][delta] b +
[x.sub.k]/[q.sub.k] [delta][[sigma].sup.2.sub.k (33)
To see the connection between the effects of transaction costs and
the shadow cost of incomplete diffusion of information among investors,
let:
[[lambda].sub.k] = [N.summation over (j)] [[lambda].sup.j.sub.k] /
N (34)
be the equilibrium aggregate shadow cost per investor. From
relation (21), equation (34) becomes:
[[lambda].sub.k] = N - [N.sub.k] / N (35)
Equation (35) can be written as:
[[lambda].sub.k] = (1 - [N.sub.k]/N) [[DELTA].sub.] (36)
From (27), equation (36) becomes:
[[lambda].sub.k] = (1 - [q.sub.k])[[DELTA].sub.k] (37)
Let [[??].sub.M] be the return on the market portfolio:
[[??].sub.M] = [n.summation over (k=1)] [x.sub.k][[??].sub.k] (38)
We assume that the securities n+1 and n+2 are inside securities so
that [x.sub.n+1] and [x.sub.n+2] are equal to zero. From relation (10),
we obtain the variance of the market portfolio as follows:
Var([[??].sub.M]) = [b.sup.2] + [n.summation over (k=1)]
[x.sup.2.sub.k] [[sigma].sup.2.sub.k] (39)
The examination of the variance of the market portfolio shows that
there are two sources of risk: a risk characterizing the common factor,
and the risk of every asset k. If we define the beta of security k as
[[beta].sub.k] the covariance of return on security k with the market
portfolio divided by the variance of the market portfolio return, then
we have:
[[beta].sub.k] = b[b.sub.k] + [x.sub.b] [[sigma].sup.2.sub.k] /
Var([[??].sub.M]) for k = 1,2,3..., n (40)
With reference to equation (37), we have:
[[DELTA].sub.k] = [[lambda].sub.k] + [q.sub.k][[DELTA].sub.k] (41)
Inserting (41) in (31) we obtain:
[[bar.R].sub.k] = R + [[tau].sub.k] + [b.sub.k][delta] b +
[[lambda].sub.k] + [q.sub.k][[DELTA].sub.k] (42)
The substitution of (32) in (42) gives:
[[bar.R].sub.k] = R + [[tau].sub.k] + [b.sub.k][delta] b +
[[lambda].sub.k] + [x.sub.k][[delta].sub.k][[sigma].sup.2.sub.k] (43)
From this relation, we try to get the covariance expression:
[[bar.R].sub.k] = R + [[tau].sub.k] + [delta]([b.sub.k]b +
x[[sigma].sup.2.sub.k]) + [[lambda].sub.k] (44)
If we multiply (44) by [x.sub.k] and sum from k=,2,3,..., n,
keeping in mind that the securities (n+1) and (n+2) are inside
securities, [x.sub.n+1] =0 and [x.sub.n+2]=0. Equation (44) becomes:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (45)
Equation (45) can be written as:
[[bar.R].sub.M] = R + [[tau].sub.M] + [delta]Var([[??].sub.M]) +
[[lambda].sub.M] (46)
with [[lambda].sub.M] = the weighted-average shadow cost of
incomplete information over all securities; [[tau].sub.M] = the weighted
average transaction cost over all securities Or we know that:
Cov([[??].sub.M], [[??].sub.k]) = [[beta].sub.k] Var([[??].sub.M])
(47)
From equation (47), we can write (44) as follow:
[[bar.R].sub.k] = R + [[tau].sub.k] + [[delta].sub.k[beta]] +
[[beta].sub.k] Var([R.sub.M]) + [[lambda].sub.k] (48)
We replace the portfolio variance by its expression from relation
(46) in (48) to obtain:
[[bar.R].sub.k] = R + [[tau].sub.k] + [[lambda].sub.k] +
[[beta].sub.k] ([[bar.R].sub.M] - R - [[lambda].sub.M] - [[tau].sub.M])
(49)
Equation (49) yields a capital asset pricing model with transaction
costs and information costs. Our Model is consistent with Merton's
(1987) and Black's (1974) asset pricing models. If the transaction
cost on asset k is equal to zero than [[tau].sub.k] =0 and [[tau].sub.M]
=0 the model reduces to Merton's (1987) model. When all investors
have the same information about security k than [[lambda].sub.k] =0 and
[[lambda].sub.M] =0, the model is reduced to Black's (1974) model.
When there are no transaction costs and no information costs, the model
yields the standard CAPM. This finding shows that in equilibrium the
market portfolio will be not efficient in the presence of information
costs and transaction costs. Relation (49) can be written as follows:
[[bar.R].sub.k] = R + [[PSI].sub.k] + [[beta].sub.k]
([[bar.R].sub.M] - R) (50)
where [[PSI].sub.k] = [[tau].sub.k] + [[lambda].sub.k] +
[[beta].sub.k] ([[tau].sub.M] + [[lambda].sub.M]). The market portfolio
is efficient if [[PSI].sub.k] =0 for all k=1,2,3,..., n. Equation (49)
gives the expected rate of return of security k as a function of the
risk free rate, the transaction costs, the shadow cost of incomplete
information and the risk premium. In this model the transaction cost and
the information cost have the same role in the asset pricing but they
are derived differently. This result contradicts the fact that the
information cost is considered as transaction costs. Relation (49) shows
the intimate relationship between the betas of assets, the effects of
transaction costs and information costs in equilibrium. So observing
portfolios is equivalent to implicitly observing these costs. Solnik
(1974), De santis and Gerard (1997), Hassan and Youssif (2000) show that
the international diversification does better than the national one. Our
model shows that the costs of investment are important in a domestic and
in an international setting and investors are willing to diversify their
portfolios if the gains exceed these costs. Our model shows the effects
of frictions in capital markets and explains the equity home bias. This
conclusion is consistent with the empirical work of Coval and Moskowitz
(2000) in which they explain the home bias by the locality of investors
and asymmetric information.
The next section tests our model to show how transaction cost and
asymmetric information explain some anomalies in portfolio choice.
IV. THE EMPIRICAL EVIDENCE OF THE MODEL
This section provides an empirical test for our model given by
equation (49). Testing this relationship directly remains difficult task
due to the existence of two non.observable variables, information costs
and transaction costs.
A. The Data
For our empirical study, we select 76 French shares taken from the
first market. We extract from the DATASTREAM database the information.
Our sample covers a ten-year period going from July 1st, 1991 to
December 1st, 2000. This represents 2460 daily observations.
The results of the empirical tests are presented only for ten
companies, but the tests are applied for the whole sample. The ten
companies are: GALERIES LAFAYETTE, HAVAS ADVERTISING, LVMH, LAFARGE,
GEOPHYSIQUE (CIE.GL.), GECINA, GUYENNE and GASCOGNE, IMERYS, INGENICO,
and KLEPIERRE. The first five companies are well known while the five
other companies are less known.
B. The Estimation Procedure
We construct a series of transaction costs on the basis of a
methodology chosen for reasons that we explain later. As for the
information costs, we couldn't construct a series for two reasons.
The first is that there are no explicit methods for such a work. The
second reason is that, the few existing methods need some data that are
not available in France. We have to note that the choice of a given
method will obviously affect the final result, (i.e, the estimate of the
parameters). The choice of one method or another for the estimation of
the transaction costs affects the statistical significance of the
transaction cost and also of the information cost parameter (considered
as constant during each year). The statistical significance of our
results depends on the method of construction of the transaction cost
series.
1. The estimation of transaction cost
We use a method proposed by Kyle (1985) in order to obtain a sample
of transaction costs related to the assets to test the model. We use the
volume of all securities in our sample and their prices. Each estimate
of transaction costs is calculated for a one-month (21 days) period
using the following formula:
|Ln[P.sub.t] - Ln[P.sub.t-1]| = [alpha] + [tau]Ln(1 + [V.sub.t])
(51)
where [P.sub.t] = the price of asset k at time t ; [tau] = the
transaction cost of asset k at time t; [V.sub.t] = the volume of asset k
at time t ; [alpha] = the intercept.
The method implemented to extract a sample of monthly transaction
costs is consistent with Falkenstein (1996). He uses the volume as a
proxy of transaction costs in order to show the effect of this friction
on preferences for stocks as revealed by the fund portfolio holdings. In
the same way, our method was recently used by Lesmond et al (1999) to
study the relation between the frequency of zero returns and transaction
costs. We have first employed the measure of Roll (1984), 2[square root
of -cov], which is a measure of the effective bid ask spread as a proxy
for the transaction costs. The method proposed by Roll (1984) is
estimated using the first-order autocovariance of security returns, but
we get some positive autocovariance with our data. We find a problem
similar to that in Harris (1990). Harris (1990) overcomes this problem
by converting the positive autocovariance to negative. Therefore we
employ the model of Kyle (1985).
2. The estimation of information costs
Jensen (1968) tests the CAPM and the market efficiency. He adds an
intercept to the capital asset pricing model to explain the part, which
is not explained by the market and attributed to the imperfection. In
our test the information cost is approximated by the intercept of Jensen
(1968). The asymmetric information hypothesis and especially the shadow
cost were tested by Kadlec and McConnel (1994) and recently by Foster
and Karolyi (1999). To test this shadow cost and how it explains the
abnormal returns, the authors use the change in the number of the
registered shareholders from pre-to post listing periods as a proxy for
[[lambda].sub.k].
For practical reasons, we couldn't apply this method because
these data are not available in France. This is why, we considered
arbitrarily that information costs are constant every year and we
implement the method employed by Jensen (1968). This is not a strong
assumption if we estimate an average cost per year. We recall that the
statistical significance of this information cost depends on the
construction of the transaction cost series. Nevertheless, the ideal
situation is of course to construct a monthly proxy for information
costs in addition to the monthly series of transaction costs. We will
carry out this applying our model to the American market in a future
work.
Table 1 displays the results for a ten-year estimation of our
model. We consider only ten companies. All the [[beat].sub.k]'s are
obviously statistically significant since the market portfolio explains
an important part of the expected return of each company. All the
transaction costs are also significant, which means that for the period
considered, they affect the expected return. Information costs, they are
significant only for five out of ten companies. We also note that they
are almost all negatively correlated with the expected return, which is
consistent with the results in Forester and Karolyi (1999) and Kadlec
and MCconnell (1994).
If we observe that for relevant companies as GALERIE LAFAYETTE or
LVMH and LAFARGE, the information cost is not significant because they
are considered as "large firms" and thus, the investors have
an easy access to the information. We observed also that HAVAS
ADVERTISING has a significant information cost, which is surprising
because it is a "large firm". Due to the fact that information
costs are not significant for "large companies", in general,
the investosr tend to purchase these firm's assets, which are
better known. Our finding is consistent with the results in Kang and
Stulz (1997) and recently Dahliquist and Robertsson (2001). Table 2 to
Table 3, estimate parameters for each year during ten years and for the
ten companies. In general, all the [[beta].sub.k]'s are
statistically significant. Transaction costs are generally not
significant. This can be the fact of the method retained to build up our
transaction cost series. Different methods imply different results. Our
method is inspired by the Kyle's model for transaction costs and it
doesn't display the results that we could have expected. It is the
same for the information cost parameter that is generally not
significant for a one-year frequency, but the estimates are always
negatively correlated with the expected return. We observe for the year
1996 that many transaction costs are significant. This can be explained
by the fact that the volume on the stock market for our ten companies
has began to rise slowly in 1996 to be the highest in 1997 for all the
decade. Besides, 1997 was the return of the economic growth in France.
The increase of the activity in the Paris Bourse may have implied a more
frequent rebalancing of portfolios, i.e., more transaction costs.
V. CONCLUSION
This paper develops a capital asset pricing model in the case of
asymmetric information and transaction costs. It is shown that these two
sources of market frictions have the same function in the model but they
are derived differently. This evidence contradicts some authors who view
the information costs as transaction costs. The empirical work provides
an explanation of the evolution of these variables. Our tests show that
the information costs are negatively correlated with the expected return
and have an asymmetric evolution with transaction costs.
We show that investors better know large firms, which explains the
bias in favor of some assets. Our model can be used to account for the
cost of capital and to show how frictions impact the capital budgeting.
ENDNOTES
(1.) The method used by Kadalec and McConnel (1994) and Foster and
Karolyi (1999) to show the relationship between the abnormal returns and
the shadow costs of incomplete information is:
[[DELTA][R.sub.k] = [[alpha].sub.0] + [[alpha].sub.1]
[DELTA][[lambda].sub.k] + [e.sub.k], where the effect of the information
cost is given by:
[DELTA][[lambda].sub.k] = [Res.sub.k] x [MKtval.sub.k] /
[NYSEhld.sub.k] - [Res.sub.k] x [MKtval.sub.k] / OTChld.sub.k]
with [Res.sub.k]= the residual variance of security k;
[Mktval.sub.k]= the market value of security k; [NYSEhld.sub.k] = the
number of NYSE shareholders for security k; [OTChld.sub.k] = the number
of OTC shareholders of the security k; and [[alpha].sub.0],
[[alpha].sub.1], are the intercept and the coefficient of this
regression.
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Makram Bellalah (a) and Sofiane Aboura
(a) Assistant Professor of finance, University of Amiens,
GRG-CRIISEA, France and ESG Group, France
[email protected]
(b) ESG Group and ESSEC Business School, France
[email protected]
Table 1
Empirical results for ten years
Intercept Slopes on
10 French [gamma] [[tau].sub.i] [[beta].sub.i]
Stocks
GALERIES -0.049730 0.259789 *** 0.404178 ***
LAFAYETTE (-1.328107) (4.152402) (9.341290)
GECINA -0.031515 0.066705 * 0.106995 ***
(-1.594517) (1.9283) (4.162084)
GEOPHYSIQUE -0.203811 *** 0.31867 *** 0.542849 ***
(CIE.GL.) (-3.6936) (5.46032) (7.95514)
GUYENNE & -0.093205 *** 0.295859 *** 5.229971 ***
GASCOGNE (-3.5412) (5.2299) (9.67065)
HAVAS -0.09695 *** 0.339519 *** 0.67402 ***
ADVERTISING (-2.61466) (0.33951) (0.148013)
IMERYS -0.061895 * 0.15218 ** 0.50336 ***
(-1.7396) (2.47265) (11.8111)
INGENICO -0.123956 ** 0.313658 *** 3.644360 ***
(-2.445262) (3.644360) (9.32097)
KLEPIERRE -0.03159 0.19420 *** 3.37239 ***
(-1.34771) (3.372390) (3.37239)
LVMH 0.008194 0.15639 *** 0.96279 ***
(0.291506) (3.256624) -30.12817
LAFARGE -0.043708 0.10356 ** 0.854505 ***
(-1.45330) (2.519234) (21.6644)
10 French Adj.[R.sup.2] DW
Stocks
GALERIES 0.0554 0.10181
LAFAYETTE 0
GECINA 0.0106 2.46910
0
GEOPHYSIQUE 0.0853 0.84353
(CIE.GL.) 8
GUYENNE & 0.0795 0.10594
GASCOGNE 5
HAVAS 0.1480 0.96715
ADVERTISING 1
IMERYS 0.0943 0.23268
2
INGENICO 0.0991 0.94313
8
KLEPIERRE 0.0165 0.23177
3
LVMH 0.4028 0.80588
0
LAFARGE 0.2888 0.99198
3
* / ** / *** Significantly different from zero at the 10 / 5 /1 percent
level.
Numbers in parentheses denote asymptotic t-statistics.
Table 2
Empirical results per year
Intercept Slopes on
GALERIES
LAFAYETTE [lambda] [[tau].i] [[beta].i]
Year 1 -0.217154 -0.00526 0.244760 **
(-0.976376) (-0.01304) (2.07467)
Year 2 -0.12197 0.35784 ** -0.06497
(-0.72243) (1.72946) (-0.47800)
Year 3 -0.085895 0.18605 0.2404 **
(-0.83774) (0.96249) (2.01341)
Year 4 0.0644 0.5305 ** 0.5020 ***
(0.56246) (2.40910) (5.0462)
Year 5 -0.25595 ** 0.34661 0.32816 ***
(-2.3066) (1.36143) (2.79015)
Year 6 -0.2177 ** 0.83527 *** 0.39294 ***
(-1.83941) (2.69332) (3.11939)
Year 7 -0.2177 ** 0.83527 *** 0.39294 ***
(-1.839417) (2.69332) (3.11939)
Year 8 0.04807 0.28483 1.15633 ***
(0.25784) (1.15633) (5.22286)
Year 9 -0.04156 0.25814 0.60084 ***
(-0.2408) (1.23043) (4.67749)
Year 10 -0.00157 0.06727 0.421240 ***
(-0.0085) (0.49064) (3.28256)
Adj.[R.sup.2] DW
Year 1 0.00239 2.27924
Year 2 0.00129 2.0358
Year 3 0.01623 2.19486
Year 4 0.09984 2.14788
Year 5 0.03829 2.19477
Year 6 0.06223 1.80927
Year 7 0.06223 1.80927
Year 8 0.09301 2.08766
Year 9 0.08301 1.80820
Year 10 0.04117 2.31233
* / ** / *** Significantly different from zero at the 10 / 5 / 1
percent level. Numbers in parentheses denote asymptotic t-statistics.
Table 3
Empirical results per year
Intercept Slopes on
GECINA [gamma] [[tau].sub.i] [[beta].sub.i]
Year 1 -0.20403 0.00485 -0.05258
(-1.0891) (0.06115) (-0.05258)
Year 2 -0.07107 0.0738 0.0885
(-0.8489) (0.79804) (1.13576)
Year 3 0.016286 0.15764 0.14726 *
(0.1677) (0.53946) (1.75148)
Year 4 -0.13609 -0.04706 0.22330 ***
(-1.4144) (-0.27422) (0.22330)
Year 5 -0.09626 0.00534 0.16433
(-0.09626) (0.02986) (1.56193)
Year 6 0.04055 0.13988 0.15034 **
(0.705970) (0.782624) (1.96966)
Year 7 -0.04730 0.22212 0.21561 ***
(-0.60835) (0.9343) (3.49525)
Year 8 0.04693 0.11586 0.0654
(0.5910) (0.38970) (1.3058)
Year 9 0.00995 0.13685 0.00767
(0.13748) (0.59760) (0.15059)
Year 10 -0.0905 0.11436 0.03503
(-1.2264) (0.38227) (0.75831)
GECINA Adj.[R.sup.2] DW
Year 1 0.0009 2.4441
Year 2 0.0051 2.6332
Year 3 0.00651 2.63272
Year 4 0.0185 2.3952
Year 5 0.00380 2.36445
Year 6 0.0117 2.38100
Year 7 0.07105 2.32289
Year 8 0.00052 2.42501
Year 9 0.00139 2.42668
Year 10 0.00259 2.71691
* / ** / *** Significantly different from zero at the 10 / 5 /1 percent
level.
Numbers in parentheses denote asymptotic t-statistics.