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 makram.bellalah@u-picardie.fr

(b) ESG Group and ESSEC Business School, France aboura@essec.fr

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.