ࡱ>  ~5@ 0Vbjbj22 +XXm 'x"""Ln8+++8+R3$` 4V `?"?6@AVVV#######$3&R( $bcV@Vbb $@A$4t4t4tb( @A#4tb#4t.4tbtJbtA3 rys+kbt#\$0$bt_)q _)bt,_)tV7Z4t\ ^VVV $ $%+sd+Localized competition in the French mutual fund market: Participation costs and performance Linh TRAN DIEU (May 2009) Abstract: The localized competition observed in French mutual fund market leads to important participation costs for investors. This reduces the intensity of performance competition, then gives funds some market power and thus increases the conflict of interest between investors and funds. In this article, we present a model that takes into account these specificities of the French market. Using an address model approach, we show that the performance proposed by funds is lower than their marginal performance corresponding to the management fees paid by investors and the marginal costs of funds performance. The model yields some testable implications. Key words: Localized competition, address model, French mutual fund market, participation costs, performance. Classification JEL: G10, G20, L20, L10 The convex relationship between mutual fund flows and performance found in literature (Ippolito (1992), Chevalier and Elison (1997), Sirri and Tufano (1998), Kempf and Ruenzi (2004)), where the best performing funds obtain great inflows whereas the worst performing funds do not experience outflows, have been explained in different ways. It is intuitive to understand why high performance funds have important inflows. However, it is not easy to understand why low performance ones are not penalized by significant outflows. Lynch and Musto (2003) explain this by the fact that funds replace lost strategies by other ones or merely change managers. Accordingly, past performance cannot predict the perspective of funds any more and investors will thus not reward their money from these funds. Huang, Wei and Yan (2007) explain the fact that low performance funds do not have significant outflows by the presence of participation costs. In fact, the investment decision of investors depends on the difference between expected performance and total costs they have to pay. Consequently, even if they are attracted by high performance funds, they could not freely move money from low performance to higher performance funds. Participation costs defined in their study contain two components: transaction costs and search costs. Before investing in a fund, investors should seek for information about the fund, search costs then represent the costs of collecting and treating information. Huang, Wei and Yan (2007) argue that greater inflows in high performance funds are explained not only by the record performance obtained by these funds, but also by the fact that at this performance level, more investors could exceed participation cost barrier. If performance is always considered as a crucial criterion for investors to evaluate funds, the presence of participation costs can reduce the competition in terms of performance among funds. In the case of the French market, participation costs are even more important due to the specificity of this market. In contrast to the American market, the majority of French funds are created, managed and distributed by banks. In addition, in France, distribution channels are almost integrated in fund families. On one hand, this mode of distribution represents some advantages for investors. In fact, many investors already have a relationship with a bank and thus investing in funds proposed by the bank appears to be simpler than opening a new account in competing families funds. On the other hand, this mode of distribution might sometimes lead to more important search and transaction costs. It could be more costly for investors, being clients of banks, to invest in the competing families funds. Moreover, banks frequently offer some privileged services to investors as long as they invest in their funds. Otten and Schweitzer (2002) mention that in Europe investors seem to value service and convenience at least as much as performance. Korpela and Puttonen (2005), examining the effect of distribution channels on fund flows in the Finnish market which has some similar characteristics in comparison with the French market, show that the existing customer relationship and convenience contribute to high inflows of funds managed by banks. Frey (2001), in her study about American bank funds, demonstrates that banks may attract investors different from those attracted to non-banks. Specifically, she finds evidence that banks may market more to individual investors than to institutional ones. In a larger sense, participation costs borne by investors could be considered as total costs they have to pay once they decide to invest in a fund. Thus, its can contain not only search and transaction costs, but also the disutility of non-usage of all privileged services offered by financial institutions in the case of investing in concurrent families funds. Indeed, clients of a bank, in particular individual investors, tend to invest in funds offered by their company even if these funds generate a modest performance because participation costs of the rival families funds are too important. As a result, in the French market, funds seem to be less competitive in terms of performance. The specificity of the French market could enhance the conflict of interest between investors and funds. In fact, if investors would like funds to maximize risk-adjusted return, the funds objective is to maximize total inflows. Although it is difficult to observe managers actions, investors could control funds in the sense that they could reward their money if funds obtain a low result. However, participation costs do not always allow them to penalize low performance funds by moving their money to higher performance ones. Jondeau and Rockinger (2004) empirically analyze the flow-performance relationship in the case of French mutual funds market. Their results show that investors are not sensitive to the past performance of funds. Thus, they conclude that, in the French market, investors seem to react like passive clients. They explain this by the fact that there exists a bank bias effect, issued to the specificity of the French market, in which investors do not sufficiently diversify across banks funds. Additionally, a part of management fees might not serve to get information in order to maximize risk-adjusted return of funds, but is used to attract new investors, such as marketing activities or expenses for brokers. This also can lead to a conflict of interest between investors and managers. Sirri and Tufano (1998), Jain and Wu (2000), Khorana and Servaes (2004) and Pagani (2006) argue that an increase in marketing expenses could reduce search costs for potential investors and, thus, attract more clients for funds. Of course, these expenses are not usually desired by existing investors, who would like funds to focus on performance activities. Consequently this might create another sort of interest conflict between investors and funds. The French mutual fund market strengthens this type of conflict because funds can easily pursue this practice since distribution channels are often integrated in the family. Using an original approach, particularly address model, in which funds differ not only in terms of performance but also in participation costs, this article presents a theoretical model where funds determine their performance level according to the management fees paid by investors and costs borne by funds for performance services. We show that performance produced by funds could be inferior to the marginal performance required because participation costs give funds some market power. This model describes French mutual fund market, in which participation costs are higher, the competition in performance would then be less intensive, consequently funds could exercise their market power by lowering performance without losing their market share. Participation costs considered in this model are slightly different from those in Huang, Wei and Yans (2006) model. They contain not only search and transaction costs but also the disutility of non-usage of all privileged services offered by banks to their own clients. This could also be characterized as the total costs borne by investors to transfer cash from one financial institution to another one. Massa (2003a, 2003b) argue that fund families, in the American market, try to reduce competition intensity by changing their structure. Precisely, fund families choose either to increase product differentiation in order to reduce performance competition intensity or to focus on performance services if their performance is not too low in comparison with their rivals. In other words, in the American case, funds would intervene in the performance competition intensity. In the French situation, the market specificities make performance competition naturally less intensive, funds would thus take this advantage and propose a relatively lower performance level. The rest of the paper is organized as follows. In section I, we present a general address approach. This section reports some characteristics in which market competition might be considered as a localized competition. Also we bring up the link between localized competition and the French mutual fund market. Section II explains the construction of the model, where a symmetric equilibrium is presented. The address approach is used to construct mutual fund demand side. A symmetric equilibrium performance will be determined as a solution of fund profits maximization. The conditions of the existence of such a symmetric equilibrium are examined in section III. Section IV analyzes proprieties of the long-run equilibrium in comparison with the welfare optimum. Some direct empirical issues are presented in section V. Finally, we conclude with some principal results of the model. I. Address model and localized competition approach. This section presents the link between French mutual fund market and localized competition. A brief introduction of localized competition and address model is also brought up. Competition in mutual fund industry is a particular case of product differentiation competition studied in industrial economies, where there exist two principal approaches: non-localized competition (Chamberlin (1933)) and localized competition (Kaldo (1935)). Chamberlinian approach suggests that a product is in competition with all other products in market. If products are homogeneous, the difference between two products is their price. Competition determines then the equilibrium price (Bertrand model). Kaldor (1935) argues that a product is in more intensive competition with its closer" products, rather than with all other products in the market. Indeed, competition is, in this case, considered as localized. A classical example of localized competition is the competition among supermarkets. A consumer would choose a supermarket which not only offers various types of products with reasonable prices, but also because it is close to his home, given the transportation costs. Thus, a consumer might prefer a proximity supermarket which proposes products even with a relatively superior price to a further supermarket because of transportation costs. This proximity supermarket is then in direct competition with other supermarkets localized in the same area. The above example highlights the concept of localized competition. The specificities of French mutual fund market explained in the introduction refer to some characteristics of localized competition. Participation costs mentioned in mutual fund competition could be considered as transportation costs in the case of supermarket competition. Yet, in the case of mutual fund market, the term localized should not be related to the geographic area. Instead, it could be simply understood that investors seem to be attracted by funds proposed by their banks. Localized competition of the French mutual fund market presents especially in the case of individual investors, who have, in general, more important search and transaction costs relatively to institutional ones. Thus, being clients of banks, they tend to invest in funds offered by their banks, unless funds proposed by competing families generate a record performance. This rejoins the argument proposed by Huang, Wei and Yan (2007). An address model is frequently used to explain demand side in localized competition. It is defined as one in which both commodities and consumers can be described by a particular point, or address, in a characteristics space. In the case of mutual fund market, funds can be considered like substitute products that are different in many characteristics such as investment categories, risk level, fund family. Then, each fund has its own address determined by these characteristics. The address of an investor is an optimal point determined by funds characteristics. In this article, we are only interested in one dimension of funds characteristics, participation costs. Thus, funds are assumed to be homogenous in all characteristics, but participation costs. Let us take a simple example, in which two funds are assumed homogenous in all characteristics but are offered by two different banks (A and B). An investor, who is a client of bank A, is a priori closer to the fund offered by bank A than the one proposed by bank B. The address of the investor is then closer to the address of the fund of bank A than the one of the fund offered by bank B. Participation costs are considered as transportation costs borne by investors to go to funds address. Shorter is the distance between investors address and funds address, lower are the participation costs. If two funds are homogenous, then investors will prefer the closest fund, provided that the difference between two performance levels does not matter. Hotellings model is a type of address model that is often used to explain demand side in localized competition. In this model, commodities and consumers are supposed to be distributed in a circle. For commodity, the distance between two variants is assumed to be equal and consumers are supposed to be uniformly distributed in the same circle. Consumers choose a variant according to the difference between price and transportation costs. It is demonstrated that a variant is in competition with at most two other variants. Transportation costs are often in quadratic form of the distance between the consumers address and the variants one. Mathematically, this is the square of the Euclidean distance between the consumers ideal point and the location of the variant. In this paper, we adopt a simple version of circle model and a more general form of transportation costs to model the demand side of mutual fund market. II. The Model Participation costs would reduce the intensity of competition in terms of performance among funds. The flow-performance relationship mentioned in literature suggests that even modest performance funds could maintain their market share. This produces some market power for funds and increases the conflict of interest between investors and managers. Theoretically, funds have to generate a marginal performance corresponding to management fees, paid by investors and marginal costs supported by funds. However, in the presence of participation costs, funds might use a part of management fees to cover commercialisation activities in order to attract new investors and thus produce an inferior performance without having market loss. In this model, we try to determine a symmetric equilibrium performance chosen by funds in the situation where participation costs are not negligible. For this, we first describe demand and offer sides, symmetric equilibrium performance will then be determined by the maximization of funds profit. A. Demand side The address model approach is utilized to model investors demand for mutual funds. Some assumptions are necessary for the construction of mutual fund demand side in an address model. Assumption 1: We assume that funds are homogenous in all characteristics but participation costs. Thus, the investment decision of investors depends on the difference between expected performance and participation costs. Assumption 2: For commodity, it is assumed that funds are equally localized on a straight line, the distance between two funds is equal to L. The distance among funds is not a geographical distance, it can rather be interpreted as a difference in participation costs of funds. Recall that, for a given fund, participation costs vary across investors (i.e. individual investors bear more participation costs than institutional ones). For a given performance level, investors would invest in the closest funds. The distance between two funds is assumed to be exogenous. This hypothesis will be relaxed later when socially optimal equilibrium is compared with the free-entry optimum.  Assumption 3: Investors are assumed to be uniformly distributed on the same line with a density, noted by a. This assumption does not mean that all clients of a financial institution have the same localization. In fact, different clients of a given bank, for example, could have a different distance relative to the fund proposed by the bank. The localization of investors depends on many characteristics of investors such as: the degree of financial sophistication of investors. Thus, ceteris paribus, the address of a sophisticated investor is different from that of a nave investor even though both of them are clients of the same financial institution. Assumption 4: It is also assumed that each investor invests only in a fund with an identical amount normalized to 1. Since the decision of investors depends on the difference between anticipated performance and participation costs, a marginal investor is indifferent between fund i and fund (i+1) if the following equation is satisfied:  EMBED Equation.3  (1) Where  EMBED Equation.3  is the expected performance of fund i. It is assumed that investors use past performance to anticipate the performance of funds. Participation costs of this marginal investor when she invests in fund i is  EMBED Equation.3 . We utilized a general form of transportation costs proposed by Anderson, De Palma and Thisse (1994), in which  EMBED Equation.3 is the location of the investor,  EMBED Equation.3 is the location of fund i. Hence,  EMBED Equation.3  is the distance between the investor and fund i. We assume that  EMBED Equation.3  so that participation costs are convex. Other things equal, an investor, who is a client of a bank, is a priori closer to funds proposed by his bank than competing families funds. Hence, the convexity of participation cost function would imply that it is very costly for investors to move from a financial institution to other ones. The parameter of participation cost intensity, EMBED Equation.3 , is supposed to be positive. The greater is EMBED Equation.3 , the higher are participation costs. It is obvious that all investors located between  EMBED Equation.3  and  EMBED Equation.3  will invest in fund i. Analogously, a marginal investor, who is indifferent between fund i and fund (i-1), has a location  EMBED Equation.3  satisfying:  EMBED Equation.3  (2) All investors located between  EMBED Equation.3  and  EMBED Equation.3 will invest in fund i. We will demonstrate later that a fund is in competition with at most two other funds. Thus, the demand of fund i contains all investors located between  EMBED Equation.3  and EMBED Equation.3 . Finally, demand of fund i is determined as follow:  EMBED Equation.3  (3) Where  EMBED Equation.3  and  EMBED Equation.3  are respectively determined by equation (1) and (2). B. Supply side Fund is profits are determined as:  EMBED Equation.3  (4) Where  EMBED Equation.3 are management fees,  EMBED Equation.3  are load fees,  EMBED Equation.3 is the marginal cost of non- performance services, such as expenses for the functioning of funds or commercial activities,  EMBED Equation.3 is the marginal cost of fund i to generate one level of performance. Finally, K is fixed costs. In general, management fees are in percentage of asset under management. Theoretically, management fees are used not only to cover the costs of performance services, but also to guarantee the functioning of funds. Accordingly, a part of management fees could serve to pay for non-performance services such as conservation of actions, publication of asset value, accountancy, audit. The functioning expenses can represent more than 50% of management fees declared by funds. Other expenses that are not related to funds operation like the remuneration of distribution channels or expenses for marketing activities are also partially financed by management fees. Thus this could violate the principle of fees equality across shareholders and increase the conflict of interest between investors and funds. It means that money of existing investors must not serve to pay for new investors (e.g. expenses for marketing activities may reduce search costs for new investors). Knuutila, Puttonen and Smythe (2006) find an important effect of distribution channels on the inflows of the Finnish mutual fund market. They show that for funds distributed by bank channels, investors seem not to react to past performance. Thus, instead of focusing on performance services, funds could have incentives to spend for commercial activities. Such a situation especially reflects the specificities of the French market, in which many fund families are subsidiaries of banks, which in turn charge to distribute funds. Theoretically, load fees must cover costs incurred in the reconstruction of the fund portfolio, issued to redeeming or purchasing fund shares, and partially finance distribution channels. C. Symmetric equilibrium performance Equilibrium performance is a resolution of a non-cooperative game. A pure strategy of each fund is its performance level, funds payoff is their profits determined by equation (4). In equilibrium, each fund chooses its performance level in order to maximize its profits given the performance levels chosen by other funds. However, we aim to find only a symmetric Nash equilibrium where each fund chooses the same performance level and the performance chosen by a fund is the best reply to the performance proposed by other funds. The conditions of the existence of such an equilibrium will be presented in the next section. In this section, we suppose the existence of such a symmetric equilibrium and then solve for the equilibrium performance. Each fund solves the following program :  EMBED Equation.3  (5) With  EMBED Equation.3  Proposition 1: A symmetric equilibrium performance of funds is determined as:  EMBED Equation.3  (6) Proof: see Appendix A. The proposition 1 leads directly to the proposition 2. Proposition 2: Since  EMBED Equation.3 , the equilibrium performance, EMBED Equation.3 , is always inferior to the marginal performance of funds,  EMBED Equation.3 . The symmetric equilibrium performance determined by equation (6) shows that the performance level chosen by funds depends on two principal sources: marginal performance (which is equal to EMBED Equation.3 ) and participation cost term (reflected in EMBED Equation.3 ). Intuitively, in the presence of participation costs, funds could propose an equilibrium performance inferior to their marginal performance without losing their market share. This suggests that participation costs strengthen the market power of funds and weaken the competition among funds. The first term of the right-hand side of equation (6) suggests that performance increases with net expenses for performance service, EMBED Equation.3 . Accordingly, a fund that charges significant management fees, does not necessarily generate high performance since a part of management fees is used to finance non- performance services. The higher are the expenses for non-performance services, the lower is the equilibrium performance. If some expenses for non- performance services are essential for the functioning of funds, commercial activity expenses, on the other hand, are not always desired by existing investors. However, it is not easy for investors to verify whether funds use correctly management fees. If in the case of the American market, funds have to declare their percentage of expenses transferred to distribution channels, in France, this information is not always accessible for investors. In contrast, the equilibrium performance of funds decreases with the marginal costs to produce one level of performance. High marginal costs mean that performance services become more expensive, thus funds have to either reduce their performance level, or increase management fees. Both ways are not desired by investors and could lead to a market loss for funds. Nevertheless, it is not easy to measure marginal costs of funds. In reality, the marginal costs of funds performance might depend on many characteristics of funds. For instance, performance costs can be different according to investment categories of funds, the ability of fund managers or the size of fund families. In general, funds belonging to big families, might take advantages of economies of scale or learning by doing to reduce the costs of their performance. As a result, these funds could offer higher performance to investors without reducing expenses for non-performance services. The second term of the right-hand side of equation (6) implies that funds can reduce their performance inferior to their marginal performance thanks to participation costs. The greater is the distance among funds (L), the lower is the equilibrium performance. Intuitively, if switching costs from a financial institution to another one are high, investors will not want to move their money. Therefore, funds would take advantage of the situation to lower their performance. On the contrary, when L tends to 0, it means that funds are so similar in terms of participation costs, the competition in performance thus becomes more intensive. Consequently, funds must produce a performance level close to the marginal one if they do not want to lose their market share. Performance decreases also with the intensity of participation costs ( EMBED Equation.3 ) and the degree of convexity of participation cost function ( EMBED Equation.3 ). The effect of these parameters is similar to the one generated by the distance. To sum up, when participation costs are not negligible, funds can under-perform without losing their market share. III. Existence of symmetric equilibrium In this section, we examine conditions for the existence of such a symmetric equilibrium. The method used for analyzing the existence of equilibrium performance is similar to the one used in a classical address model (See Anderson, De Palma and Thisse (1994)). First, we demonstrate that a fund is in direct competition with at most two funds. Second, we determine the interval of fund is equilibrium performance. Finally, we determine the equilibrium strategy chosen by fund i. If  EMBED Equation.3  is the unique best response of fund i for  EMBED Equation.3 chosen by other funds, we can conclude that the symmetric Nash equilibrium exits. It is obvious that a fund does not want to produce a performance level superior to its marginal one,  EMBED Equation.3 , because in this case it will generate negative profits. Indeed, we can demonstrate a classical result of an address model, translated in our model as below: Proposition 3: A fund does not have incentives to take all market share of its two closest neighbors. In other words, a fund is in direct competition with at most two funds. Proof: See Appendix B Moreover, we can determine the interval of the equilibrium performance proposed by fund i. Our intuition is that a fund could not freely reduce their performance inferior to a certain level without losing their market share even though participation costs are important. Similarly, a fund would not like to raise significantly their performance to attract clients of other funds because profits made by an increased market share would be inferior to expenses for a supplementary performance level. Proposition 4: The best reply performance chosen by fund i given that all other funds choose  EMBED Equation.3  must belong to  EMBED Equation.3 . Proof: See Appendix C For each level of performance proposed by fund i, there exists only one position of a marginal investor, who is indifferent between fund i and (i-1). Therefore, determining  EMBED Equation.3  is equivalent to determining the position of this marginal investor. Consider the distance between the marginal investor and fund i,  EMBED Equation.3 . From the proposition (4),  EMBED Equation.3 , the marginal investor must locate between fund i and fund (i-1), thus  EMBED Equation.3  and  EMBED Equation.3 . Proposition 5: The position of the marginal investor determines all the roots of the  EMBED Equation.3  in [0,1]:  EMBED Equation.3  (7) Proof: See Appendix D. It is obvious that the position of the marginal investor only depends on the degree of the convexity of participation cost function, EMBED Equation.3 . Moreover, it follows that h = 0.5 is a root of  EMBED Equation.3 , which means that there exists a marginal investor located exactly at the middle between fund i and fund (i-1). This implies directly that  EMBED Equation.3 is one of the best responses of fund i to  EMBED Equation.3  chosen by other funds. However, it might not be the unique best reply of fund i since  EMBED Equation.3  can have more than one solution. Thus, the existence of the symmetric Nash equilibrium depends on the condition at which EMBED Equation.3  has a unique root in [0,1]. The detail of this analyze is presented in the appendix E, we summarize here principal results. Proposition 6: For EMBED Equation.3   EMBED Equation.3 has an unique root, h=0.5, this means that the symmetric Nash equilibrium exists. For  EMBED Equation.3 ,  EMBED Equation.3  has at least two solutions, consequently  EMBED Equation.3 is not the only best reply of fund i to EMBED Equation.3  chosen by other funds. In other words, such a symmetric equilibrium does not exist. Intuitively, for sufficiently high value of EMBED Equation.3 , participation costs become too expensive for investors. Consequently, a fund could lower their performance under the equilibrium performance without reducing much its demand. IV. Long-run vs. welfare optimum equilibrium In this section, we characterize the long-run equilibrium in comparison with the welfare optimum. So far the distance between two funds has been exogenous. In this section, L is endogenously determined in the long-run equilibrium and in the welfare optimum. Precisely, we compare the long-run distance between two funds with the socially optimum. This allows us to better understand the behavior of funds in long term. Indeed, in the long run equilibrium, funds would entry in the market until their profits equal to zero. The socially optimal distance between two funds is obtained by minimizing the total resource cost borne by investors and funds. The total costs are determined as:  EMBED Equation.3  (8) The first two terms of the right-hand side of equation (8) are the costs borne by fund i. The last term is the participation costs of investors. Since in the symmetric equilibrium, the demand of fund i is aL,  EMBED Equation.3  is the variable costs. As investors will invest in their closest fund and there are aL/2 investors, located between fund i and fund (i-1) will invest in fund i, the participation costs born by these investors are:  EMBED Equation.3 , where x is the distance between an investor and fund i. By symmetry, the participation costs of aL/2 investors located between fund i and fund (i+1) are  EMBED Equation.3 . Accordingly, the total participation costs of investors are  EMBED Equation.3 . Per unit of market area, the total resource cost, which we denote by EMBED Equation.3 , is:  EMBED Equation.3  (9) Using  EMBED Equation.3  from equation (6) in (9), we get:  EMBED Equation.3  (10) The first order condition:  EMBED Equation.3  The socially optimal distance between two funds is thus:  EMBED Equation.3  (11) In the long-run equilibrium with free-entry, funds generate a zero profit:  EMBED Equation.3  The distance between two funds in the long-run equilibrium,  EMBED Equation.3 , is:  EMBED Equation.3  (12) The distance among funds in the long-run equilibrium increases with the fixed costs of funds and decreases with the marginal costs of performance and the parameters of participation costs. In fact, if fixed costs are significant, the number of funds offered to investors would be smaller and the distance among funds would be greater. Consequently, the competition in terms of performance is less intensive. On the contrary, a low marginal cost of performance enhances the competition in performance among funds. Since no funds would like to compete in performance, they try to maintain their market power by keeping a sufficiently high distance from each other. Similarly, the density of investors reduces the long-run distance. In fact, when the market size increases, more funds would be offered to investors. Let us now compare the long-run equilibrium distance with the welfare optimal one. From (11) and (12) we have:  EMBED Equation.3  (13) It follows that  EMBED Equation.3 . It leads straight forward to the following proposition. Proposition 7: The long-run equilibrium distance is greater than the welfare optimal one if  EMBED Equation.3 . Intuitively, if marginal costs of performance services are sufficiently low given the power of participation costs, EMBED Equation.3 , it is less expensive to produce performance. Therefore, funds would have more incentive to generate higher performance, as a result it would strengthen the competition in performance. In order to maintain the market power, funds would keep their distance above the welfare optimum level. From (13) we have:  EMBED Equation.3 . (14) It follows that the right-hand side of equation (14) is a decreasing function of  EMBED Equation.3  . For EMBED Equation.3  sufficiently great so that  EMBED Equation.3 is inferior to 1, the long-run equilibrium distance could decrease to the level below the social optimum. Intuitively, when participation cost power,  EMBED Equation.3 , is too high, the participation barriers become very important so that even with a small distance among funds, they could still keep their market power. Consequently, funds could reduce the distance below the welfare optimum level without raising the intensity of performance competition. V. Empirical implications In this section, we discuss some of the models empirical implications: Implication 1: The role of participation costs in investors decision could be empirically analyzed in the sense that individual investors, who have relatively more important participation costs, would less actively react to performance. The model presented in this paper describes especially the situation in which it is very costly for investors, being clients of banks, to invest in competing families funds. Jondeau and Rockinger (2004), cited in the introduction, have empirically analyzed the response of investors to past performance in the French mutual fund market. They show that investors seem not to be sensitive to past performance of funds and conclude that investors react like passive clients. In contrast to individual investors, institutional investors, who have relatively smaller participation costs, can react more actively to past performance of funds. Del Guercio and Tkac (2002) note that in the case of pension fund market, where most clients are institutional investors, poor performance funds are punished by significant outflows. Implication 2: Do funds managed by banks under-perform in comparison with non-bank funds? Theoretically, bank funds have relatively more market power than non-bank funds, which allows them to reduce their performance without losing their market shares. However, some empirical results from the U.S market as well as the European market are quite mixed. For instance, Frye (2001) shows that in the American market, bank managed mutual funds do not under-perform relative to non-bank funds. Whereas, Korkeamaki and Smythe (2004), in their study on the Finnish market, find that bank managed funds charge higher expenses but investors are not compensated with higher risk-adjusted returns. Implication 3: Investors might tend to switch from funds to others belonging to the same family rather than moving their money to competing families, because of high participation barrier. Yet, this implication is not easy to empirically verify since we do not always have access to data in which each movement of investors is observed. Instead, previous studies deal with this question by verifying whether high performance funds of a family can experience more inflows (Kempf and Ruenzi (2004), Jondeau and Rockinger (2004)). However, this method sometimes leads to some biased conclusions since the best performing funds of a family are often stars of market. Consequently, inflows in these funds are usually issued not only from existing investors of the family but also from clients of competing families as record performance allows these investors pass participation barrier. Additionally, Massa (2003a) suggests that each family responds to investors heterogeneity by offering various types of funds. It allows the family to avoid moving money into rival families. Implication 4: The performance mark-up of funds, defined as the difference between the performance generated by funds and their marginal performance, can be different with respect to client types. We can imagine that funds which serve individual investors could have a larger performance mark-up than institutional funds, as individual investors bear higher participation costs than institutional ones. However, performance mark-up is not easy to calculate, it might be more convenient to simply compare performance across funds. Yet, the empirical evidence on this issue needs to be interpreted with some care because institutional funds often have lower marginal costs thanks to economies of scale, so higher absolute performance of institutional funds might be a result of their lower marginal costs due to economies of scale. Implication 5: Funds market power may lead to, ceteris paribus, relatively inferior average performance in French in comparison with the American market. However, it would be complex to verify and interpret this implication because funds are considered in different context. Instead, previous studies have tried to verify whether funds could beat the market. In the American market, Grinblatt and Titman (1992), Ibbotson and Goetzmann (1994) and Brown and Goetzmann (1995) find an evidence of winner repetition. On the contrary, Bergeruc (2001), Aftalion (2001) and De Marchi (2006) show that French mutual funds do not generate results superior to market return. Implication 6: Ceteris paribus, funds charging high management fees should generate high performance. This implication follows directly from equation (6). Implication 7: Given an amount of net expenses on performance activities, different funds might produce different performance; this depends on the marginal costs of funds performance. How to understand the marginal costs of funds performance? On one hand, the marginal costs of performance can depend on the ability of funds managers. Funds that are managed by experience and competent managers could invest more efficiently and thus obtain high performance. On the other hand, the marginal costs of performance could depend on funds characteristics like size of the family, size of funds, or the investment specialty of family. For instance, funds that belong to a big family might have relatively lower marginal costs thanks to economies of scale. Accordingly, they could offer higher performance without imposing greater management fees. Implication 8: The principal-agent problem could be empirically analyzed in the sense that management fees could not be properly used by funds. In fact, funds might spend an sufficient amount on commercial activities in order to experience more inflows even if it leads to modest performance. Gruber (1996) and Cahart (1997) show that higher expenses are associated with inferior rather than superior management. As a result, investors should compare net management expenses for performance activities across funds rather than gross management fees. Implication 9: Even though investors are interested in price-quality, performance still plays a crucial role in their decision. Fund families could use it as a commercial argument by reducing management fees of certain funds so that these funds could display high performance, which is, in reality, calculated after subtracting management fees from gross result of funds. Moreover, fund families might sometimes use fees collected by a fund to finance other funds activities. This cross-fund subsidization strategy allows the family to have some flagship funds which can attract more attention of investors. Guedj and Papastaikoudi (2005) and Gaspar, Massa and Matos (2006) argue that families strategically transfer performance across member funds to favour those that are more likely to increase overall family profits. VI. Discussion and Conclusion This model has been developed to describe the specificities of the French mutual fund market. These specificities are reflected in the fact that French funds have relatively more market power, due to higher participation costs borne by investors. This allows funds to lower their performance below their marginal level without being penalized. In this model, we adopt an original approach, the address model, to explain the demand of funds. This allows us to take into account the characteristic of localized competition in the French market. Finally, this model may also be applied in some European markets like Spain or Finland, where mutual fund distribution channels are dominated by banks. This model describes a situation, in which, being clients of a financial institution, it is very costly for investors to invest in competing families funds. What happen with investors who would like to invest in mutual funds but they are not clients of any banks or they have different accounts in different financial institutions? How can we place these types of investors in the localized competition? For instance, Huang, Wei and Yan (2007) distinguish two types of investors: new investors, who never invest in the fund considered and existing investors, who already hold their shares in the fund. The latter type is assumed to incur lower search costs than new investors do. Nevertheless, this distinction is not necessary in our model because it is supposed that investors are able to compare their participation costs once they decide to invest in funds. Therefore, investors could feel closer to certain funds than others. Indeed, the decision of investors always depends on the difference between anticipated performance and participation costs. Appendix A We will determine the symmetric equilibrium performance  EMBED Equation.3 . Let us suppose that all funds but i choose the same performance level  EMBED Equation.3 . The marginal investor located at EMBED Equation.3  is indifferent between fund i and fund (i-1) if  EMBED Equation.3  is a solution of equation (2) rewritten as:  EMBED Equation.3  Take the total derivative of the above equation ( EMBED Equation.3 fixed):  EMBED Equation.3  The above equation leads straight forward to:  EMBED Equation.3  (A.1) Moreover, by symmetry, we have  EMBED Equation.3 . The demand of fund i is then equal to:  EMBED Equation.3  The profit of fund i is as follow:  EMBED Equation.3  Assume that the second order condition is satisfied, the first order condition leads to:  EMBED Equation.3  (A.2) A symmetric equilibrium in which fund i generating the same performance level,  EMBED Equation.3 , implies that  EMBED Equation.3 . It means that the marginal investor is located exactly in the middle between fund i and fund (i-1). This leads to:  EMBED Equation.3  (A.3) By plugging (A.1) and (A.3) into (A.2), we have:  EMBED Equation.3  (A.4) Solving directly for  EMBED Equation.3  from equation (A.4) leads to:  EMBED Equation.3  % Appendix B We will show that a fund is in competition with at most two funds. In fact, to take all market shares of two neighboring funds, fund i must propose a performance at least equal to:  EMBED Equation.3  (B.1)  At this performance level, the furthest investor (A) of fund (i-1), located in the middle between fund (i-2) and fund (i-1), is indifferent between fund i and fund (i-1). We can verify that this performance is higher than marginal performance. By plugging  EMBED Equation.3  from equation (6) into equation (B.1), we will demonstrate that:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  (B.2) The equation (B.2) is always hold for  EMBED Equation.3   % Appendix C We will demonstrate that the equilibrium performance of fund i,  EMBED Equation.3 , should belong to the following interval  EMBED Equation.3 . If fund i chooses a performance inferior to  EMBED Equation.3 , it will have a zero demand since the closest investors of the fund, locating at the same point of the fund, would like to invest in one of two neighboring funds (fund (i-1) or (i+1)) as performance proposed by fund i is too low. As a result, fund i should propose a performance  EMBED Equation.3 . Now let us show that fund i does not want to increase its performance superior to  EMBED Equation.3 since in this case it will generate a profit lower than the profit obtained if it chooses  EMBED Equation.3 . Intuitively,  EMBED Equation.3  is the performance level, at which fund i could certainly attract all investors located between fund (i-1) and fund (i+1). If fund i proposes a performance superior to  EMBED Equation.3 , the maximum market share that fund i could obtain are 3La, while its performance has to be at least equal to EMBED Equation.3 . The maximum profit generated in this case is:  EMBED Equation.3  (C.1) We show that this profit is lower than the profit generated with  EMBED Equation.3 , which is equal to:  EMBED Equation.3  (C.2) Using (6), (C.1) and (C.2), we can calculate the difference between two profits:  EMBED Equation.3  We have  EMBED Equation.3 since  EMBED Equation.3  for  EMBED Equation.3  . Finally, the best reply performance of fund i, EMBED Equation.3 , to EMBED Equation.3 chosen by other funds should belong to EMBED Equation.3 . % Appendix D From (A.1) and (A.2):  EMBED Equation.3  (D.1) Moreover, a marginal investor is indifferent between fund i and fund (i-1) if the following equation is hold:  EMBED Equation.3   EMBED Equation.3  Replacing  EMBED Equation.3 in equation (D.1) and eliminating  EMBED Equation.3  in the two hands of the above equation we have:  EMBED Equation.3  (D.2) Recall that  EMBED Equation.3  and  EMBED Equation.3 . From (D.2), we have:  EMBED Equation.3  (D.3) Set  EMBED Equation.3 . Thus, determining the best reply performance of fund i is equivalent to determine all the roots of  EMBED Equation.3  in [0,1]. % Appendix E Let analyze numerically the below function:  EMBED Equation.3  with  EMBED Equation.3  and  EMBED Equation.3  It is easy to find that h=0.5 is a solution of the function H(h)=0. Plot the function H(h) for different values of beta with 2-11 step (The below figure illustrates the function H(h) for some values of EMBED Equation.3 ). We can find that for  EMBED Equation.3 , H(h)=0 has only a solution h=0.5. For  EMBED Equation.3 , H(h)=0 has more than one solution. We will try to find  EMBED Equation.3 at which H(h)=0 has more than one turning point. Beside, we have EMBED Equation.3  for all  EMBED Equation.3  and  EMBED Equation.3 . Then, if the function has more than one solution, there must be a solution that belongs to (0, 1/2). Moreover,  EMBED Equation.3  for all positive values of beta, thus EMBED Equation.3  is the value at which there exist a value  EMBED Equation.3  satisfying  EMBED Equation.3  since if  EMBED Equation.3  there always exists a solution belonging to (0,1/2). Programming with Matlab, we obtain EMBED Equation.3  equal to 5,9688. We can thus conclude that for EMBED Equation.3  superior or equal to 5,9688 the function H(h)=0 has at least two solution. For EMBED Equation.3  inferior to 5,9688, H(h)=0 has only one solution h=0.5.  Figure: Function H(h) for some values of  EMBED Equation.3  Reference Aftalion A, 2001, Les performances des OPCVM actions franaises, Banque & March. Anderson, S., de Palma A., & Thisse J.-F.,1994, Discrete Choice Theory of Product Differentiation, The MIT Press, (423p) Berk, J. and Green, R., 2004, "Mutual Fund Flows and Performance in Rational Markets" Journal of Political Economy, 112, 1269-1295. Brown, S.J. and Goetzmann, W.N., 1995, Performance Persistence, Journal of Finance, vol 50, 679-698. Carhart, M.M., 1997, On Persistence in Mutual Fund Performance, Journal of Finance, Vol 52, No 1, p 57 82. Chevalier Judith A. and Ellison,Glenn D., 1997, Risk Taking by Mutual Funds as a Response to Incentives, The Journal of Political Economy, vol 105, No 6. COB Bulletin October, 2002. De Marchi R., 2006, La persistance des performances des OPCVM actions franaises, Banque & March Del Guercio, D and P. Tkac, 2002, The determinants of the flows of funds of Managed Portfolio: Mutual funds vs Pension Funds, Journal of Financial and Quantitative Analysis 37, 523-558. Frye M,B., 2001, The Performance of Bank-managed mutual funds, Journal of Financial Research, Vol 26, No 3, p 419-442. Gaspar J,M., Massa M. and Matos P., 2006, Favoritism in Mutual Fund Families? Evidence on Strategic Cross-Fund Subsidization, Journal of Finance, 73 p104. Javier G,B., 2003, The Black Box of Mutual Fund Fees, Working paper, Universidal del Pais Vasco. Grinblatt, M. and Titman S., 1992, The Persistence of Mutual Fund Performance, Journal of Finance, vol 47, 1977-1984. Gruber, M.J., 1996, Another Puzzle: The Growth in Actively Managed Mutual Funds, Journal of Finance, Vol 51, No 3, p 783-810. Guedj I and Papastaikoudi, 2005, Can Mutual Fund Families Affect the Performance of Their Funds?, Working paper,  HYPERLINK "JavaScript:WinOpen(523041);" EFMA 2004 Basel Meetings Paper. Huang J, Wei K,D. and Yan H., 2007, Participation Costs and the Sensitivity of Fund Flows to Past Performance, Journal of Finance, p1273-1311. Ippolito R,A., 1992, Consumer Reaction to Measures of Poor Quality: Evidence from the Mutual Fund Industry, Journal of Law and Economic, vol 35, No 1. Jain, P.C. and Wu, J.S., 2002, Truth in Mutual Fund Advertising: Evidence on Future Performance and Fund Flows, Journal of Finance, Vol 55, No 2, p 937-958. Jondeau E. and M. Rockinger, 2004, The Bank Bias: Segmentation of French Fund families, Notes dEtudes et de Recherches de la Banque de France n107. Kempf A and Ruenzi S., 2004, Family Matters: The Performance Flow Relationship in the Mutual Fund Industry, Working paper, EFMA 2004 Basel Meetings Paper. Khorana A and Servaes H, 2004, Competition and Conflicts of Interest the U.S. Mutual Fund Industry, Working paper, Georgia Institute of Technology. Knuutila, M., Puttonen, Vesa. and Smythe Tom., 2006, The Effect of Distribution Channels on Mutual Fund Flows, Journal of Financial Services Marketing. Korkeamaki, T. and Smythe, T., 2004, An empirical analysis of Finnish mutual fund expenses and returns, European Financial Management, Vol 10, No 3, p 413-438 Korpela, M. and Puttonen, Vesa., 2005, Mutual Fund Expenses: Evidence on the Effect of Distribution Channels, Journal of Financial Services Marketing, vol 11, No 1, p 17-29. Laurent Bergeruc, 2001, La mesure de la performance des OPCVM actions franaises: le phnomne de persistance, Banque & March, N 50, 23-38. Lynch and Musto, 2003, How Investors Interpret past Fund Returns, Journal of Finance, vol 58, No 5. Massa. M, 2003(a), How do Family Strategies Affect Fund Performance? When Performance maximization is not the Only Game in Town, Journal of Financial Economics, 249-304. Massa. M, 2003(b), Why so many mutual funds? Mutual fund families, market segmentation and financial performance, Working paper, INSEAD. McDonald. J., 1973, French Mutual Fund Performance: Evaluation of Internationally-Diversified Portfolios, Journal of Finance, 28, 1161-1180. Nanda  HYPERLINK "http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=17302" \o "View other papers by this author" \t "_blank" V,K., Wang  HYPERLINK "http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=255347" \o "View other papers by this author" \t "_blank" Z,J and Zheng L., 2003, Family values and the Star Phenomenon, Working paper,  HYPERLINK "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=254626" \l "#" AFA 2003 Washington, DC Meetings. Otten, R and D. Bams., 2002, European Mutual Fund Performance, European Financial Management, 8, 75-101. Otten, R. and Schweitzer, M., 2002, A Comparison between the European and the U.S Mutual Fund Industry, Managerial Finance, Vol 28, No 1, p 14-35. Pagani M., 2006, The Determinants of the Convexity in the Flow-Performance Relationship, Working Paper, San Jos State University. Sawicki, J, 2000, Investors Response to the Performance of Professional Mutual Managers: Evidence from the Australian Funds Wholesale Market, Australian Journal of Management 25, 47-67. Sawicki, J, 2001, Investors Differential Response to Managed Fund Performance, Journal of Financial Research 24, 367-384. Sirri, E., Tufano, P, 1998, Costly Search and Mutual Fund Flows, Journal of Finance, Vol 53, No 5. I thank Bellando Raphalle, Fontaine Patrick, Gallais-Hamonno Georges, Pollin Jean-Paul, Yusupov  HYPERLINK "javascript:popup_imp('/horde_per/horde/imp/compose.php',800,650,'to=Nurmukhammad+Yusupov+%3Cnyusupov%40audencia.com%3E&thismailbox=INBOX');" Nurmukhammad  for helpful comments. Laboratoire dEconomie dOrlans. Facult de Droit, dEconomie et de Gestion. Rue de Blois, BP 6739, 45067 Orlans Cedex 2. Mail:  HYPERLINK "mailto:linh.tran-dieu@univ-orleans.fr" linh.tran-dieu@univ-orleans.fr  For an investor, search costs are often different across funds, for example, a fund that has important marketing activities could relatively reduce search costs for investors. Analogously, for a fund, search costs can be different across investors, it depends on investors financial sophisticated degree. In general, search costs are relatively less important for institutional investors than for individual ones.  82% flows of French mutual funds are realized via distribution channels integrated in banks (BCG-rapport (2003) and FFSA (2004)). In addition, Otten and Schweitzer (2002) show that European mutual funds predominantly use banks as the principal distribution channel with a market share of 53%, whereas in the American market, only 8% of funds are commercialized through banks.  A fund family is a group of funds managed by the same management company (e.g. in the case of the French market, a group of funds created and managed by the same bank is often considered as a family).  This ambiguity might lead to flawed comparison of management fees across funds.  Source: COB rapport (2002). In reality, about 2/3 market assets are distributed by banks and 10 greatest bank groups represent 60% market (Source: Europerformance (2003)).  The first derivate is  EMBED Equation.3   Others argue that French funds should beat the market as they are managed by banks, which have possibility to access to non-public information of enterprises and thus use this information to make abnormal return (McDonald (1973)).  This proxy needs to be used with some care since big families propose in general different types of funds. Also, there is a trade-off with the advantage of learning by doing, due to the investment deepening in one category and the risk diversify, issued to the different types of funds proposed to investors. Hence, performance marginal costs of big families might not necessarily be lower than the one of other families funds.  Note that  EMBED Equation.3  is an increasing function as its first derivate,  EMBED Equation.3 , is always superior to zero with  EMBED Equation.3  . Moreover, we have:  EMBED Equation.3 . 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Let us analyse the function: EMBED Equation.3  . The first derivate of this function is equal to  EMBED Equation.3 , which is equal to zero at  EMBED Equation.3 . Moreover,  EMBED Equation.3 . Consequently,  EMBED Equation.3 has a unique minimum at  EMBED Equation.3 . Otherwise EMBED Equation.3 . This leads to  EMBED Equation.3 .     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