Measuring market power in the Spanish mutual funds industry for retail investors

Transcription

1 Measuring market power in the Spanish mutual funds industry for retail investors Ramiro Losada July 2015 Abstract The mutual fund industry is characterized by high concentration and a high number of funds offered. The reported accounts of Spanish investment management companies reveal that, in recent years, they have enjoyed an average margin, measured by the Lerner index, of between 23 and 25 per cent. We use an econometric structural model of competition among investment management companies to show that mutual fund elasticities are low in the retail market. This result casts doubts on the effectiveness of the fee-caps currently in place. Moreover, if we assume that this market follows a monopolistic competition pricing model, the estimate of the actual average margin in the industry rises to above 40 per cent. Keywords : Competition, Market Power, Differentiation. JEL Classification : G23, L11. I gratefully acknowledge the data provided from my colleagues from the Statistics department at CNMV and the comments and help from two anonymous referees, Alfonso Sanchez, Vicente Garcia, Juan Manuel Garcia, Alicia Barroso, Maria J. Moral, Jordi Jaumandreu, Carlos Urbaneja and the participants at the XXII Foro de Finanzas and the XXXIX Simposio de Analisis Economico. The usual disclaimer applies. Comision Nacional del Mercado de Valores. c/edison 4, Madrid, 28006, Spain. Tlf: rlosada@cnmv.es 1

2 1 Introduction According to the OECD: Market power refers to the ability of a firm (or group of firms) to raise and maintain price above the level that would prevail under competition. Economic theory shows the social welfare gains of perfect competitive markets compared to markets where firms enjoy market power. In the latter, there is a net loss of social welfare as the exercise of market power leads to reduced output. For this reason, economic authorities have always been aware of the importance of curbing levels of market power in industries, such as utilities, whose structures would otherwise allow market power to flourish. The mutual fund industry is characterized by high concentration, agile launch and withdrawal of new funds, and aggressive brokering by branches of credit institutions looking to place them with retail investors. In principle, the type of competition in this industry may be broadly described as monopolistic competition. 1 However, the fact that investment management companies compete in a market of this type does not, in itself, prove that they enjoy market power. In the classic description of monopolistic competition, there are many firms and many consumers in the market, and each firm faces downward sloping demand. This means that they are not price takers and have a certain degree of control over price. The other two important features of this model are consumers perfect information on the products offered in the market and low barriers to exit and to entry. Under these assumptions, although there may be firms which enjoy high profits at a certain point in time, these profits cannot be maintained in the long run as new firms would enter to close the gap. So, this type of competitive environment ends up in competitive outcomes very close to perfect competition. However, although it is readily apparent that the barriers to entry and exit in the mutual fund industry are low, it is equally clear that investors do not enjoy perfect information on the mutual funds being offered. They face searching costs, and derived from those searching costs, switching costs. They are usually loyal to a single credit institution when deciding where to invest their savings. These frictions open the door for investment management companies to exercise market power. Also, a key feature of these markets is 1 Monopolistic competition is a type of imperfect competition where many producers sell products that are differentiated from one another, usually by branding and/or quality, and hence are not perfect substitutes, see Chamberlain (1933). 2

3 the huge number of funds that management companies offer and, as Gavazza (2011) and Cambon and Losada (2014) have shown, this wide offer is neither neutral nor positive. It has a negative impact on the terms of competition. This mechanism may be a clue as to how investment management companies come to enjoy market power. The aim of this paper is therefore to study, through a structural econometric model, whether investment management companies can translate the frictions present in the mutual funds industry in actual market power and, if so, to what extent. 2 The financial regulation has not been traditionally aware of competition issues. Only the U.K. Financial Conduct Authority has the mandate of promoting effective competition. Thus, it is important to study the competition in financial markets and to provide evidence of those which can be working far from the perfect competition paradigm. The paper is structured as follows. Section 2 describes the mutual fund industry for retail investors. Section 3 presents the data used to study the Spanish mutual fund market. Section 4 explains the empirical analysis we carried out for this paper, in which the market power of investment management companies is measured. Section 5 presents and analyses the results of the empirical analysis. Finally, the last section lays out the conclusions. 2 The mutual fund industry for retail investors A mutual fund is a type of professionally managed collective investment scheme that pools money from many investors to purchase securities. 3 Mutual funds offer investors several advantages compared to direct investing in individual securities, including, principally, increased diversification, daily liquidity and professional investment management. In exchange for these advantages, investors must pay fees, mainly to the investment management companies which administer the funds. These collective investment vehicles are sold to the general public. This is the main reason why mutual funds are regulated. 4 One of the major goals 2 As it was shown in Berry et al. (1995), if the classic logit model were used, the model could suffer from the independence of irrelevant alternatives restriction at individual level. This could lead to estimations of elasticities and margin, and by extension to a measure of market power in this industry, very far from the actual ones. 3 U.S. Securities and Exchange Commission definition, available at 4 The main current Spanish regulations on mutual funds are Law 31/2011 of the 4 th 3

4 of these regulations is to try to overcome any possible asymmetric information between investors and the funds investments and outcomes, including the possibility of fraud. So, the main target of this regulation is the retail investors market. Any information asymmetry is more likely to be found in the retail than in the wholesale market, where investors are supposed to be more sophisticated. These differences in the participants of both markets make it natural to consider them as two different markets. 5 In Spain, as in most countries, mutual funds and investment management companies must be registered with the securities supervisory authority, the CNMV. Unlike what happens in the United States and the United Kingdom, where there is a different system of brokering, in most European countries, mutual funds are mainly brokered through the branches of the credit institution their investment management company belongs to. One effect of this is to make the mutual fund industry heavily vertically integrated. 6 As will be shown, this characteristic may be one of the reasons why investment management companies enjoy high margins and it makes this market as very attractive in order to study lack of competition in a financial market. Focusing on the Spanish market, the number and assets of mutual funds grew significantly in the period The big driver of the increase was the popularisation of this type of financial vehicles among retail investors. One important feature was that most of the mutual funds assets were managed by investment management companies belonging to credit institutions. Specifically, this type of investment management company administered between 92 and 95 per cent of the assets invested in mutual funds. Independent investment management companies only had a significant presence in the segment of equity and mixed funds aimed at wholesale investors. 7,8 According to of October, which modifies Law 35/2003 of the 4 th of November on collective investment schemes and the Royal Decree 1082/2012 which expands on the Law 35/2003 of the 4 th of October on collective investment schemes. 5 In Gavazza (2011) and Cambon and Losada (2014), the authors found different demand and supply patterns in the retail and wholesale mutual fund markets. 6 A vertically integrated industry can be defined as one where firms own the whole supply chain. In most cases, this means that the same firm produces and sells a product. 7 Conservative funds are money market funds, all fixed-income funds and guaranteed funds. Equity funds and mixed funds also include global funds. 8 Mutual funds have been divided into wholesale and retail funds. Wholesale funds are those with more than 50 per cent of assets in the hands of investors with a minimum holding of 180,000 euros. Note that different criteria are used for distinguishing wholesale and retail funds between 1999 and 2011, as a result of a CNMV Circular changing the 4

5 Cambon and Losada (2014), the presence of a wide variety of funds may be a key factor in explaining why the conditions for competition in the mutual fund industry are so far from the perfect competition paradigm. As shown in figure 1, the total and the average number of funds administered by investment management companies in the retail market was more than twice the number of funds offered to wholesale investors. Moreover, the retail market accounted for 76.9 per cent of the total average assets under management during the period. 9 Figure 1: Average and total number of funds managed by management companies in the wholesale and retail markets (by year) Source: CNMV The financial industry is characterized by the fact that investors, particularly retail investors, tend to concentrate their purchases of financial products with a single supplier. As said, this feature is specially important in Spain in comparison with other larger markets as U.K. and United States. This reserved information statements that investment management companies must fill out for supervisory purposes. In this period, money market funds and short-term fixed-income funds are considered as wholesale if more than 50 per cent of their assets are in the hands of investors with a minimum of 300,000 euros. Other types of funds are considered as wholesale when more than 50 per cent of their assets are held by investors with a minimum holding of 150,000 euros. 9 For further details about the supply of mutual funds in Spain over the period , see Cambon and Losada (2012). 5

6 behaviour may be due to the high cost of searching for financial products among a number of different suppliers. As argued in Klemperer and Padilla (1997), in industries which share this feature, such as, for example, retail sales in supermarkets, variety is a strategic variable that companies can use to ease competition. So, it may be interesting to study the outcomes of competition in the mutual fund market. Figure 2 shows the volume market shares (assets under management) of the four, six and eight largest investment management companies in the retail market from 1995 to It can be observed that this market is served by a concentrated industry, specially since The rise of concentration was partly due to a wave of mergers and acquisitions among credit institutions in the late 90s 10 Anyhow, any concentration of a industry may be troublesome because the industry leaders very often earn consistently high profits. Figure 2: Volume Market Shares in the Retail Market Source: CNMV 1. C4 refers to the market share of the four largest management companies. 2. C6 refers to the market share of the six largest management companies. 3. C8 refers to the market share of the eight largest management companies. One important point to note is that the market power investment management companies may enjoy is not an exclusive characteristic of the Spanish 10 For example, Banco Santander and Banco Central Hispano merged in Banco Bilbao Vizcaya and Argentaria also merged in

7 industry. Gruber (1996) and Korkeamaki and Smythe (2004) found evidence in the Finnish and U.S. industries of the existence of economies of scale which were not benefiting final investors. Ferreira and Ramos (2009) calculated a Herfindahl index for the fund industry in Spain of 0.1 in 2006, which was very close to the average index in a sample of Eurozone countries (0.12), composed of Austria, Belgium, Finland, France, Germany, Italy, the Netherlands and Portugal. Although there are important differences among these countries with regard to their retail markets, the concentration levels suggest that these markets could also be far from the perfect competition paradigm. 3 Data description The model is estimated for the Spanish mutual fund market. The original sources of the data set for this market are the Spanish Securities and Exchange Commission (CNMV), the Spanish Banking Association (AEB), the Spanish Confederation of Savings Banks (CECA) and the National Union of Credit Cooperatives (UNACC). The main source of the data set is the CNMV. This institution periodically collects information as part of its duty to supervise collective investment schemes. Data on all existing mutual funds and investment management companies, including those now defunct, was obtained on a yearly basis from 1995 to 2011 (17 years) from the CNMV. The other sources of data provided information on the characteristics of the credit institutions that non-independent investment management companies belonged to. As will be shown, this latter source of information is important to identify good instruments for the estimation. Although the CNMV collects data on all mutual funds registered in Spain, this paper only considers mutual funds purchased by retail investors. 11 Treating each mutual fund/year as a single observation, the total sample size is 11 Mutual funds have been divided into wholesale and retail funds. Wholesale funds are those with more than 50 per cent of assets in the hands of investors with a minimum holding of 180,000 euros. Note that different criteria are used for distinguishing wholesale and retail funds between 1999 and 2011, as a result of a CNMV Circular changing the reserved information statements that investment management companies must fill out for supervisory purposes. In this period, money market funds and short-term fixed-income funds are considered as wholesale if more than 50 per cent of their assets are in the hands of investors with a minimum of 300,000 euros. The other types of funds are considered as wholesale when more than 50 per cent of their assets are held by investors with a minimum holding of 150,000 euros. 7

8 24,397 observations and the total number of funds considered is 3,504. The information obtained for each mutual fund includes: 1. Market share (s jt ): defined as the ratio between the assets of each fund and the total amount of retail investor financial holdings. 2. Fees (p jt ): defined as the sum of the management fees, depositary fee, 1/7 of the subscription fee and 1/7 of the redemption fee of each fund in each of the periods making up the sample Return (return jt ): defined as the percentage change in the net asset value of a unit of each fund between the close of one year and the close of the previous year. 4. Volatility (volat jt ): defined as the typical annualized deviation of funds monthly returns over the last 12 months. This is a standard risk measure to assess the profile of mutual funds. 5. Type of fund (equity jt ): This is a dummy variable which is 1 when the fund falls within the equity class and 0 when it is conservative. For these purposes, equity funds include equity and mixed funds as well as global funds. Non-equity funds include money market funds, all fixed-income funds and guaranteed funds. Information on the investment management companies that mutual funds belong to includes: 1. Variety (NumV oc jt ): defined as the ratio between the number of fund types offered by the investment management company and the total number of types of fund available on the market in a particular year. 2. Type of investment management company (CI jt ): This is a dummy variable set to 1 when the investment management company belongs to a credit institution and 0 when the investment management company is independent. In addition to the variables that characterize the mutual funds and the investment management companies, other variables are used as instruments in the estimation of the model: 12 This variable has been defined as in Gavazza (2011) and Cambon and Losada (2014). It is assumed that investors invest over a time horizon of seven years. 8

9 1. Return of the other funds belonging to the same category as fund j in period t (reti jt )). 2. Number of branches of the financial group the management company belongs to (numofi jt ). 3. Number of employees of the financial group the management company belongs to (numemploy jt ). 4. Marketing expenses which the investment management companies pay in order to place their mutual funds (maktexp jt ). Other sources of information used are the INE and the Bank of Spain. 13 The INE provided the distribution of the Spanish income per capita (annual mean and standard deviation). 14 The Bank of Spain provided information on household deposits, which has been considered as the alternative investment to mutual funds. As stated in Ispierto and Villanueva (2010), the characteristic that best describes the behaviour of Spanish retail investors is their net wealth. Investors with different net wealth decide to hold different portfolios of financial assets. However, due to a lack of annual data on this variable, we have had to use a second-best proxy. This is to consider income as the variable that describes the heterogeneity in the behaviour of the Spanish retail investors. One may regard the definition of the alternative investment as deposits as overly restrictive. However, although Spanish retail investors may hold equities in their portfolios, there are three reasons why deposits are taken as the sole alternative investment. Firstly, according to Ispierto and Villanueva (2010), the average Spanish retail investor is very conservative. Most would only consider deposits as an alternative to mutual funds. Secondly, the Bank of Spain only supplies aggregate data on the investment of retail investors in public and private equity. As most of the equity held by retail investors is private, basically property rights in businesses run by the holders, this equity should not be considered as a pure financial investment. Lastly, other possible investment instruments, such as pension funds, are chosen to a different time horizon, which makes them unsuitable as close substitutes for mutual funds. 13 INE are the acronyms of the Spanish Statistical Office. 14 The income distribution is assumed to be lognormal and its parameters are estimated from INE data. Particularly, the estimated standard deviation is σ y and the mean m t is the sample mean for each year. 9

10 Table 1 shows a summary of the main descriptive statistics of the main variables considered in the empirical analysis. With regard to the variables that characterize the mutual funds, the average market shares of the funds and the alternative investment in the period under consideration are and per cent respectively. The average return of the funds was 3.18 per cent, whereas the fee paid by the retail investors was 1.61 per cent. It is also important to point out that the average volatility was high, this means that the number of equity funds in the sample is high. Regarding the variables that characterize investment management companies, the average percentage of fund types offered is This means that Spanish investment management companies cover a high percentage of fund types and, by extension, offer a large number of funds to retail investors. Table 1: Descriptive statistics of the data set Average Standard deviation Market share (mutual funds) Market share (alternative investment) Fee NumVoc Return Volatility Marketing expenses (thousand euros) 9,352 15,241 Number of branches Number of employees Return (instrument) Number of observations Number of funds 3504 Source: CNMV, AEB, CECA and UNACC. 4 The empirical framework The empirical strategy follows Nevo (2001) and considers different models of supply conduct. For each model of supply, the pricing decision depends on mutual fund demand, which is modeled as a function of mutual fund 10

11 characteristics and investor preferences. 15 Demand parameters are estimated and, afterwards, used to compute price-cost margins (PCM) implied by the different models of investment management companies conduct. 4.1 Demand model The investment management companies problem that will be proposed in the supply side description will allow us to estimate PCMs and split them up into different components. However, this task relies heavily on the ability to consistently estimate funds own and cross-fee elasticities. No easy task in an industry like mutual funds where many funds may be considered to be very close substitutes. So, the dimensionality problem is circumvented by projecting the different mutual funds onto a characteristics space. This makes the space characteristics of the mutual funds the relevant variable, and not the number of mutual funds in the market. Following this approach, taken by the discrete-choice literature, let be t = 1,..., T the markets that are observed, each with i = 1,..., I investors. In this case, it is assumed that each of the considered years is a market. The conditional indirect utility of investor i from fund j at market t is: u ijt = x jt β 1 α i p jt + ξ j + ϵ ijt, (1) where x j is a K-dimensional vector of observable mutual fund characteristics, p jt is the total fee of fund j in market t, ξ j is the mean valuation of the unobserved (by the econometrician) mutual fund characteristics and ϵ ijt is a zero mean stochastic term. Finally, β i = (α i, β 1 ) are K + 1 individual coefficients. 16 The investors heterogeneity is picked up by α i. This parametrization follows Barroso and Giarratana (2013). The observed characteristics of funds that we consider are the following: the variety offered by the investment management company of a given mutual fund, return, volatility, whether or not the investment management company belongs to a credit institution and whether the mutual fund is an equity fund. It is assumed that investment management companies as well as investors 15 This empirical framework is further explained in Nevo (2000) and Rasmusen (2007). 16 The total fee paid by the investors of a mutual fund in each period/market is the sum of the management fee, the deposit fee, 1/7 of the subscription fee and 1/7 of the redemption fee. This variable has been defined in a similar manner to that of Gavazza (2011) and Cambon and Losada (2014). 11

12 observe all product characteristics and take them into consideration when making decisions. The distribution of the consumers fee parameter is normal (conditional on demographics) with a mean that is a function of a demographic variable (individual income) and parameters to be estimated. Let be: α i = α + θ 1 ν i + θ 2 d i, ν i N(0, 1), (2) where d i is the demographic variable, in this case income, θ 2 is a coefficient that measures how the taste characteristics vary with the demographic variable. θ 1 is a coefficient and measures how the consumer reacts to any change in his characteristics, for example education, that are picked up by his income. Thus, this model specification allows the individual characteristic to be composed by the observed characteristics, d i and the unobserved characteristics, ν i. 17 The specification of the demand system is completed with the introduction of an alternative investment (deposits). This allows investors to decide not to put their money in any of the available mutual funds. Without this alternative, a homogeneous price increase in all products would make no difference to the quantities purchased. The indirect utility from the alternative investment is kept as simple as possible: u i0t = ϵ i0t. (3) Let be Γ = (β, θ) as the vector which contains all parameters of the model, β = (α, β 1 ) and θ = (θ 1, θ 2 ); then, combining equation (1) and (2), the following reduced form equations can be written: u ijt = δ jt (x j, p jt, ξ j ; β) + µ ijt (x j, p i, ν i, d i ; θ) + ϵ ijt, (4) δ jt = x j β 1 αp jt + ξ j, µ ijt = p jt (θ 1 ν i + θ 2 d i ), (5) By using equation (4), investors utility is expressed as the mean utility, δ jt and a deviation from that mean, µ ijt + ϵ ijt which captures the effect of the random coefficient. 17 The distinction between observed and unobserved individual characteristics make references to use of the auxiliary data sets. The distribution of observed characteristics are estimated from these additional sources, in this case, the data from INE. 12

13 An important assumption of this model, although very common in discrete choice literature, is that investors only purchase a fixed amount (normalized to 1) of the mutual fund that provides the highest utility. 18 This defines the set of the unobserved variable that makes possible the choice of mutual fund j: A jt (x, p.t, δ.t ; θ) = {(d i, ν i, ϵ it ) u ijt u ilt, l = 0,..., J} (6) where x are the characteristics of all available mutual funds in the market, p.t = (p 1t,..., p Jt ) and δ.t = (δ 1t,...δ Jt ). Under the assumption that ties occur with zero probability, the market share of the j th mutual fund as a function of the mean utility levels of all mutual funds, given the parameters, is s jt (x, p.t, δ.t ; θ) = dp (d, ν, ϵ) = dp (ϵ)dp (ν)dp (d), (7) A jt A jt where P (.) is the population distribution functions. The second equality comes from the assumption of independence between d, ν and ϵ. The assumptions on the distributions of the individual attributes (d i, ν i, ϵ i.t ) are needed in order to compute the previous integral analytically or numerically. Given that fees and market shares are known, a natural estimation strategy is to try to search for the parameters that minimize the distance between the actual market shares and those predicted by the model. Bearing this idea in mind, the actual estimation adds a higher degree of complexity as it has to cope with the correlation between fees and demand shocks, which enter the integral nonlinearly. It also has to take into account that, as shown in Cambon and Losada (2014) for the Spanish market, an important demand driver for mutual funds is the variety that their investment management companies offer (proxied by the number of funds and/or fund types) which is also correlated with demand shocks. The most common assumption to try to solve the integral is that consumers heterogeneity enters the model only through ϵ ijt, and these shocks are i.i.d. and distributed according to a Type I extreme-value distribution. 18 A portion of retail investors may choose to invest in more than one mutual fund, however most of retail investors decide to invest only in a single mutual fund, which is the relevant fact for this modeling assumption. Nevertheless, if one is still unwilling to accept this is not a main driver of this market, then this model can be viewed as a good approximation to the true choice model. 13

14 This assumption reduces the model to a well-known Logit model. This type of model is very tractable, although by assumption, it restricts own and cross fee elasticities. 19 Logit models assumptions imply that cross-price elasticities are a direct function of market share. This implies that if two funds with very different characteristics have the same market share, the substitution from a third fund towards any of the two former funds will be the same. This result always arises independently of how close the characteristics of the third mutual fund are to the other two funds. However, in general and intuitively, if the latter mutual fund fee rises, one would expect the fund with closer characteristics to win more market share than the one with not so close characteristics. The literature has tried to close this gap by using less restrictive models. In these, the i.i.d. assumption is replaced by a more complex structure. Within this category of models, the Nested Logit model and the principles of differentiation generalized extreme value model (McFadden (1978) and Bresnahan et al. (1997)) were the first attempts to try to overcome the Logit model s restrictions. However, although they are less restrictive, both models generate substitution patterns that only partly overcome the problem of Logit models, as they are conditional on a priori assumptions over how products in a market are related. The model presented in this section, which follows Nevo (2001) and Berry et al. (1995), nests all the previous models and has a major advantage over them. This model allows for flexible own-fee elasticities, which are driven by the different sensitivity to fees of retail investors in the mutual fund market. This flexibility can achieve outcomes closer to what we can observe in the real world Supply model Although there are fee caps in place in the Spanish mutual fund market, the results from demand estimation will show how using the standard monopolist competition pricing model is a good approximation in order to assess market power in this market. So, suppose there are F management companies, each 19 See for example MacFadden (1981) or Berry, Levinsohn and Pakes (1995). 20 McFadden and Train (2000) showed that the type of model used in this paper can approximate arbitrarily any choice model. In particular, the multinomial probit model (Hausmand and Wise (1978)) and the universal Logit (McFadden (1981)). 14

15 of which offers some subset, I f, of the j = 1,..., J of mutual funds. The profits of firm f are: Π f = j I f (p j mc j )Ms j (p) C f (8) where s j (p) is the market share of mutual fund j, which is a function of the fees of all mutual funds, M is size of the market that year, and C f is the fixed cost of the management company. Assuming the existence of a pure strategy Bertrand-Nash equilibrium fees, and that the fees that support it are strictly positive, the fee p j of any mutual fund j placed by management company f must satisfy the following first-order condition: s j (p) + r I f (p r mc r ) s r(p) p j = 0 (9) This set of J equations implies fee-costs margins for each fund. The margins can be solved explicitly by defining S jr = s r / p j, j, r = 1,..., J, { 1 if f : r, j Ω If jr = 0 otherwise. Let Ω be a J J matrix with Ω jr = Ω jr S jr. In vector notation, the first-order conditions become: s(p) Ω(p mc) = 0, (10) where s(.), p, and mc are J 1 vectors of market shares, fees, and marginal costs, respectively. This implies a margin equation: p mc = Ω 1 s(p) (11) Using estimates of the demand parameters, PCM can be estimated without observing actual costs. Three different causes of the margins can then be distinguished: the effect due to differentiation among the mutual funds, the portfolio effect and the effect of price collusion. This is done by evaluating the PCM in three hypothetical industry conduct models. The first structure is that of single fund investment management companies, in which the fee of a mutual fund is set by a profit-maximizing investment management company that considers only the profits from that mutual fund. The second 15

16 is the current structure, where multi-fund investment management companies set the fees of all their funds jointly. The final structure is the joint profit-maximization of all mutual funds in the market, which corresponds to monopoly or perfect fee collusion. Each of these structures is estimated by defining the proper ownership structure, I f and matrix, Ω. The PCM of the first structure depends solely on how different investors perceive the mutual funds in the market. The difference between the margins in the first two market structures considered is due to the portfolio effect. The last structure measures the increase in the margins due to fee collusion. 4.3 Estimation of the demand model The demand equation is estimated by means of the following algorithm: 1. In order to start the algorithm, select arbitrary values for δ and θ = (θ 1, θ 2 ) and for β. It is important to remind that δ is the vector of the mean utility from each of the funds, that θ is the matrix of parameters showing how observed and unobserved investors characteristics and product characteristics interact and generate utility, and that β is the average value of the parameters across investors. 2. Random values for (ν i, d i ) for i = 1,..., n s are drawn from the distributions functions P ν (ν) and P D (D) for a sample size n s, where the bigger n s the more accurate the estimate will be. 3. By means of the starting values and the random values, and also the assumption that the ϵ ijt follow the extreme-value distribution, the integral for market share that results from aggregating across i is approximated by s jt = ( 1 n s )s ijt (12) s ijt = n s i=1 e δ jt+p jt (θ 1 ν i +θ 2 d i ) 1 + J m=1 eδ jt+p jt (θ 1 ν i +θ 2 d i ) (13) where ν i and d i for i = 1,..., n s are the random draws from the previous step. From this step, predicted markets shares for given values of the 16

17 individual investor parameters θ = (θ 1, θ 2 ) and for given values of the mean utilities, δ, are obtained 4. θ = (θ 1, θ 2 ) are kept fixed at their starting points, values of δ are found by means of the following iterative process: δ h+1.t = δ ḥ t + (ln(s.t ) ln(s.t )) (14) where S.t is the observed market share and s.t is the predictive market share from the previous step. This contraction mapping starts with an arbitrary δ 0 which comes from step 1. If the observed and predicted market shares are equal, then δ.t h+1 = δ ḥ t and the series converge. In practice, the algorithm is kept iterating until ln(s.t ) ln(s.t ) is small enough given a set accuracy. From this step the values of δ come out. 5. The value of the moment expression is figured out, using the alternative values for β = (α, β 1 ) from step 2 and the δ estimated from the previous step. Next, calculate the error term ω jt and the value of the moment expression ω jt = δ jt (αp jt + x jt β 1 ) (15) ω ZΦ 1 Z ω (16) where Φ = E(Z ωω Z) and Z is the matrix of instruments. As usual, the procedure starts with a consistent estimator of Φ = Z Z. 6. Better estimates of all the parameters are computed: the common parameters, β = (α, β 1 ), the individual parameters, θ = (θ 1, θ 2 ) and the weighting matrix Φ. An estimate of the common parameters is found by using the GMM method: (α, β 1 ) = (X ZΦ 1 Z ZX) 1 X Z ZΦ 1 Z δ (17) This is a linear estimator that can be found analytically by multiplying matrices. The parameters that can be linearly estimated are separated 17

18 out from the parameters that require a search algorithm. This is why all these steps are used instead of simply setting up the moment expression and then using a minimization algorithm to find parameter values that minimize it. Searching takes a computer longer than multiplying matrices and is less reliable in finding the true minimum, or, indeed, in converging to any optimum. The value of the error term, ˆω, is estimated, and afterwards, the moment expression, ω ZΦ 1 Z ω, is used to improve the estimates of β = (α, β 1 ) from the last estimation. The value of the weighting matrix Φ = Z ωω Z is estimated by using the ˆω that has just been calculated: ωˆ jt = δ jt (ˆαp jt + x jt ˆβ1 ) (18) Finally, a search algorithm is used to find new values for θ = (θ 1, θ 2 ). In this case, the search algorithm used was of a Nelder-Mead type. 21 With the new values taken out from the algorithm result, the procedure starts again from step 3. The iteration procedure keeps searching for parameters β and θ until the value of the function, ω ZΦ 1 Z ω, is close enough to zero. An important point to note is that in estimating our model for the mutual fund industry we must include two endogenous variables among the defining characteristics: first, the variety offered by the funds investment management company, i.e., the percentage of fund types offered and, second, the fee. These are the two main variables that the investment management company chooses in order to maximize profits. Gavazza (2011), through a theoretical model that applies the Sutton (1991) model of sunk costs to the mutual fund industry, has shown that these variables are key when an investment management company competes in the mutual fund market. Thus, if one tried to estimate the linear parameters of the model without using instruments for these variables, the outcomes of the estimations could be inconsistent. 22 In this case, the best approach to getting a good estimate for the model is to identify the right instruments. These must be related to the variety of 21 The Nelder-Mead algorithm or simplex search algorithm is one of the best known algorithms for multidimensional unconstrained optimization without derivatives. For further details about this algorithm, see Nelder, J.A. and Mead, R. (1965). 22 See Khorana and Serveas (2012) 18

19 the funds supplied by the investment management company and to fees; at the same time, they must not be related to demand shocks. To capture variety, the variables we used as an instrument are: the number of branches, the number of employees of the parent credit institution and the investment management companies marketing expenditures. These instruments are only valid for our purpose if they are immune from any positive demand shock, i.e. a demand shock should not translate into an increase in the variables used as an instrument. The variables have to meet a number of conditions that guarantee they are correlated with the original variable, the one that measures variety, and not with any idiosyncratic error of demand. To test the validity of the instruments we need to consider the number of employees and branches over the period of analysis. Neither should have increased or decreased due to an unexpected increase in demand for funds. This assumption seems reasonable if we assume that none of the past shocks were of high intensity. With regard to marketing expenses, the validity of this instrument seems at first sight more doubtful. It seems quite clear that as more funds are sold, irrespective of the cause, more marketing expenses are generated. However, marketing incentives in the Spanish banking market are based on estimates set in advance. Such a system makes it less obvious that a demand shock would automatically result in higher marketing expenses. Under this scheme, mutual fund sellers have few incentives to exceed their start-of-year sales target. Most of the time, the profits from placing mutual funds above the target do not compensate for the costs (higher sales estimates for future years). This could cause a ratchet effect as described in Laffont and Tirole (1998). In the case of fees, the instruments are the same as in previous papers, e.g. Berry (1994) and Nevo (2001). Specifically, the instrument is defined as the average return of all other funds in the data set in a particular year. The suitability of this instrument relies on the assumption that the demand errors affecting each particular fund are independent. In this case, these assumptions should hold as most of the retail investors are not aware of other mutual funds returns as it is costly for them to access that information. To conclude this section, a short note on the identification of the model. As Nevo (2000) states, there may be two problems regarding this issue when a random-coefficient is estimated. The first problem is related with the endogenous variables a model may have. This problem has just been tackled in this section. The second problem arises because a random coefficients model 19

20 needs great variety in the data set. In this case, such variety is achieved by the number of years/markets considered, principally because these years included two recession and two booms, which resulted in wide variations in mutual fund market shares. 5 Results 5.1 Demand estimation Table 2 shows the estimations from both the logit and the full model (random logit coefficient). For both types of models, the dependent variable is ln(s ij ) ln(s 0t ). Two of the estimations consider the instrumental variables already discussed and time dummy variables, the other estimation also consider dummy variables but it estimated the model by OLS. In order to have good estimates from the full model, predicted market shares from step 3 of the estimation algorithm were based on the empirical distribution of demographics (Spanish income per capita) reported by INE, independent normal distribution (for ν) and Type I extreme value (for ϵ) (see equation (1) and (2)). 23 For the cases of the demographic variable and the ν, 7500 individuals were sampled for each year. The first column displays the result from the logit model estimated by OLS, the second column displays the result from the logit model estimated by instrumental variables while the third to fifth columns show the results from the full model. The third column gives the estimations of an average investor s demand behaviour in response to the different characteristics of funds. The other two columns show how different types of investor react to fee changes. As the estimates show, the two latter models give very close results. Although the logit model usually yields restrictive and unrealistic substitution patterns among products (making it frequently unsuitable for measuring market power in an industry), this is not always the case. Point estimations and their significance are very similar. Only the variance coefficient is not significant in the logit model. But where these two models really come close together is in their results for the sensitivity of heterogeneous investors to fees, θ 1 and θ 2. Both parameters estimations are very close to zero. In addition, none of them is significant. These results mean that investors do not differ in their sensitivity, however heterogeneous they may be. The reaction 23 INE are the acronyms of the Spanish Statistical Office. 20

21 of all investors to a change in a mutual fund fee is very likely to be the same. These results also mean that, for this industry, the logit model estimated by instrumental variables is a good approximation with which to measure market power. This is an important result and deserves further explanation. One would expect price sensitivity to differ between investors. As most retail investors are advised by the sellers who place mutual funds at the credit institutions branches, one would expect investors with lower income to have more inelastic demand. However, what we find is the opposite. The sellers who place mutual funds among retail investors can discriminate among them and can influence them in the same way independently of how different they are. This result may be indicative of investment management companies enjoying high market power in this industry. Anyhow, the fee coefficient obtained in the full model is negative and significant, which means that all retail investors face downward sloping demand for mutual funds. Table 2: Estimation results Fee NumVoc Return Volat CI Equity OLS Logit estimation IV Logit estimation Full model estimation β β β 1 θ (0.019) (0.441) (0.039) (1.306) (0.346) (0.043) (0.306) (0.018) (0.0008) (0.001) (0.0001) (0.0017) (0.009) (0.0007) (0.035) (0.046) (0.0009) (0.025) (0.192) (0.014) Number of observations Number of funds Fixed effects test (Hausman) No No Hansen test (p-value) GMM Objective β regressors of both models were estimated by GMM 2.Regressions include time dummy variables 3.Estimates are robust to heteroskedasticity and autocorrelation 4.Estimated standard deviations in brackets 21

22 With respect to the other results obtained from the full model, we should highlight the importance of all the characteristics of mutual funds considered. All of them appear to be significant. The variety parameter is positive, which indicates how important it is to offer a wide range of funds of different types. Even though an alternative investment has been considered in the analysis, this result is in line with Gavazza (2011) and Cambon and Losada (2014), where the authors made no such assumption. There are other two important results that arise from the estimation. The funds from investment management companies that belong to credit institutions enjoy higher market shares, and retail investors are less keen to invest in equity funds. The first result may be a demonstration of how funds from investment management companies of credit institutions exercise greater market power. Even when mutual funds have identical characteristics, it is easier for this type of investment management company to place their funds than it is for independents. The second result shows the preferences of retail investors. It appears that retail investors are very conservative and risk averse, which is in line with the results in Ispierto and Villanueva (2010). Given the results from the full model of demand, the mutual fund elasticities can be figured out. As the heterogeneity coefficients, θ 1 and θ 2, were not significant, the elasticities can be computed by using the following close form: 24. η ijt = s { jt p kt αpjt (1 s = jt ) if j=k p kt s jt αp kt s kt otherwise Figure 3 shows the distribution of the elasticities across all the mutual funds in the data set. Most of the mutual fund own elasticities, in absolute values, are between 2 and 4. Only a few have an elasticity higher than 4. These results mean that investment management companies enjoy a high margin in most of the mutual funds. Using the Lerner index as a measure of margins suggests that investment management companies would enjoy a margin in each mutual fund of at least: p mc p = own 1 elasticity 24 For further details, see for example Rasmusen (2007) 22

23 Figure 3: Elasticities density function Source: Own figure So, as the figure shows, in most funds investment management companies enjoy a margin of at least 25 per cent, which is really a long way from the perfect competition paradigm. This result casts some doubt on the effectiveness of the current fee cap in place in this market. 25 Investment management companies and, specially, credit institutions, are multiproduct firms that may price discriminate among their investors. 5.2 Price-Cost margins By using the demand parameters estimated and the supply model presented in the previous section, price-cost margins for different conduct models can be computed. We computed price-cost margins for three hypothetical industry structures, enabling bounds to be placed on the importance of the different causes for the price-cost margins. Table 3 presents the mean pricecost margins weighted by assets under management for the full model using the demand estimates in Table 2. The different rows present the price-cost 25 So, not considering the fee caps when analysing the monopolistic competition of this market may be a good approach for this market, as it seems the fee caps are not binding constraints for most of the investment management companies. Currently, the main caps for monetary funds are: 1 per cent for management fees and 0.15 per cent for depositary fees. For other mutual funds, the main fee caps are: 2.25 per cent for management fees and 0.2 per cent for depositary fees. 23

24 margins that the three pricing conducts predict. In principal, each year has different average predicted margins. Table 3: Weighted average margins (per cent) Full Model Single mutual fund management companies Actual structure of the industry Monopoly/Perfect price collusion Source: Own table 1.Margins are defined by means of the Lerner index: (p mc)/p From these predictions, one can conclude that investment management companies enjoy a high margin in any of the market structures considered. It is important to point out the small difference in the margins between the actual structure of the industry and the one where it is supposed each fund is sold by a different investment management company. These results imply important features for this industry. First, although the investment management companies are multiproduct firms, this situation is of almost no benefit to them. The portfolio effect is negligible for this industry. In fact, if the variance of the margins of the funds of each management company is computed, it can be shown that it tends to zero. This may indicate that mutual funds sold by investment management companies are seen by retail investors as not very close substitutes. This result highlights how credit institutions branches influence retail investors perception of funds. They perceive all mutual funds are different when, for many of them, their actual characteristics are very close. Second, although investment management companies supply mutual funds that are very similar, apart from some specialized independent investment management companies, it seems that they can differentiate their offer from those of their rivals. This result suggests that branding and offering a wide range of funds are key in this industry. These mechanisms are the ones which allow the investment management companies and by extension, credit institutions, to relax competition and extract rents from retail investors. This intuition can be confirmed by figure 4, where it can be observed the distribution of margins across management companies. So, most of management companies enjoy a margin about 50 per cent. Only a few more specialized 24