Does Size Matter? Investment Management Companies**

Transcription

1 Scale and Bidding Scope Economies Strategies Alexander Schaefer/Raimond Maurer* Does Size Matter? Scale and Scope Economies of German Investment Management Companies** Abstract Standard measures of economies of scale and scope show that size does matter for German investment management companies. The average investment management company faces an increase in costs of 0.71% for a 1% increase in assets under management. Small to mid-sized companies in our example exhibit statistically significant scale economies. These economies of scale show a size trend. Furthermore, there is empirical evidence of economies of scope between retail and institutional funds, but the cost savings are greater for large investment management companies. Economies of scope also exhibit a size trend, i.e. larger companies show fewer scope economies. JEL Classification: C23, D24, G23, L25 Keywords: Economies of Scale; Economies of Scope; Fixed-Effects Model; Investment Management Companies; Mutual Funds. 1 Introduction Size does matter for German investment management companies. The average investment management company exhibits scale economies as expressed by a cost elasticity of 0.71, i.e. for a 1% increase in assets under management the costs of managing such assets increase by 0.71%. Results on scale economies are statistically significant for small to mid-sized companies when measured by assets under management. None of the companies exhibit statistically significant diseconomies of scale. Furthermore, there is empirical * Alexander Schaefer, Allianz Global Investors, Mainzer Landstr , Frankfurt, alexander.schaefer@allianzgi.com; Raimond Maurer, Goethe-Universität Frankfurt, Grüneburgplatz 1, Frankfurt, maurer@finance.uni-frankfurt.de. This paper is a revised and extended version of the paper formerly entitled Does Size Matter? Economies of Scale in the German Mutual Fund Industry. ** For helpful comments and suggestions we thank an anonymous referee, Michael Feldhoff, Gerold Hornschu, Marcel Fischer, Olivia Mitchell, Marco Navone, Felix Noth, Steffen Sebastian, seminar participants at the Goethe- University, the 2009 Eastern Finance Association Annual Meeting, and the 2009 European Financial Management Association Annual Meeting. Support of the Bundesverband Investment und Asset Management e.v. (BVI) in providing some of the data is gratefully acknowledged. Opinions and errors are solely those of the authors. sbr 65 April

2 A. Schaefer/R. Maurer evidence of economies of scope of an average of 0.37, i.e. by jointly offering products to retail and institutional investors an investment management company incurs 37% less in costs compared to the expenses incurred by offering these products separately. One third of the investment management companies exhibit significant scope economies, but the cost savings due to the joint offering of retail and institutional funds is economically negligible. Finally, there are economies of scope for different types of retail security funds that are particularly strong for the largest investment management companies. We derive these results by estimating a hedonic quadratic cost function, which we derive by using a unique data set based on the annual reports of German investment management companies. The inclusion of hedonic variables, i.e. other variables in addition to outputs, in the cost function allows us to control for characteristics in the production technology that might systematically affect costs. In contrast to previous research, this procedure allows us to infer direct cost estimates instead of relying on an aggregation of expenses that occur at the individual fund level (which are revenues for the investment management company). We measure size by output in the form of assets under management, distinguishing between retail and institutional funds. We further divide retail security funds into the subcategories of equity, fixed income, and other security funds. We use operating expenses, commission expenses and depreciation on fixed assets as costs. To control for company-specific effects and technical progress, we include hedonic variables and a time trend in the cost function. The estimates of the coefficients in the hedonic quadratic cost function are used to calculate scale and scope measures. We evaluate these measures for each investment management company individually, and then average them across companies and over the sample period. In the course of the paper, we follow Securities and Exchange Commission (SEC) (1966) in defining an investment management company as a. group of funds under common management. Management consists of investment advice and administrative services (see Mahoney, 2004). We use the term investment management company to clarify that we are dealing with economies of scale and scope on the company level, not on the level of individual funds. As pointed out by Glazer (1970), there may be costs in operating an investment management company that have to be borne by more than one fund. Therefore, Baumol et al. (1990) argue that an analysis of scale economies requires the consideration of the operating processes that are implemented at the company level. By studying economies of scale and scope on the level of individual mutual funds, researchers do not properly consider the costs for these shared activities. In the literature there are two methods for analyzing the existence and importance of economies of scale and scope for investment management companies. One group of studies examines scale economies of investment management companies indirectly. In these studies, the authors add assets under management or the number of funds of the investment management company as control variables when assessing econo- 1 For literature on economies of scale on the individual fund level see e.g. Golec (2003), Luo (2002) or Malhotra, Martin, and Russel (2007). Economies of scale may also play an important role in determining the performance of mutual funds, see e.g. Chen et al. (2004) and Indro et al. (1999). 138 sbr 65 April

3 Scale and Scope Economies mies of scale with respect to fees and expense ratios of individual mutual funds. This method is implemented by Berkowitz and Kotowitz (2002), Christofferson (2001), Deli (2002), Dowen and Mann (2004), Khorana, Servaes, and Tufano (2009), Korkeamaki and Smythe (2004) and Lesseig, Long, and Smythe (2002). These studies find strong evidence of scale economies on the level of investment management companies. Such an approach has the drawback in that it only allows inference on the existence of scale economies per se. Since these studies assume a linear relation between scale economies and the size of the company, they provide no further insights on to what extent the strength of the scale measure depends on the company size. Furthermore, these studies do not incorporate an analysis of scope economies. According to Ang and Lin (2001) and Banko, Beyer, and Dowen (2010), there is little evidence of economies of scope at the individual fund level. Yet these authors do not control for company-specific characteristics such as assets under management. Another strand of literature concentrates on the investment management company itself. Baumol et al. (1990) investigate the cost structure of U.S. investment management companies for the years 1982 to They find strong evidence of scale economies. This result is confirmed by Collins and Mack (1997) who use a more recent and comprehensive data set of U.S. investment management companies for the time period 1990 to In the analysis of Baumol et al. (1990) there is also evidence of economies of scope. Bonanni, Dermine, and Röller (1998) and Dermine and Röller (1992) detect scale and scope economies for small to mid-sized institutions by using a data set of French investment management companies for the years 1987 and Our analysis on investment management companies differs in several aspects from this prior research. First, the studies as have cited above, use data on assets under management and expenses on the fund level which the various authors then aggregate into the appropriate numbers on the company level. But, as noted above, expenses on the fund level are revenues on the company level, which have to cover the costs incurred by the company. We avoid this aggregation issue by using a unique data set based on the annual reports of investment management companies. Be doing so we are able to analyze costs that are directly incurred at the company level. Second, Baumol et al. (1990) and Collins and Mack (1997) only perform standard ordinary least squares regressions, although panel data is available. Hence, they do not use all the information contained in the data in estimating the parameters of the cost function. To obtain more efficient estimates for the parameters of the cost function, we apply panel data regression techniques. Bonanni, Dermine, and Röller (1998) and Dermine and Röller (1992) find their results by using only cross-section regressions which do not allow for the analysis of the evolution of the scale and scope measures over time. Third, Baumol et al. (1990) focus on companies offering money market funds so the results of such an analysis cannot be generalized to the overall investment industry. Collins and Mack (1997) deal with this issue by analyzing a more comprehensive data set that also includes companies offering fixed income and equity funds. Yet they do not consider economies of scope. Therefore, we contribute to the literature by simultaneously analyzing scale and scope economies for a unique and comprehensive data set of investment management com- sbr 65 April

4 A. Schaefer/R. Maurer panies. We do so by applying panel data estimation techniques. The paper proceeds as follows. In section 2 we present our econometric specification and measures of scale and scope economies. In section 3 we describe our data set. The empirical results are discussed in section 4. Section 5 concludes. 2 Method 2.1 Econometric Specification We base our analysis of economies of scale and scope on a hedonic quadratic cost function. Thereby, we implicitly assume that the investment management companies follow a cost minimizing behavior. By including hedonic variables we can take into account further characteristics of the investment management companies that might affect their operational processes and thus their costs. The reason for choosing the quadratic functional form over the more commonly used translog specification in our sample is not that outputs can be zero, because we could use the method of Battese (1997) which facilitates the use of translog functional form even in the presence of zero outputs. The reason is rather that the conditions of our test for scope economies cannot be technically met by a translog function (see Berger, Hanweck, and Humphrey, 1987). Alternatively, we could have applied the Fourier flexible form which is a translog cost function augmented by a Fourier series. Yet the Fourier flexible cost function results in a substantial loss in the degrees of freedom inducing less efficient estimates and possibly introducing the problem of multicollinearity. Due to the lack of data on input prices, we cannot estimate the cost function simultaneously with the factor share equations. Following Dermine and Röller (1992), we assume that input prices are embedded in the constant term. As a result of this assumption, we are not able to analyze certain properties of the cost function, e.g. the elasticities of substitution between inputs. We model costs that are used as the dependent variable y as a function of M output levels q m, C hedonic (control) variables h c and a time trend t in both linear and quadratic form. Due to the low number of cross-sectional observations in our sample, we estimate the cost function based on panel data. Suppressing the cross-section and time subscripts for convenience purposes, the regression model in its general form for investment management company i (i = 1,, I) for year t (t = 1,, T) is M y(q) = α + ß m q m + _ 1 2 C + c = 1 m = 1 M m = 1 δ c h c + γ 1 t + _ 1 2 γ 2 t2 + ϵ M ß mm qm 2 + m = 1 M l = 1 l m in which the symmetry constraint ß m l = ß lm is imposed for all m and l. ß ml q m q l (1) 140 sbr 65 April

5 Scale and Scope Economies To estimate equation (1), we allow for cross-section specific intercepts, but assume that the slope coefficients are identical across companies and that they do not vary over time. We further assume that the random error term is normally distributed, but we allow for cross-sectional heteroskedasticity, i.e. ϵ it ~ N(0, σ 2 i). Based on the procedure outlined in appendix A.1 and on the results of the regularity tests described in appendix A.2, we estimate the cost function using fixed-effects. Our sample consists of I = 40 investment management companies for the time period 2002 to 2007 (see appendix B for a detailed list), thus T = 6. In our base case we consider two outputs, M = 2, and two hedonic variables, C = 2. More details about the variables used in the analysis are provided in section Economies of Scale We use the estimated coefficients of equation (1) to calculate measures of economies of scale. Hereby we follow Berger, Hanweck, and Humphrey (1987) and use the ray scale elasticity (RSCE) which can be expressed as ln y(λq) RCSE = (2) ln q λ=1 M = m = 1 M = m = 1 ln y(q) ln q m y(q) q m q m y(q). With the function specified in equation (1), the scale measure in equation (2) can be expressed as M RCSE(q) = 1 y(q) m = 1 M ( ß m + ß mm q m + l = 1 M l = 1 l m l) ß m l q q m. (3) RSCE (q) is the relative cost increase caused by a relative increase in outputs by raising the levels of all outputs proportionally. A value of the scale measure less than unity indicates cost increases which are less than proportional to increases in outputs. Thus, economies of scale are present if RSCE(q) < 1. In order to test if economies of scale are statistically significant different from unity, we must compute the standard error of the ray scale elasticity. The derivation is outlined in appendix A.3. The scale measures are calculated for each investment management company in each year of the sample period. These measures are then averaged for the whole sample as well as for size quartiles across the investment management companies for each year. sbr 65 April

6 A. Schaefer/R. Maurer The scale measure we employ in our analysis has at least two drawbacks in case of a multi-product environment. First, the analysis is based on the assumption that outputs are changed proportionally. Second, the measure does not take into account the different product mixes. To avoid these two shortcomings, Berger, Hanweck, and Humphrey (1987) suggest an alternative measure called expansion path scale economies (EPSCE). This measure captures the effects of changing scale and product mix simultaneously. Thus, it is a generalization of the ray scale elasticity. The EPSCE is calculated by comparing two firms that are immediate neighbors in the size distribution, but which do not necessarily share the same output structure. For a multi-product environment, EPSCE is usually only computed if all outputs of the larger firm are greater than those of the smaller one. In our sample there are no two adjacent companies for which both outputs of the smaller company are simultaneously lower than for the larger one. In such situations, Berger, Hanweck, and Humphrey (1987) propose comparing average firms of adjacent size quartiles rather than adjacent firms directly. But because we only consider four size classes, doing so would result in only three measures of average expansion path scale economies. In order to exploit more information from our data set, we stick to the ray scale elasticity, which can be calculated for each investment management company individually. 2.3 Economies of Scope The estimated coefficients of equation (1) will also be used to calculate measures of economies of scope. Baumol et al. (1988) show that a sufficient condition that enables a twice differentiable multi-product cost function to exhibit scope economies is the existence of cost complementarities. Cost complementarities for outputs q m and q l are defined as 2 y(q) < 0. (4) q m q l The condition in equation (4) can be used to test for the existence of economies of scope. With the function specified in equation (1) the condition for cost complementarities in equation (4) for outputs q m and q l becomes ß ml < 0. Therefore, the estimated coefficient for the cross-products of the respective outputs can be used to test for the existence of economies of scope, i.e. our test statistic is based on COMP(q m, q l ) = ß ml. (5) The standard deviation of this scope measure is the standard error of the estimated coefficient Std[COMP(q m, q l )] = Std[ß ml ]. (6) Based on the test for scope economies as defined in equation (5), we can only test for overall economies of scope independent of the sample period and the individual in- 142 sbr 65 April

7 Scale and Scope Economies vestment management companies. Therefore, we also calculate the standard measure for economies of scope (SCOPE) formally introduced by Panzar and Willig (1981). SCOPE is the relative cost increase from producing a firm s output vector in two or more different firms that specialize in some of the outputs. In this case, scope economies for company i are the proportional cost increases from dividing the output vector q = (q 1, q 2,, q M ) into the output vectors q 1 = (q 1, 0,, 0), q 2 = (0, q 2,, 0) up to q M = (0, 0,, q M ), which are mutually exclusive, provided by M hypothetical companies; hence, [ M m = 1 y(q )] m y(q) SCOPE (q) =. (7) y(q) If SCOPE(q) > 0, then there are economies of scope for the company under consideration. To test the significance of this result, the standard error of the scope measure SCOPE(q) has to be computed. The derivation is outlined in the appendix A.4. To calculate SCOPE(q) it is necessary to set some components of the output vectors equal to zero. Doing so is a major drawback in samples in which no firm is completely specialized, but due to the choice of outputs in our sample, there are indeed investment management companies that are fully specialized. Again, Berger, Hanweck, and Humphrey (1987) propose an alternative scope measure called expansion path subadditivity (EPSUB). To calculate EPSUB we must compare one firm to a representative firm smaller in size than the firm under study, and also to a hypothetical firm such that the combined outputs of the smaller and the hypothetical firms are the same as for the firm for which the scope measure is specified. Evans and Heckman (1984) go a step further and compare pairs of firms with exactly the same outputs as the firm under study. They do so by using a grid search in the area of possible outputs of the sample to find the respective firm pairs. But we face the same obstacles in the calculation of EPSUB as in the case of EPSCE, i.e. difficulties in finding admissible pairs of adjacent companies. Thus, we use only COMP(q) and SCOPE(q). 3 Data 3.1 Data Set In Germany, mutual funds are specific collective investment schemes ( Sondervermögen ) that are managed by a licensed investment management company according to the principle of risk diversification. The investment management company is either a limited liability company or a joint stock corporation which usually manages various mutual funds with different investment objectives and for various groups of investors. The relationship between the investment management company and the mutual fund is constituted on a contractual basis. This legal construction means that unit certificates held by the investors do not represent the typical corporate rights of a stock owner, e.g. unit holders cannot appoint new fund managers, directors or board members. Instead, sbr 65 April

8 A. Schaefer/R. Maurer the investors unit certificates are specific securities that represent ownership claims against the mutual funds assets and a contractual claim of the unit holder against the investment management company s portfolio management services. Further, the shareholders of the investment management company are mostly commercial banks, insurance companies, or independent asset managers, not the investors in the fund. To provide investor protection, the business activities of investment management companies are regulated by an extensive legal framework primarily codified in the Investment Company Act ( Investmentgesetz ) and supervised by the German Financial Supervisory Authority (BaFin). Regulation includes licensing requirements, eligible assets, transactions that are permitted in derivative instruments for the funds, valuation of assets, and a general fiduciary duty of the investment management company to act on behalf of the investors. The assets of the mutual funds are strictly separated from the assets of the investment management company by using segregated bank or security accounts administered by a depositary bank. This separation of assets serves as protection for the unit holders if the investment management company should go bankrupt. The various types of mutual funds offered by German investment management companies can be classified according to two important peculiarities: The first notable characteristic of the German investment industry is the distinction of retail funds (known as Publikumsfonds ) and institutional funds (known as Spezialfonds ). Retail funds are offered primarily to private households, although institutional investors are allowed to invest in this asset class. In contrast, institutional funds are only accessible to institutional investors, which must be legal entities. Institutional funds serve as a way of outsourcing the management of the assets of insurance companies, commercial banks, or pension funds within the framework of the German investment regulation. A second peculiarity is attributable to the investment objectives. German investment management companies offer security funds investing in equities, fixed income, money market instruments, or a portfolio of these basic asset classes. They are also allowed to offer open-end real estate funds, which invest in portfolios of income producing properties. By the end of 2007, the total assets under management of mutual funds launched according to German investment law amounted to EUR 1.03 bn, of which 65% were institutional funds and 10% were open-end real estate funds. Following this taxonomy, for our (balanced) sample of 40 German investment management companies table 1 reports the assets under management invested (AuM) in these types of mutual funds (security-/ real-estate-funds and retail-/ institutional funds) as a fraction of the AuM of the total industry. Our primary sources for data are the yearly balance sheets and the profit and loss statements of the various investment management companies. Due to a lack of data on assets under management for institutional funds before 2002, the sample period begins in 2002 and ends in Although data is available on total assets under management and on assets under management for retail funds over a longer time period, this is not the case for the assets under management for institutional funds. Since we distinguish output into retail and institutional funds for the reasons stated in section 3.2, we cannot extend the data further back in time. 144 sbr 65 April

9 Scale and Scope Economies Table 1: Representativeness of the Sample as Share (in %) of Assets under Management Year Sample Security Product type Real Estate Investor category Retail Institutional Mean All numbers describe assets under management of the investment management companies in our sample as percentage of total assets under management of the investment industry in Germany. The data on the assets under management for the investment management companies in the sample are provided by the Bundesverband für Investment and Asset Management (BVI). The German central bank provided data on assets under management for the entire German investment industry. The shares for product type and investor category do not add up to 100, because investment management companies in Germany may offer both security and real estate funds to both retail and institutional investors. The sample covers, on average, 65% of the German investment industry (see Table 1). While the coverage for providers of security funds rises during the sample period, from 68% to over 80%, the already lower coverage for real estate fund providers decreases from 44% to 33%. The coverage of funds offered to retail and institutional investors is similar with 66% and 65%, respectively. To provide further information about the representativeness of our data set, Table 2 reports the average values of AuM and mean numbers of funds offered by investment management companies, for our sample and for the entire German investment industry. For example, in 2007 an investment management company in our sample (the entire industry) administered on average (77.13) mutual funds, whereby the size of funds for retail investors amount to EUR 5.84 billion (4.53 billion). Table 2 shows that the companies in our sample are on average larger in size and offer a greater number of funds than does the average German investment management company. This result is valid for both product types (security and real estate funds) and for both investor categories (retail and institutional) over the whole sample period. Hence, our results may overstate scale economies and extrapolating to the German investment industry should be done with caution. sbr 65 April

10 A. Schaefer/R. Maurer Table 2: Comparison of the Sample with the Entire German Investment Industry (Mean Values) Year Panel A: Industry Assets under management (in EUR bn) Retail Institutional Security Real Estate No. Funds Panel B: Sample All numbers are the equally weighted mean values across number of investment management companies of the respective variables. Assets under management are reported in billion (= 10 9 ) of Euros. The data on the assets under management for the investment management companies in the sample are provided by the BVI. The German central bank provided data on assets under management for the entire German investment industry. Investment management companies in Germany may offer both security and real estate funds to both retail and institutional investors. 3.2 Description of Variables The value chain provided by investment management companies can be broadly grouped into the following categories: research and portfolio management, trading and execution, accounting and reporting, customer services as well as marketing and distribution. The production of these services causes costs. These costs are covered by unit holders, who pay front-end loads which are usually expressed as a percentage of the unit value and deducted when an investor buy fund units. Periodic management fees are paid out of the fund s assets to the investment management company. In addition some expenses are directly debited to the fund assets. In Germany, transaction costs in trading the fund assets are directly debited to the individual fund. The same procedure applies to the costs for reporting and auditing. Therefore, cost savings in these activities due to scale and scope economies are directly reflected on the fund level. 146 sbr 65 April

11 Scale and Scope Economies Distribution costs occur through sales commissions to compensate brokers (mostly retail banks) who sell the fund units. To cover these costs, investors pay brokers a frontend load and/or a periodic distribution fee. The front-end load is usually paid directly from the investor to the selling broker when they buy fund units. Sometimes the investment management company pays a periodic distribution fee to the broker out of the annual management fee. Thus, costs for distribution are also reflected on the level of the individual fund. The main costs that accrue at the level of the investment management company are for research and portfolio management, accounting, customer services and marketing. To complete these activities, personnel and information technology, which are the main cost drivers for investment management companies, are necessary. Since the investment management company may use established data processing capacities and personnel resources for the administration of various mutual funds, irrespective of the size and the type of the funds, these are the costs we analyze for economies of scale and scope. We refer to these costs as operating costs and use them as dependent variable y in the estimation of equation (1). The output variables are the assets under management of retail (q 1 ) and institutional funds (q 2 ). The two control variables are the number of funds issued (h 1 ) and the share of real estate funds in the assets under management (h 2 ). The time trend is denoted by t. All monetary values are expressed in real terms with base year 2005 using the Consumer Price Index (CPI) deflator reported by the German Federal Statistical Office. In the following we describe each of these variables in more detail. Operating costs (OpCosts): Operating costs are the sum of operating expenses, commission expenses, and depreciation on fixed assets. Operating expenses which comprise material costs, salaries, and the depreciation on fixed assets, can be considered as the fixed costs component of assets under management. Commission expenses consist of the fees paid by the investment management company for third-party portfolio management or advisory services. These fees are primarily based on assets under management and thus can be considered as variable costs. The sources for the data on operating expenses, commission expenses, and depreciation on fixed assets are the profit and loss statements of the individual investment management companies. Assets under management (AuM): The assets under management of retail funds (AuM Ret) represent the sum of the assets under management of retail security and retail real estate funds. The assets under management of institutional funds (AuM Inst) is the sum of institutional security and institutional real estate funds issued by the respective investment management company. Security funds comprise equity, fixed income, money market and other (e.g. mixed assets) funds. We use assets under management for retail and institutional funds as output variables. We focus on these broad output categories because there are no data on assets under management for institutional money market, fixed income, or equity funds. We note that we could have restricted our sample to investment management companies that offer only retail funds, but this restriction has two drawbacks. First, we would have to ignore a major part of sbr 65 April

12 A. Schaefer/R. Maurer the business of German investment management companies. Second, this restriction would result in a substantial reduction in our sample size, since 33 out of 40 companies offer both retail and institutional funds. The data on assets under management is provided by the Bundesverband Investment und Asset Management (BVI). As alternative output variables we might use the number of funds or aggregate performance measured by the change in assets under management not caused by fund inflows or outflows. But to a large extent, the underlying economic mechanisms that cause changes in the number of funds or aggregate performance are captured by the assets under management. The issuing of a new fund results in an inflow of new money and thus increases the assets under management. The only exception occurs when all money flowing into the new fund is withdrawn from another fund offered by of the same investment management company. It is further reasonable to assume that closing or merging of funds corresponds in an outflow of assets under management. Therefore, to a certain degree a change in the number of funds is reflected in the change of assets under management. A correlation of 0.86 between the number of funds and assets under management in our sample suggests that assets under management are indeed a reasonable proxy for the number of funds. Due to the lack of data on inflows and outflows for some of the investment management companies in the sample, we cannot use aggregate performance as output variable. But since performance is reflected by a change in assets under management, it is reasonable to assume that assets are also a appropriate proxy for performance. We distinguish outputs between the assets under management for retail and for institutional funds in our sample because as figure 1 shows, there are only a few companies offering either retail funds, (figure 1(a)), or institutional funds (figure 1(b)). In contrast to the investor groups the majority of German investment management companies almost exclusively issue either security or real estate funds (see figure 1(c) and figure 1(d)). Therefore, to facilitate the calculation of a meaningful measure of economies of scope, we restrict the outputs to retail and institutional funds. Furthermore, as mentioned above, providers of real estate funds are under-represented in our sample. Hence the use of real estate funds as output would bias our results by placing too much emphasis on security funds. To take into account the differences between security and real estate funds, we include the share of real estate funds in the total assets under management as a control variable. Number of funds (No. Funds): To account for the influence of the number of funds offered by a specific company on operating costs, we include this figure as a control variable. Again, our data source is the statistics from the BVI. Share of Real Estate Funds (Share RE): We include the share of real estate funds in the assets under management as a control variable to account for the heterogeneity of the two product types of security and real estate funds offered to investors. We note that due to the heterogeneity of the underlying property portfolios, there is less standardization in the management of real estate funds. 148 sbr 65 April

13 Scale and Scope Economies Figure 1: Percentages of Companies Issuing Exclusively a Single Fund Type 100 (a) Retail funds % of companies Year 100 (b) Institutional funds % of companies (c) Security funds Year % of companies Year 100 (d) Real Estate funds % of companies Year These figures display the percentages of investment management companies in the sample that offer only one fund type. The number of observations is 240. Figure (a) shows the percentage of companies that issue only retail funds; figure (b) displays the percentage of companies that provide only institutional funds; figure (c) presents the proportion of companies that only offer security funds; figure (d) shows the percentage of companies that issue only real estate funds. Investment management companies in Germany can offer both security and real estate funds to both retail and institutional investors. sbr 65 April

14 A. Schaefer/R. Maurer Time trend: We account for changes in the dependent variable that are attributable to technical progress by including linear and squared time trends. We use the assets under management in each year to divide the sample into four size quartiles, using the 25% quantile, the median, the 75% quantile, and the maximum value as boundaries. Therefore, size quartile 1 contains all companies with assets under management greater than zero and lower or equal to the value of the 25% quantile, size quartile 2 contains all companies with assets under management greater than the 25% quantile and lower or equal than the median value and so forth. In the following, we refer to the four size quartiles as size classes. Table 3: Descriptive Statistics of the Sample Variable Operating Costs (in EUR mn) Assets under Management (in EUR bn) Assets under Management Retail Funds (in EUR bn) Assets under Management Institutional Funds (in EUR bn) Number of Funds Share of Real Estate Funds (in %) Sample (126.48) (17.79) 5.46 (10.28) 9.12 (13.40) (145.94) (43.14) Size class (6.33) 2.13 (1.06) 0.65 (0.50) 1.48 (1.17) (24.32) (32.37) (14.36) 5.41 (1.09) 2.94 (2.26) 2.47 (2.12) (25.75) (49.46) (31.81) (2.75) 5.08 (4.38) 5.83 (4.90) (59.75) (43.74) (208.93) (19.07) (17.69) (16.34) (172.55) 6.67 (25.15) Reported are the equally weighted mean values across investment management companies and over time. The number of observations is 240. The standard deviations appear in parentheses below the mean values. All Euro amounts are expressed in real terms with the base year Operating costs (OpCosts) are the sum of commission expenses, operating expenses including material costs and personal expenses as well as depreciation on fixed assets. Assets under management (AuM in billion = 10 9 ) are the sum of assets under management of security and real estate funds offered to retail and institutional investors. Assets under management for retail funds (AuM Ret) and assets under management for institutional funds (AuM Inst) represent the sum of assets of security and real estate funds offered to retail or institutional investors, respectively. Number of funds (No. funds) is the sum of security and real estate funds offered to retail and institutional investors. The share of assets in real estate funds (Share RE) is the fraction of assets under management of retail and institutional real estate funds on total assets under management of the respective investment management company. The data on operating costs is taken from the profit and loss statement. The data on the assets under management and the number of funds are provided by the BVI. Size class 1 comprises all companies with AuM greater than zero and lower or equal to the value of the 25% quantile, size class 2 contains all companies with AuM greater than the 25% quantile and lower or equal than the median value, size class 3 all companies with AuM greater than the median value and lower or equal to the 75% quantile, and size class 4 the remaining companies with AuM above the 75% quantile. Investment management companies in Germany can offer both security and real estate funds to both retail and institutional investors. 3 The compositions of the size classes are relatively stable over time. On average more than 75% of the investment management companies remain in their size classes. 150 sbr 65 April

15 Scale and Scope Economies Table 3 contains descriptive statistics for our variables for the whole sample and for the four size classes. Table 3 shows, that there is a clear size trend in operating costs for AuM. The development of the number of funds issued for the different size quartiles corresponds to the development of the assets under management for our two output categories. Only from the first to the second size class is there a slight decline in the number of funds. The explanation is because the higher share of real estate funds in size class 2 exhibit higher average assets under management than do the security funds. The investment management companies in the highest size class are dominated by companies that offer institutional security funds. In contrast, their share of real estate funds is negligible. Since the asset management business for institutional investors allows only low margins compared to retail funds (i.e. low management fees for AuM), the existence of size effects in operating costs has key importance for the profitability of these companies. 4 Empirical Results 4.1 Economies of Scale Table 4 column 1 of panel A reports the equally weighted mean values for the economies of scale measure RSCE for the whole sample and for the different size classes. We exclude observations for which the estimated costs, using equation (1), are negative; out of our 240 observations, this procedure results in the exclusion of three observations that have negative estimated costs. To determine the significance of the RSCE measure, for each investment management company in each year we test the null hypothesis H 0 : RSCE = 1 against the alternative hypothesis H 1 : RSCE 1. Columns two to four in panel A of Table 4 report the percentages of observations in the sample and in the respective size classes for which RSCE < 1 and for which the null hypothesis can be rejected at the 1%, 5% and 10% levels of significance. The value of 0.71 in column 1 panel A indicates, there are economies of scale for the total sample. To put this value into perspective, we consider the numbers for operating costs and AuM given in Table 3. Using these numbers, an RSCE of 0.71 corresponds to an average increase in costs of EUR 0.48 mn (which is approximately 0.7% of total operating costs) for a 1% increase in the average assets under management of approximately EUR 146 mn. Columns two to four show that the economies of scale measures are only statistically significant for about one third of observations in the sample. Yet none of the companies in our sample exhibit statistically significant diseconomies of scale. sbr 65 April

16 A. Schaefer/R. Maurer Table 4: Economies of Scale and Scope Panel A: Economies of scale RSCE Percentages of companies 1% 5% 10% Sample Size class Size class Size class Size class Panel B: Economies of scope SCOPE Percentages of companies 1% 5% 10% Sample Size class Size class Size class Size class Reported are equally weighted mean values over the sample period and across the investment management companies of the total sample as well as of the respective size quartiles. The first column in panel A contains the values of the ray scale elasticity measure (RSCE). Observations are excluded for which the estimated costs using equation (1) are negative. The number of observations is 237 out of 240. Columns two to four in panel A show the percentages of investment management companies with a p-value of 1%, 5% and 10% or lower for testing the null hypothesis H 0 : RSCE = 1 against the alternative H 1 : RSCE 1 and for which RSCE < 1. The first column in panel B contains the values of the standard scope measure (SCOPE). Observations are excluded for which the estimated costs for the respective company and its hypothetical companies using equation (1) are negative and for which only one fund type is issued. The number of observations is 154 out of 240. Columns two to four in panel B show the percentages of investment management companies with a p-value of 1%, 5% and 10% or lower for testing the null hypothesis H 0 : SCOPE * = 0 against the alternative H 1 : SCOPE * 0 and for which SCOPE * > 0. Our result of the estimated scale economies metrics for the entire sample is qualitatively in line with previous studies on scale economies on the level of investment management companies. For two different model specifications, both of which use assets under management as output measures, Baumol et al. (1990) report scale economies of and The difference in the results might be due to the authors focus on investment management companies that offer money market funds, while the companies in our sample mainly provide equity, fixed income, and real estate funds. Bonanni, Dermine, and Röller (1998) present scale economies in the range of 0.2 to 1.33, and Dermine and Röller (1992) estimate ray scale elasticities between and The sample of both studies consists of French investment management companies that were dominated by money market funds. Collins and Mack (1997) report a scale measure of 152 sbr 65 April

17 Scale and Scope Economies for their sample based on the entire US mutual fund industry. With the exception of real estate funds, the sample of Collins and Mack (1997) resembles our sample in that equity funds are the major fund type, followed by fixed income funds. Looking at the average scale measures for the different size classes, there is a clear size trend: the higher the level of assets under management, the lower the scale economies, i.e. the higher the values of RSCE. Using the numbers for operating costs and assets under management displayed in Table 3 for the four size classes results in a 0.71% cost increase of EUR 0.05 mn for a 1% increase in assets under management of EUR 20 mn for size class 1 and in a 0.71% cost increase of EUR 2.0 mn (which is approximately 1% of total operating costs) for a 1% increase in assets under management of EUR 400 mn for size class 4. Of particular interest are the results for the percentages of observations with statistically significant economies of scale reported in columns two to four. Almost all investment management companies in size class 1 are characterized by statistically significant scale economies. For size class 2 only 30% of the observations exhibit significant scale economies whereas the largest 50% of the companies in our sample exhibit no statistically significant scale economies at all. The drop in the percentage from size class 1 to 2 might be explained by the large share of real estate funds offered by the companies in size class 2. The results for the size classes differ from the results reported in prior research. Although Baumol et al. (1990) do not report economies of scale for different size classes, in both specifications with assets under management as outputs all companies in their sample exhibit statistically significant economies of scale at a level of at least 5%. Bonanni, Dermine, and Röller (1998) find diseconomies of scale for the class with the largest investment management companies. Collins and Mack (1997) obtain similar results. Dermine and Röller (1992) report scale economies for all size classes. These differences might be due to the differences in the sample structure. The major differences between our sample and the ones in the studies cited above are the existence of separate fund categories for institutional clients and for investing in real estate. Figure 2(a) shows that our findings are valid for the whole sample in each year of the sample period. In addition, figures 2(b) to 2(e) confirm these results for all size classes. The line charts, which depict the mean values of the RSCE measure, confirm the size trend of the scale measure. In addition, the bar charts (percentages of companies with statistically significant RSCE measures less than unity at least at the 1% level of significance) validate that only small and mid-sized investment management companies exhibit economies of scale. Although size class 1 even faces a slight increase in the number of observations with statistically significant scale economies over the sample period, there is a downward trend for size class 2. For the total sample, the result of few observations with statistically significant scale economies is relatively stable. sbr 65 April

18 A. Schaefer/R. Maurer Figure 2: Economies of Scale by Size Class over the Sample Period RSCE Year (a) Sample % RSCE < RSCE % RSCE < 1 RSCE % RSCE < Year Year (b) Size class 1 (c) Size class RSCE % RSCE < 1 RSCE % RSCE < Year Year (d) Size class 3 (e) Size class 4 These figures display the results for economies of scale for each sample year from 2002 to The line charts show the results for RSCE (left-hand scale). The bar charts present the percentages of investment management companies with a p-value of 1% or less for testing the null hypothesis H 0 : RSCE = 1 against the alternative H 1 : RSCE 1 and for which RSCE < 1 (right-hand scale). We exclude observations for which the estimated costs, using equation (1), are negative. The number of observations is 237 out of 240. Figure (a) shows the results for the total sample; figures (b) to (e) display the results for size classes 1 to sbr 65 April

19 Scale and Scope Economies Figure 3: Rank-order Correlations for Economies of Scale and Scope by Size Class over the Sample Period 1 a) RSCE Rank-order correlation Rank-order correlation Year b) Scope Year These figures display the Spearman rank-order correlations (RC) for the scale and scope measures with the assets under management for the years 2002 to 2007 for the total sample. Figure (a) shows the rank-order correlations for RSCE. Observations are excluded for which the estimated costs, using equation (1), are negative. The number of observations is 237 out of 240. Dots indicate significance at least at the 1% level for testing the null hypothesis H 0 : RC 0 against the alternative H 1 : RC > 0 whereas a cross indicates no significance. Figure (b) shows the rank-order correlations for SCOPE. Observations are excluded for which the estimated costs for the respective company and its hypothetical companies, using equation (1), are negative and for companies that issue only one fund type. The number of observations is 154 out of 240. A dot indicates significance at least at the 1% level for testing the null hypothesis H 0 : RC 0 against the alternative H 1 : RC < 0 whereas crosses indicate no significance. Another method for determining the degree to which economies of scale are related to the output level is to compute the Spearman rank-order correlation (RC) between the measure of economies of scale and the size of an investment management company (see Baumol et al., 1990). The rank-order correlation between RSCE and the sum of assets under management facilitates the assessment of whether investment management companies with relatively lower economies of scale are relatively larger in size. In order to determine the statistical significance of the RC measure, we also compute the p-value for testing the null hypothesis H 0 : RC 0 against the alternative hypothesis H 1 : RC > 0. sbr 65 April

20 A. Schaefer/R. Maurer Figure 3(a) shows the equally weighted rank-order correlations across the sample period for all investment management companies. As indicated by the circles, the rank-order correlation is statistically significant greater than zero at least at the 1% level for each year. The average correlation across all investment management companies and over the sample period is This result is qualitatively in line with the rank-order correlation of for both specifications with assets under management as outputs reported by Baumol et al. (1990). 4.2 Economies of Scope Based on our estimate for ß 12 (see Table A1 in the appendix), our value for testing cost complementarities between the assets under management of retail and institutional funds is COMP = , which is not statistically significant below zero with a p-value of Yet this test is only a sufficient, but not a necessary condition for the existence of scope economies. Therefore, in panel B of Table 4 we report the results for the SCOPE measure for the entire sample and the various size classes. We exclude observations for which the estimated costs, using equation (1), for the investment management company and its corresponding hypothetical company are negative. Furthermore, we do not calculate the scope measure for companies that issue only one type of our defined outputs. Out of our 240 observations this procedure results in the exclusion of 82 observations due to negative estimated costs and of 43 observations due to the investment management company issuing only one fund type. Since there are observations which fulfill both of these exclusion criteria, the total loss of observations is 86 which leaves us with 154 observations. To derive the statistical significance of the scope measure, for each investment management company in each year we test the null hypothesis H 0 : SCOPE = 0 against the alternative hypothesis H 1 : SCOPE 0. In panel B of Table 4 columns two to four we report the percentages of companies in the entire sample and in the respective size class for which the null hypothesis cannot be rejected at least at the 1%, 5% and 10% level of significance. The scope measures for all size classes are positive, indicating economies of scope between the assets under management of retail and institutional funds. The relative value of 0.37 for the sample corresponds to an absolute increase in costs of EUR 25 mn by managing the same assets under management in two separate investment management companies. This number reflects the high share of fixed costs in total operating costs for German investment management companies, which would be incurred twice by offering both product types separately. Similar to the results for scale economies, the scope measure is only statistically significant for about one-third of observations in our sample. The existence of economies of scope is qualitatively in line with the previous studies. Depending on the specification of the model, Baumol et al. (1990) report scope economies either for all or for two thirds of the companies in their sample. Bonanni, Der- 156 sbr 65 April