The efficiency of mutual fund companies: Evidence from an innovative network SBM approach

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Omega ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Contents lists available at ScienceDirect

Omega journal homepage: www.elsevier.com/locate/omega

The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach$ Carlos Sánchez-González a, José Luis Sarto b, Luis Vicente b,n a b

University Espíritu Santo – UEES. UEES Business School, Km 2,5 Vía La Puntilla, EC091650 Samborondón, Ecuador Department of Accounting and Finance, University of Zaragoza. Faculty of Economics and Business Administration, C/ Gran Vía 2, 50005 Zaragoza, Spain

art ic l e i nf o

a b s t r a c t

Article history: Received 29 October 2015 Accepted 22 October 2016

This paper is the ﬁrst DEA (Data Envelopment Analysis) evaluation of the efﬁciency of a sample of mutual fund companies in a large Euro fund industry, i.e. Spain. Our novel network model links the efﬁciency of the core activities (portfolio management and marketing/distribution) of a mutual fund company to the efﬁciency of its operational management function. Our results highlight the important networking effects at the marketing stage and question the prime role of portfolio management skills in the overall efﬁciency of a mutual fund company. The evaluation of robust efﬁciency clusters indicates that the efﬁciency rankings obtained with our network model persist signiﬁcantly along our sample period. Finally, the application of the SBM (Slacks-Based Measure) Variation III to our network model allows us to identify a large number of globally inefﬁcient but locally efﬁcient companies with reference to competitors with similar management resources. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Mutual fund companies Network DEA SBM variations Portfolio management efﬁciency Marketing efﬁciency Operational management efﬁciency

1. Introduction While an extensive body of DEA literature has been devoted to banking and insurance, the efﬁciency of mutual fund companies has scarcely been studied. Berger and Humphrey [4], Berger [5], Fethi and Pasiouras [20] and Paradi and Zhu [43] review DEA applications for recent decades in the banking industry across different techniques and countries. We ﬁnd an increasing amount of DEA research on individual mutual fund performance since the original contribution of Murthi et al. [41],1 whereas only Zhao and Yue [57] and Premachandra et al. [44] use DEA to assess the relative efﬁciency of mutual fund companies in China and the US, respectively. Despite the importance of fund families for investors’ decisions (e.g., [37,32]), the literature review on methodologies other than DEA techniques ﬁnds that research at the individual fund level is far more extended than that at the fund family level.

☆

This manuscript was processed by Associate Editor Kao. Corresponding author. E-mail addresses: [email protected] (C. Sánchez-González), [email protected] (J.L. Sarto), [email protected] (L. Vicente). 1 These new DEA measures that assess the relative efﬁciency of individual funds with multiple inputs and multiple outputs may be considered as an alternative approach to traditional performance models that assume functional relationships between return and risk (e.g., [52,47,33]). Lamb and Tee [38] discuss the possible shortcomings of these DEA techniques in evaluating the performance of individual investment funds and provide further research topics for this ﬁeld. n

Premachandra et al. [44] address that this scarce literature at the mutual fund company level is possibly due to the intricate nature of the analysis involved. The core activities of these ﬁnancial institutions require speciﬁc models and variables that differ from the well-known banking and insurance models. These interactions between the business unit decisions made by mutual fund companies require a more sophisticated approach than merely aggregating the variables used to evaluate individual mutual funds.2 Some of these decisions are related to the number of mutual funds managed by the company, the fund types supplied by the company to the market, the outsourcing of management and selling of funds, etc., which will result in rather different operational strategies and efﬁciency consequences for the fund companies. Our study ﬁlls this gap in the literature by analysing a major Euro mutual fund industry for the ﬁrst time. Based on the governance structure addressed by Berkowitz and Qiu [6], we assess the relative efﬁciency of a comprehensive sample of Spanish mutual fund companies. We propose an innovative network slacks-based model [51] that includes several linking variables to address the interactions between the core competencies of a mutual fund company. Similarly to Zhao and Yue [57] we divide the core business of a mutual fund company into a portfolio 2 This is not an exclusive issue of mutual funds. Examples of multifaceted interactions captured through network DEA models are also provided in other nonﬁnancial ﬁelds of study (e.g., [26]).

http://dx.doi.org/10.1016/j.omega.2016.10.003 0305-0483/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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2

management stage and a marketing stage. However, Zhao and Yue [57] omit any ﬂuent interaction between both core competencies in their multi-subsystem fuzzy DEA approach. According to this core business, the company attempts to enlarge its asset value continually by obtaining positive portfolio returns and net money ﬂows into the mutual funds managed by the company. But that is not enough to address the overall efﬁciency of the company because both core competencies must be operationally developed, thereby affecting the ﬁnal proﬁts earned by the company's shareholders. Our model also includes this responsibility of the company to its shareholders; therefore, its operational management efﬁciency interacts with the efﬁciency of both portfolio management and marketing core competencies and the ﬁnal proﬁts earned by the company. In other words, the mutual fund company delegates responsibility for managing and selling its mutual funds to either external or internal agents to enlarge its total net asset value and thereby earn the highest fees with the least amount of marketing and management expenses. This approach is also present in the general two-stage DEA model proposed by Premachandra et al. [44], in which the overall efﬁciency of a fund company is decomposed into operational efﬁciency and portfolio efﬁciency components. However, their operational function does not detail the inﬂuence of both core activities on the net asset value of the company. Our network structure identiﬁes the efﬁciency of the core competencies separately and their links with the operational efﬁciency. Hence, our model answers these interacting questions: How efﬁcient is the portfolio management core process of a fund company? How efﬁcient is the selling core process of mutual fund units? How efﬁcient is the operational management function of a fund company? Our model considers that investors make their decisions based on an asymmetric perception of prior performance, i.e., unitholders invest disproportionately more in funds that performed well the prior period (e.g., [31,48,15,19]). Thus, our model captures the fact that portfolio management outputs may be understood as intermediate inputs in the selling process of mutual funds. This link between portfolio management and marketing and the link between both core activities and the operational function of the company aim to determine the contribution of each activity to the overall efﬁciency of the fund company. Hence, our approach is oriented towards both the management of the company and the investors and it should highlight the interest of the company's stakeholders in our model. First, mutual fund managers and sellers should be interested in our results because they are the main agents involved in the core activities of the company. Moreover, mutual fund unitholders should pay attention to how the company is managing and selling the mutual funds where they invest their money. Do unitholders invest in mutual funds that perform well? Or do they invest in mutual funds only as a result of a brilliant selling process? Finally, the company's shareholders should pay attention to the operational management efﬁciency as a key determinant of the ﬁnal proﬁts earned by the fund company. The paper is organised as follows. Section 2 includes the background of our study. Section 3 discusses our network model. Section 4 presents the sample and the variables used in our model. Section 5 shows the empirical results, and Section 6 summarises the major ﬁndings.

2. Background By the end of 2013, the Spanish fund industry was ranked fourth in the Euro Zone fund industry in terms of the number of mutual funds and ﬁfth in assets [17]. The top 5, the top 10 and the top 25 of the existing 81 Spanish fund companies control 55%, 74%

and 92% of the total fund assets of the Spanish fund market, respectively [29]. If we compare these ﬁgures with the US mutual fund industry, we ﬁnd that competition in Spain is much more concentrated than that in the largest fund market in the world, where the top 5, the top 10 and the top 25 out of the existing 801 US companies manage approximately 40%, 53% and 72% of the total assets of the US fund industry in 2013, respectively [30]. Furthermore, the Spanish market has an average Herﬁndahl– Hirschman Index of 0.1001 for the last ﬁfteen years, which is double that in the US market (0.0481) as of December 2013. Previous DEA research on the efﬁciency of mutual fund companies does not discuss how market concentration may affect their models and results, thereby highlighting the interest of efﬁciency studies on concentrated markets different from the well-known US fund industry. Traditional DEA techniques may fail to identify the appropriate ‘best practice’ competitors when the reference frontier is formed by companies with extremely different characteristics than the target company to be analysed. This limitation might call into question the accuracy of DEA results in the industries with assorted competitors, such as the Spanish mutual fund industry. Premachandra et al. [44] consider only US fund companies with total assets under management of at least $1 billion USD. As a consequence, 97 out of the 198 US fund families with a residual market share are dropped from the original sample. Zhao and Yue [57] do not report any standard by which they select their Chinese fund companies. Considering that DEA efﬁciency scores are obtained relative to all the competitors within the sample, the exclusion of any fund company from the analysis may involve biased results. In other words, the systematic exclusion of fund companies from the ﬁnal sample based on size requirements will result in a partial evaluation of the target industry, which could be extremely biased in markets that are more concentrated than the US fund industry. Our approach overcomes this partial evaluation problem in two ways. First, we do not exclude any fund company based on minimum size conditions, which allows for the evaluation of the whole set of competitors. Second, Variation III of the slacks-based measure (SBM) model [50] allows us to identify ‘locally efﬁcient’ companies, deﬁned as efﬁcient companies in reference to a cluster of competitors with similar management resources. This approach is related to the study of meta-frontiers and cluster-frontiers with respect to efﬁciency performance measurement (e.g., [42]). The major novel aspect of this variant is the comparison of companies with homogeneous frontiers, which makes it to be a more suitable approach in fund industries with assorted management resources. This innovative SBM variation overcomes the potential sensitivity of our model to those companies with signiﬁcantly different management resources than the competitors that are included in the reference frontier.

3. The network model 3.1. The network approach to efﬁciency Based on Farrell [18], the seminal paper of Charnes et al. [9] developed DEA as a nonparametric methodology to estimate efﬁciency frontiers. This technique has been extensively used to evaluate the relative efﬁciency of ﬁnancial institutions, possibly due to the lack of any restrictions on the functional form between the multiple inputs and outputs allowed in this multidimensional framework. The selection of inputs and outputs in DEA, however, is largely controversial, particularly in the banking literature. The well-known disagreement as to the role of the deposits in the bank production process (deposit dilemma) may create inconsistency in the efﬁciency results across the two major approaches

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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the real dynamics of mutual funds. TNAi;t þ 1 ¼ TNAi;t 1 þ Ri;t þ 1 þ MF i;t þ 1

Portfolio Decision Portfolio Manager W Management Company OE

mNAV

Mutual Fund (1-m)NAV (NAV)

Unitholders

mNAV-W-OE Shareholders

Fig. 1. The mutual fund structure proposed by Berkowitz and Qiu [6]. OE is the operating expenses of the company, W represents the wages received by the portfolio manager, m is the management expense ratio of the company, and NAV is the net asset value of the mutual fund.

to treating bank liabilities: the production approach and the intermediation approach. Fethi and Pasiouras [20] provide a relevant survey about the selection of inputs and outputs in the banking literature. Recent applications to ﬁnancial institutions develop network DEA models that help to evaluate the efﬁciency of each component of the whole management process. These models incorporate intermediate variables that link the different management stages of the ﬁnancial institutions. As a result, these intermediate measures are considered neither pure inputs nor pure outputs, thereby helping to solve the substantial controversy concerning the proper selection of inputs and outputs. Kao [36] classiﬁes ﬁve types of network structures in an exhaustive review of the network DEA models used in the literature: series, parallel, mixed, hierarchical, and dynamic. These authors ﬁnd that ﬁnancial institutions have the largest number of network applications, which are mostly conducted by series structures. Recent studies in this area include, Kao and Hwang [35], Chen et al. [10], Fukuyama and Weber [21], Zha and Liang [56], Holod and Lewis [27], Yang and Liu [55], Wu and Birge [54], Akther et al. [1] and Avkiran [2,3]. Our network approach to efﬁciency is based on the governance structure proposed by Berkowitz and Qiu [6]. Fig. 1 illustrates how a fund company is responsible to its shareholders and pays either an internal or external agent to manage its mutual fund portfolios. These management decisions will affect the net asset value of the mutual fund. The results of this portfolio management will be provided to fund unitholders after subtracting the company's management expenses to recover wages paid to the managers and other operating expenses. As a result, the company's shareholders will receive the ﬁnal proﬁts of this structure. However, this representation omits any inﬂuence of the marketing and selling activities on the net asset value of the mutual fund and on the management incomes earned by the company. Omitting marketing efforts to increase net money ﬂows into the mutual fund, deﬁned as the net of all money inﬂows and outﬂows after fund sales, redemptions and exchanges, could severely bias this framework because it ignores one of the main determinants of the fees earned by the company. This bias might be particularly relevant in industries in which the management fees are largely based on assets under management instead of performance-based fees, such as in Spain [16]. We overcome this bias by modelling both the portfolio management and the marketing as linking core activities to explain the assets under management of a fund company. The following expression,3 which has been largely used in the literature on mutual fund ﬂows (e.g., [58,46]), reﬂects quite well the core competencies of a mutual fund company that attempts to increase its total assets by means of both portfolio returns and money ﬂows from the market. This expression maps our network model with 3

A more reﬁned version of expression (1) corrects the increase in total assets due to fund mergers during period tþ 1.

3

ð1Þ

where TNAi,t is the total net assets of fund i at the end of period t; Ri,t þ 1 is the return obtained by fund i during period tþ1; and MFi, t þ 1 is the net money ﬂows into fund i during tþ 1. Money ﬂows into the mutual fund are obtained through the selling activities of the company, but these activities cannot be considered an independent stage of portfolio management because the results of these portfolio decisions inﬂuence investors’ purchase and sale of mutual fund units.4 Expression (1) denotes that the asset-based fees earned by the company depend on portfolio returns and on the selling process of mutual fund units. In addition, the efﬁciency of the operational cost structure, which includes portfolio management and marketing costs, in obtaining the highest returns and the largest money ﬂows will determine the ﬁnal proﬁts received by the company shareholders. Thus, an efﬁcient company obtains higher mutual fund returns and larger money ﬂows with fewer costs than the competitors. 3.2. The model Our model (Fig. 2) illustrates the management interactions within a mutual fund company j as a network structure with three relevant management activities: Portfolio Management Stage, Marketing and Selling Stage, and Operational Management Stage (hereinafter referred to as the Portfolio Stage, the Marketing Stage, and the Operational Stage, respectively). This network approach assumes the management process proposed by the governance structure of Berkowitz and Qiu [6] previously shown in Fig. 1. Our network model completes previous DEA structures in fund companies [57,44] by detailing more clearly the links existing between core competency activities and their inﬂuence on the efﬁciency of the operational structure of the company. Dimensionality curse problems might arise in our model as a result of these additional link variables. However, according to Coelli et al. [12], we easily meet the DEA convention that the minimum number of companies must be greater than three times the number of variables. According to Kao [36], our network model corresponds to a series structure, which thus generalises the two-stage structure previously proposed by Premachandra et al. [44]. Note that Premachandra et al. [44] consider operational management as a previous stage to portfolio management because the ﬁnal objective of this two-stage problem is to obtain the highest company portfolio return, whereas we extend this two-stage model to incorporate how the core activities of a fund company inﬂuence the ﬁnal proﬁts earned by the company's shareholders. Thus, this network approach is valid and generalizable for those efﬁciency models that incorporate the responsibility of a fund company to its shareholders as a relevant part of the governance structure of a company. The lack of this responsibility in the model could drive biased results and conclusions due to an incomplete model speciﬁcation. At the Portfolio Stage, labour (Lj) and capital resources (SEj) of the company assume a speciﬁc level of risk (PRj) to obtain higher gross returns (GRj) in as many mutual funds (NFj) and fund types (FTj) as possible. The rationale behind this stage is that a company with efﬁcient portfolio management skills is able to obtain higher gross returns than a competitor in terms of lower levels of risk for a large and well-diversiﬁed supply of mutual funds without assuming extra personnel expenses and capital resources. Several 4 Ferreira et al. [19] provides innovative evidence by analysing the ﬂowperformance relationship across 28 markets. and for the extensive literature on ﬂow determinants in the US fund market.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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Labour (Lj) Capital (SEj) Risk (PRj)

Portfolio Management Stage Net Returns (NRj)

Link Number of Funds (NFj) Fund Types (FTj) Link Gross Returns (GRj)

Marketing and Selling Stage

Unitholders Flows (UFj)

Link Money Flows (MFj)

Total Assets (TAj)

Operational Management Stage

Profits (Pj)

Fig. 2. Network representation of mutual fund companies. Lj, SEj, PRj are the input variables at the Portfolio Stage; NRj is the input variable and UFj is the output variable at the Marketing Stage; TAj is the input variable and Pj is the output variable at the Operational Stage. There are also four linking variables (dotted lines). NFj, FTj are outputs at the Portfolio Stage that are used as inputs at the Marketing Stage; GRj is an output at the Portfolio Stage that is considered an input at the Operational Stage; and MFj is an output at the Marketing Stage that is used as an input at the Operational Stage.

assumptions are drawn from this rationale. First, similarly to Zhao and Yue [57], we assume that companies with a diversiﬁed supply of funds require more management resources than companies with few and less diversiﬁed funds. In our sample, the type and number of funds is strongly correlated with the personnel and capital resources of the Spanish fund companies [29]. Second, the personnel and resources of the company are mainly involved at the Portfolio Stage. These hypotheses make sense because portfolio management outsourcing is a rare practice in our sample. In 2016, less than 1% of Spanish mutual funds are subadvised by external managers (Morningstar Direct). These assumptions are not only context speciﬁc to Spain and may be generalizable for a wide range of fund industries in the world. The delegation of portfolio management responsibilities to external subadvisors has grown considerably in the US fund market5 over the last decade, but it is still residual in Europe. In 2016, less than 13% of European open-end funds are subadvised by external managers (Morningstar Direct). Finally, contrary to Premachandra et al. [44], turnover ratio is missing in our model because we do not assume that higher levels of active portfolio management are paid off with higher returns. Malkiel [40] ﬁnds strong evidence that supports passive management for a wide range of markets and securities, thereby questioning that fund managers should follow active strategies to get higher returns than passive strategies. At the Marketing Stage, the fund company attempts to gain unitholders (UFj) and money ﬂows (MFj) from the market into every fund managed by the company. As a consequence of the universal banking model in Spain, this selling process in our sample is commonly outsourced in the front ofﬁce of banks and 5 There are different types of subadvisory arrangements according to the contracts registered. Independent Directors Council [28] explores the practices related to subadvisory agreements in the US market. In those fund industries where the labour and management resources are largely subadvised, these inputs can be easily replaced in our model by the subadvising costs of the company. Thus, the rationale of our network approach would not change.

insurance companies that mostly own mutual fund companies.6 In 2014, less than 7% of Spanish mutual fund assets are managed by independent fund companies [29]. Thus, the number and variety of mutual funds and their return records offered by the company are particularly salient to this goal. Because these mutual fund records are determined by portfolio management activities, the outputs at the Portfolio Stage are intermediate inputs at the Marketing Stage, which thereby link both core activities of the company in our network approach. However, the returns supplied to the unitholders are after management fees and other expenses which are charged by the company. Therefore, net returns ðNRk Þ rather than gross returns (GRk) are an input at the Marketing Stage. Finally, the Operational Stage represents the operational management function of the fund company. This stage aims to obtain the highest proﬁt (Pj) as possible to remunerate company shareholders. According to expression (1), the asset-based fees earned by the company are driven by gross returns (GRj) at the Portfolio Stage, by money ﬂows (MFj) at the Marketing Stage and by the assets managed by the company (TAj) at the beginning of the period analysed. In our model, we use gross returns and money ﬂows as intermediate inputs to link the Portfolio Stage and the Marketing Stage to the Operational Stage. A company with an efﬁcient operational structure will obtain higher proﬁts with fewer assets under management than its competitors, as these assets are a consequence of both portfolio management and marketing core activities.

4. Data and the methodological approach 4.1. Data, sample selection, and variable construction The data on Spanish fund companies are hand-collected from several databases. Financial data on companies are obtained from the Iberian Balance-sheets Analysis System (SABI) and the Spanish Ofﬁcial Business Registry. The information about mutual funds is obtained from the Spanish Securities Exchange Commission (CNMV) and the Spanish Association of Mutual and Pension Funds (Inverco). We initially examine all mutual fund companies and mutual funds registered in the CNMV on the 31st of December of each year included in our 2005–2012 sample period. We exclude those companies that mainly manage Real Estate Investment Funds, Open-Ended Investment Companies (SICAV), Hedge Funds and Foreign Collective Investment Schemes because these institutions may have signiﬁcantly different models of operation and the objective of our study only pertains to mutual fund companies. In addition, those companies with inception dates close to yearend are dropped from the initial year to avoid any inception bias in the model variables. A total of 44 company year-end observations are dropped from the initial sample. These exclusions represent 5% of company year-end observations and less than 1% in terms of assets managed by the Spanish fund industry. Similar to Premachandra et al. [44], we consider multiple share classes of a mutual fund as separate mutual funds existing at the end of each year of our sample period.7 Our work also assumes a minor overestimation of the efﬁciency results (survivorship bias) because 6 Nearly half of mutual fund-owning households in the US hold mutual fund shares through multiple distribution channels [30]. On the other hand, Europe is a very fragmented market according to mutual fund distribution channels [45]. Therefore, in those fund industries with alternative and relevant distribution channels, such as investment professionals, employer-sponsored retirement plans, and fund supermarkets, our network model should incorporate an additional input at the marketing stage to consider the distribution costs of these channels out of the direct relationship between the fund company and end client. 7 The consideration of share classes as separate mutual funds at the Portfolio Stage might be controversial because the portfolio is the same for all share classes.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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Table 1 Summary statistics of Spanish mutual fund companies.

Number of companies Mutual funds per company Unitholders per company Assets in million € Max. assets in million € Min. assets in million €

2005

2006

2007

2008

2009

2010

2011

2012

102 26 (43)

102 28 (48)

95 31 (53)

93 31 (54)

95 27 (42)

89 28 (41)

86 27 (40)

74 29 (41)

82,809 (255,312) 2569 ( 7966) 61,873 4.22

82,809 (260,916) 2651 ( 7964) 61,663 4.42

84,749 (241,650) 2682 ( 7416) 53,063 4.87

63,659 (177,150) 1888 ( 5287) 34,238 3.73

57,631 (154,350) 1795 ( 4849) 32,581 4.46

57,982 (144,351) 1616 ( 4034) 24,294 4.07

56,218 (136,048) 1539 ( 3755) 21,828 4.44

59,007 (128,529) 1663 ( 3633) 19,236 4.46

This table illustrates the year-end average statistics per company in our sample. Standard deviation is in brackets.

Table 2 Input, output and intermediate variables. Portfolio Stage

Marketing Stage

Inputs:

Outputs:

Labour (Lj) is the number of employees of company j on the 31st of December. Capital (SEj) is the stockholders capital in € of company j on the 1st of January. Portfolio Risk (PRj) is the fund size-weighted average of the normalised value of the standard deviation of the daily gross returns of all funds managed by company j on the 31st of December.

Number of Funds (NFj) is the number of funds managed by company j on the 31st of December. Fund Types (FTj) is the number of investment categories covered by company j on the 31st of December according to the ofﬁcial classiﬁcation of CNMV. Gross Returns (GRj) is the fund size-weighted average of the normalised value of the daily average gross returns of all funds managed by company j on the 31st of December. Outputs:

Inputs:

Number of Funds (NFj) is the number of funds managed by company j on Unitholders Flows (UFj) is the normalised value of unitholder inﬂows the 31st of December. minus unitholder outﬂows for company j from the 1st of January to the 31st of December. Money Flows (MFj) is the normalised value of the implied net money Fund Types (FTj) is the number of investment categories covered by company j on the 31st of December according to the ofﬁcial classiﬁcation ﬂows for company j from the 1st of January to the 31st of December.a of CNMV. Net Returns (NRj) is the fund size-weighted average of the normalised value of the daily average net returns (after management and custodial fees) of all funds managed by company j on the 31st of December. Operational Stage Inputs: Outputs: Total Assets (TAj) is the total assets in € managed by company j on the 1st of Proﬁt (Pj) is the normalised value of the proﬁt obtained by company j January. from the 1st of January to the 31st of December. Money Flows (MFj) is the normalised value of the implied net money ﬂows for company j from the 1st of January to the 31st of December.a Gross Returns (GRj) is the fund size-weighted average of the normalised value of the daily average gross returns of all funds managed by company j on the 31st of December. Intermediate variables are printed in bold. a We assume that these money ﬂows occur at the end of the period for which we are computing this measure. Zheng [58] determines that this approach is robust under other timing assumptions.

we only consider the mutual funds existing at the end of each year of our sample period. A total of 1557 mutual funds cease operations in our study, which is about 7% of total year-end observations and less than 1% of the total assets of our sample. Our ﬁnal sample comprises 736 company year observations, which range from a minimum of 74 mutual fund companies in 2012 to a maximum of 102 in 2005 and 2006. Table 1 shows the large dispersion of the summary statistics in our sample, thereby highlighting the assorted characteristics of the Spanish mutual fund companies. Furthermore, the yearly evolution of these statistics since 2008 provides evidence of the large impact of the worldwide crisis on the decreasing trend of the average magnitudes of the Spanish fund industry. (footnote continued) However, this issue is not important in our study because the SBM efﬁciency scores using both variables show a Spearman rank correlation that is higher than 99%.

Table 2 lists the input and output variables used in our network representation and how they are calculated. Some of these variables are obtained as the sum of the values of individual mutual funds. However, a similar approach to variables associated with return and risk might distort the accuracy of these measures. We agree with the claim by Premachandra et al. [44] that returns weighted by fund size to some extent represent the portfolio skills of a company, but the different size and return patterns of the diverse fund types covered by a company might distort the sizeweighted returns and the levels of risk associated with a company. For instance, a company specialising in equity funds might obtain upwards-biased returns in years with bullish stock markets compared with a company specialised in bond funds. Zhao and Yue [57] solve this problem by using a membership function to characterise fund types. In our case, we compare the daily average gross return for each fund existing on the 31st of December with respect to all funds in the market that are included in the same fund type and during the same period. Then, we calculate the

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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6

normalised value between 0 and 1 of these average gross returns and compute the size-weighted average of thee normalised values for each company. This annual normalisation could remove time effects from the analysis but it is really consistent across the fund types managed by a company, which provides accuracy to the annual efﬁciency rankings. We follow a similar process for the standard deviation of the daily gross returns as a measure of portfolio risk. 4.2. Methodological approach After deﬁning our network structure, we describe the suitable procedure to model this approach. We work with n fund companies (j ¼ 1, …, n) consisting of 3 stages (k ¼ 1, 2, 3). Let mk and rk be the numbers of inputs and outputs to stage k, respectively. The link from stage k to stage h is denoted by (k,h) nand the set o of links k and the by L. The inputs of company j at stage k are xkj A Rm þ n o outputs of company j at stage k are ykj A Rrþk , where (j¼1,…, n; k n¼ 1, 2, 3). o The link variables from stage k to stage h are tðk;hÞ (j¼1,…, n; (k,h) A L), where t(k,h) is the number of zðk;hÞ A R þ j items in link (k,h). λ A Rnþ is the intensity vector of stage k, and sk þ and sk- are the non-negative vectors of input excesses and output shortfalls, respectively. Premachandra et al. [44] justify the variable returns-to-scale (VRS) hypothesis, as some of the variables included in their model (e.g., returns) can be negative. This reason makes no sense for our normalised variables that have been described in Table 2. We use VRS assumption because it better evaluates efﬁciency when not all the companies operate at the optimal scale. Thus, the production possibility set P is spanned by the convex hull of the existing companies. n k k k P ¼ ðxk ; yk ; zðk;hÞ Þ= xk Z X k λ ; yk r Y k λ ; zðk;hÞ ¼ Z ðk;hÞ λ ; o h k k ð2Þ zðk;hÞ ¼ Z ðk;hÞ λ ; eλ ¼ 1; λ Z 0 k

Note that if we exclude eλ ¼ 1 from expression (2), the production possibility set P is deﬁned under the constant returns-toscale (CRS) assumption. According to Tone and Tsutsui [51], we have two major alternatives for measuring the efﬁciency of our network approach (Fig. 2) based on the original SBM model (Tone, [49])8: a Network SBM (NSBM) and a SBM-based separation model. The NSBM, proposed by Tone and Tsutsui [51], employs the weighted SBM model [13,53] to decompose the overall efﬁciency of the fund company into partial efﬁciencies for each management stage of a network structure. NSBM assumes that the overall efﬁciency is the weighted average of partial efﬁciencies where the weights are set exogenously. The original approach allows for the continuity of intermediate variables between management stages, but it does not take into account the inefﬁciency of these intermediate variables. NSBM does not integrate the slacks of the link variables individually and independently into an efﬁciency score because these slacks are only considered through link constraints. We follow one of the NSBM extensions that is also proposed by Tone and Tsutsui [51] to overcome this shortcoming. This extension incorporates slacks of the intermediate variables into the NSBM objective function.9 k

8

SBM is a non-radial model for measuring efﬁciency when inputs and outputs may change non-proportionally. The unoriented SBM version works with excess inputs and output shortfalls simultaneously and can be applied under CRS and VRS assumptions. See details of the original SBM model in Appendix A. 9 Appendix B shows the NSBM model and its extension. Section 6.1 of Tone and Tsutsui [51] offers further details.

By contrast, the SBM separation model evaluates stage efﬁciencies individually using intermediate variables as ordinary inputs or outputs, thereby omitting any continuity of linking activities. In other words, the SBM separation model computes efﬁciency scores for each stage while considering the slacks of all variables included in the model as ordinary inputs and outputs, but it does not capture the inﬂuence of the linking activities on the model. The comparison of efﬁciency scores and rankings between NSBM and the SBM separation models will be particularly important to identify what Tone and Tsutsui [51] call the “networking effects” of the model. Thus, the existence of signiﬁcant “networking effects” would validate and offer conﬁdence on the accuracy of our network model. However, Tone [50] states that the objective function expressed by the original SBM might project the evaluated company onto a very remote point on the reference frontier because SBM aims to ﬁnd the worst efﬁciency score associated with the maximum slacks under the constraints of the model (Appendix A, model A1). These remote projections can be hard to interpret in terms of appropriate efﬁciency comparisons. To overcome this limitation, Tone [50] explores the supporting hyperplanes (facets) of the production possibility set to deﬁne the existence of a facet that includes efﬁcient linear combinations of the companies analysed. In most DEA models, the production possibility set is a polyhedral convex set whose vertices correspond to the efﬁcient companies found by the corresponding DEA method. Tone [50] argues that a polyhedral convex set can be deﬁned by its vertices or by its supporting hyperplanes and suggests four variants of the original SBM, which are based on the hyperplanes instead of the vertices.10 According to this contribution, SBM Variation III is the best variant for our research purposes. Variation III aims to ﬁnd the nearest referent point on the efﬁcient frontier by clustering all facets of the production possibility set. This model clusters homogeneous competitors to identify globally inefﬁcient but locally efﬁcient companies within these clusters. Variation III requires four steps. First, we classify all companies into homogeneous clusters. Second, we obtain the s efﬁcient companies for each management stage k according to the SBM k separation model (A1), thereby identifying the inputs ξ ¼ ξk1 ;⋯;ξks A Rmk xs and outputs ηk ¼ ηk1 ;⋯;ηks A Rrk xs for these SBM efﬁcient companies. Third, we enumerate all facets of the production possibility set and select only the clustered maximal friends facets (mk ¼1,…,Mk) composed by combinations of SBM efﬁcient companies at stage k within the same cluster. Tone [50] deﬁnes an algorithm for ﬁnding these maximal friends facets. A subset of SBM efﬁcient companies is called friends if a CRS or VRS linear combination of this subset is also efﬁcient. The maximal friends facets are those friends facets formed when any addition of an efﬁcient company (not in the friends) to the friends is not more efﬁcient than the friends. Finally, a friends facet is a dominated friends facet if it is a subset of others. If none of the companies in the cluster analysed are efﬁcient, Tone [50] proposes picking up the efﬁcient companies in the adjacent clusters to form the maximal friends facets. However, this solution may really bias the process when the adjacent clusters include efﬁcient companies with major differences from the evaluated companies. Finally, for every stage k, SBM Variation III looks for the nearest point on the 10 SBM Variation I aims to obtain the minimum slacks-based measure point on the facets that the SBM ﬁnds for the objective company. Thus, it aims to ﬁnd the nearest referent point on the efﬁcient frontier. SBM Variation II extends this approach to consider all facets of the production possibility set. Finally, there are two additional variants because the exhaustive enumeration of all facets required in Variation II may need huge computing resources: Variation III clusters all facets, and Variation IV conducts a random search of these facets.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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reference set by minimising the slacks-based measure from each clustered maximal friends facet. Thus, SBM Variation III under VRS is deﬁned as follows Pmk ski 1 1 k mk iþ1 x max io k ρm ð3Þ o ¼ k k kþ λ ; s ; s 1 þ 1 Prk skr þ r ¼ 1 yk rk ro

subject to

ξmk λk þ sk ¼ xko ηmk λk sk þ ¼ yko eλ ¼ 1 k

λk ;sk ;sk þ Z 0;

m where ξ k ;ηmk is the set of inputs and outputs of those efﬁcient companies that span each clustered maximal friends facet (mk) selected in the third step of this variant. Therefore, we solve model (3) at stage k for each clustered maximal friends facet. Then, the k efﬁciency score ρVarIII at stage k is ﬁnally computed as the maxo k imum ρm obtained for all the clustered maximal friends facets (Mk). o If model (3) ﬁnds no feasible solution for the new within-cluster facets, the company is efﬁcient in its cluster, i.e., globally inefﬁcient but locally efﬁcient in relation to the companies with common management resources. Notably, if we delete the constraint k eλ ¼ 1, the model (3) would be solved under the CRS assumption.

5. Empirical analysis First, we compare the results obtained by the SBM separation model (Appendix A, model A2) and the extended NSBM model (Appendix B, model B6) for each management stage of our network approach illustrated in Fig. 2. Thereafter, we apply nonparametric tests to contingency tables formed by homogenous efﬁciency clusters to check for the persistence of the efﬁciency across time and across companies. Finally, we run the innovative SBM Variation III to obtain locally efﬁcient fund companies with respect to competitors with similar management resources (Fig. 3). 5.1. Results of the SBM separation and the NSBM models Panel A of Table 3 shows the results of the SBM separation model (under VRS), in which the links between the management stages within a fund company are neglected. The efﬁciency of each management stage is obtained separately, and overall efﬁciency is obtained as the arithmetic average of the three individual efﬁciencies considered in our network approach. This equally weighted hypothesis is also used in the extended NSBM model, and it assumes the equal importance of the Portfolio Stage, the SBM separation model (Appendix A) (Table 3. Panel A) Rank correlations (Tables 4, 5) Network approach (Fig. 2)

Network SBM model (Appendix B) (Table 3. Panel B) Local vs Global efficiency (Table 10) SBM Variation III (Equation 3) (Table 10)

Fig. 3. Empirical analysis.

Persistence analysis (Tables 6, 7, 8, 9)

7

Marketing Stage and the Operational Stage in the efﬁciency function of a fund company as a whole. Panel B of Table 3 shows the results of the NSBM extension (under VRS), which incorporates the link ﬂows into the efﬁciency scores.11 Considering 2008 as the consensus breakpoint of the recent ﬁnancial crisis, the last three columns of Table 3 show the average of the yearly efﬁciency scores before the crisis, after the crisis, and for the whole sample period, respectively. There is not a signiﬁcant change in the average results before and after 2008. If we relate this result to the decreasing number of mutual fund companies competing in the Spanish fund industry (Table 1), we can conclude that crisis survivors are not signiﬁcantly increasing the efﬁciency records of the Spanish fund industry. If we extend our attention to the efﬁciency scores weighted by the assets managed by each company at year-end, we ﬁnd that these scores are signiﬁcantly higher than the equally weighted measures, with only the exception of the Marketing Stage in the SBM separation model. This result supports that size seems to play a positive role in the efﬁciency of mutual fund companies. This ﬁnding is substantially explained by the good efﬁciency records of the three largest companies, which manage approximately 45% of the assets of the Spanish market during our sample period. This evidence is robust across all years and management stages for both the SBM separation and the NSBM models.12 Finally, the comparison between Panel A and Panel B shows some differences in the efﬁciency patterns provided by both the SBM separation and the NSBM models. A further analysis of the Spearman rank correlations between the efﬁciency rankings obtained by the two techniques (Table 4) will help us to better identify these differences.13 Table 4 shows that the rankings obtained by both the SBM separation and the NSBM models are quite correlated, particularly at the Operational Stage. However, the rankings differ substantially at the Marketing Stage, where we ﬁnd many years with independent rank correlations, which support the notion that the links affecting the Marketing Stage are very important in our network model. These links are not properly captured by the SBM separation model, which neglects them when they actually exist, thereby explaining the differences in efﬁciency and rankings with respect to the NSBM model. This networking effect makes sense according to Fig. 1, in which the Marketing Stage plays a relevant intermediate role between the Portfolio Stage and Operational Stage. According to Tone and Tsutsui [51], the efﬁciency scores of the management stages cannot be compared fairly because the number of inputs and outputs differs across the three management stages. The comparison between the efﬁciency rankings therefore provides more accurate conclusions about the linking effects in our network model. Panel A of Table 5 conﬁrms that the omission of the networking effects may bias the efﬁciency rankings of a network structure. Spearman rank correlations show that most of the rankings obtained by the SBM separation model are independent and even negatively correlated. The only exception is Overall Efﬁciency, which is a consequence of its equally weighted construction based on the scores of each individual stage. This biased independence is explained as a result of the omission of the links by the SBM separation model when they are actually present in a fund company structure. 11 For the sake of brevity, we omit the complete yearly rankings and detailed reference sets of all the mutual companies included in our empirical analysis. These results are available upon request. 12 This evidence is also robust for the efﬁciency scores obtained under the CRS assumption. We ﬁnd an average Spearman rank correlation higher than 80% between the rankings provided under the VRS and CRS hypotheses. 13 Kendall rank correlations provide similar conclusions as the Spearman coefﬁcients displayed in Table 4.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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8

Table 3 Efﬁciency scores: SBM separation and NSBM models under VRS. Panel A SBM separation model

2005

2006

2007

2008

2009

2010

2011

2012

2005– 2008

2009– 2012

2005–2012

Portfolio Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

34 0.658 (0.295) 0.876

28 0.578 (0.308) 0.880

32 0.628 (0.312) 0.858

26 0.555 (0.322) 0.834

28 0.623 (0.290) 0.854

29 0.595 (0.322) 0.841

32 0.585 (0.345) 0.775

36 0.740 (0.282) 0.899

30 0.604 (0.309) 0.862

31 0.635 (0.309) 0.842

30 0.620 (0.309) 0.852

Marketing Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

6 0.337 (0.232) 0.422

10 0.431 (0.255) 0.391

11 0.482 (0.229) 0.303

9 0.276 (0.280) 0.141

7 0.342 (0.225) 0.221

4 0.277 (0.190) 0.248

8 0.311 (0.271) 0.245

14 0.580 (0.256) 0.339

9 0.381 (0.249) 0.314

8 0.377 (0.235) 0.263

8 0.379 (0.242) 0.288

Operational Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

15 0.365 (0.304) 0.633

19 0.385 (0.332) 0.719

14 0.359 (0.301) 0.626

10 0.278 (0.270) 0.666

14 0.388 (0.287) 0.723

8 0.301 (0.265) 0.542

12 0.300 (0.308) 0.617

15 0.565 (0.256) 0.739

14 0.346 (0.301) 0.661

12 0.388 (0.279) 0.655

13 0.367 (0.290) 0.658

Overall Efﬁciency Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

2 0.453 (0.178) 0.644

1 0.464 (0.157) 0.663

3 0.490 (0.172) 0.596

2 0.370 (0.170) 0.547

0 0.451 (0.156) 0.599

1 0.391 (0.147) 0.543

0 0.399 (0.172) 0.546

1 0.628 (0.129) 0.659

2 0.444 (0.169) 0.612

1 0.467 (0.151) 0.586

1 0.455 (0.160) 0.599

2005

2006

2007

2008

2009

2010

2011

2012

2005– 2008

2009– 2012

2005–2012

Portfolio Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

11 0.494 (0.266) 0.729

15 0.501 (0.286) 0.785

12 0.487 (0.287) 0.705

13 0.566 (0.278) 0.785

12 0.552 (0.255) 0.806

9 0.505 (0.259) 0.728

13 0.548 (0.258) 0.768

17 0.737 (0.206) 0.848

12 0.512 (0.279) 0.751

12 0.586 (0.244) 0.788

12 0.549 (0.261) 0.769

Marketing Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

14 0.565 (0.247) 0.760

14 0.596 (0.264) 0.826

15 0.584 (0.262) 0.744

13 0.648 (0.227) 0.822

13 0.659 (0.195) 0.869

10 0.577 (0.236) 0.793

15 0.640 (0.224) 0.834

16 0.796 (0.150) 0.895

14 0.598 (0.250) 0.788

14 0.668 (0.201) 0.848

14 0.633 (0.226) 0.818

Operational Stage Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

18 0.589 (0.257) 0.772

22 0.639 (0.264) 0.840

19 0.631 (0.261) 0.758

16 0.654 (0.239) 0.827

17 0.667 (0.203) 0.879

12 0.570 (0.243) 0.784

17 0.665 (0.224) 0.822

18 0.777 (0.153) 0.852

19 0.628 (0.255) 0.799

16 0.670 (0.205) 0.834

17 0.649 (0.230) 0.817

Overall Efﬁciency Number of Eff. companies Equal W efﬁciency score (Standard deviation) Asset W efﬁciency score

10 0.549 (0.244) 0.754

12 0.579 (0.256) 0.817

9 0.567 (0.255) 0.736

11 0.623 (0.234) 0.811

11 0.626 (0.200) 0.851

8 0.551 (0.234) 0.768

12 0.618 (0.219) 0.808

15 0.770 (0.151) 0.865

11 0.580 (0.247) 0.780

11 0.641 (0.201) 0.823

11 0.610 (0.224) 0.801

Panel B Network SBM model

This table shows the number of efﬁcient companies per management stage and year. It also provides both the equally weighted average and the asset weighted average of the efﬁciency scores obtained by the SBM separation model (Panel A) and the Network SBM model (Panel B). Standard deviation of the efﬁciency scores is in brackets.

These former results are properly corrected after including the networking effects by the NSBM model. Panel B of Table 5 shows a signiﬁcant increase in the similarity between the rankings as a consequence of incorporating link ﬂows into efﬁciency scores. Rank correlations between the Marketing Stage and the Operational Stage are signiﬁcantly the largest among the correlations between the three management stages. In fact, efﬁciency at the Marketing Stage is much more related to efﬁciency at the Operational Stage than at the Portfolio Stage. If we extend this analysis

to the Overall Efﬁciency rankings, we ﬁnd that the Marketing Stage and the Operational Stage are more relevant for explaining the Overall Efﬁciency of a company than are portfolio management skills. These results question the prime role of portfolio management skills in the overall efﬁciency of our sample. This controversial ﬁnding makes sense in our study period because net money ﬂows in the Spanish fund industry as a result of marketing activities are about -117,000 million € and total assets increase due to portfolio management are about 20,000 million € [29].

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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9

Table 4 Rank correlation: SBM separation vs NSBM under VRS.

Portfolio Stage Marketing Stage Operational Stage Overall Efﬁciency

2005

2006

2007

2008

2009

2010

2011

2012

2005–2008

2009–2012

2005–2012

0.47nn 0.42nn 0.94nn 0.79nn

0.26n 0.36nn 0.77nn 0.73nn

0.56nn 0.26nn 0.80nn 0.64nn

0.50nn 0.12 0.60nn 0.64nn

0.56nn 0.32nn 0.64nn 0.82nn

0.37nn -0.01 0.75nn 0.63nn

0.46nn 0.09 0.58nn 0.69nn

0.38nn 0.29n 0.72nn 0.70nn

0.45nn 0.28 0.78nn 0.70nn

0.44nn 0.17 0.67nn 0.71nn

0.45nn 0.23 0.73nn 0.71nn

This table shows the Spearman rank correlations between the efﬁciency rankings obtained by the SBM separation and the NSBM models under VRS. This information is provided per each management stage and year. n

5% signiﬁcance level; 1% signiﬁcance level.

nn

Table 5 Rank correlation across management stages. Panel A: SBM separation model 2005

Portfolio Stage (PS) Marketing Stage (MS) Operational Stage (OpS) Overall Efﬁciency (OvE)

2006

2008

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

0.01 1

0.07 0.38nn 1

0.58nn 0.50nn 0.64nn 1

0.30nn 1

0.23n 0.17 1

0.36nn 0.38nn 0.58nn 1

0.17 1

0.02 0.18 1

0.64nn 0.31nn 0.58nn 1

0.41nn 1

0.01 0.20 1

0.63nn 0.08 0.36nn 1

2009

Portfolio Stage (PS) Marketing Stage (MS) Operational Stage (OpS) Overall Efﬁciency (OvE)

2007

2010

2011

2012

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

0.23n 1

0.06 0.06 1

0.60nn 0.23n 0.61nn 1

0.35nn 1

0.21n 0.05 1

0.66nn 0.04 0.37nn 1

0.14 1

0.03 0.21n 1

0.61nn 0.29nn 0.46nn 1

0.21n 1

0.23n 0.04 1

0.52nn 0.41nn 0.43nn 1

Panel B: Network SBM model 2005

Portfolio Stage (PS) Marketing Stage (MS) Operational Stage (OpS) Overall Efﬁciency (OvE)

2006

2008

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

0.76nn 1

0.74nn 0.95nn 1

0.89nn 0.96nn 0.95nn 1

0.77nn 1

0.77nn 0.98nn 1

0.88nn 0.97nn 0.97nn 1

0.76nn 1

0.74nn 0.99nn 1

0.87nn 0.97nn 0.97nn 1

0.77nn 1

0.74nn 0.93nn 1

0.89nn 0.96nn 0.94nn 1

2009

Portfolio Stage (PS) Marketing Stage (MS) Operational Stage (OpS) Overall Efﬁciency (OvE)

2007

2010

2011

2012

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

MS

OpS

OvE

0.59nn 1

0.58nn 0.83nn 1

0.85nn 0.87nn 0.88nn 1

0.78nn 1

0.71nn 0.95nn 1

0.87nn 0.97nn 0.95nn 1

0.67nn 1

0.63nn 0.92nn 1

0.84nn 0.95nn 0.92nn 1

0.64nn 1

0.62nn 0.88nn 1

0.87nn 0.90nn 0.88nn 1

Panel A of this table shows the Spearman rank correlations between the efﬁciency rankings obtained by the SBM separation model under VRS for the different management stages of our network approach (Fig. 2). Panel B provides similar information corresponding to the efﬁciency rankings obtained by the NSBM model under VRS. n

5% signiﬁcance level; 1% signiﬁcance level.

nn

5.2. Persistence of efﬁciency scores across time and mutual fund companies Mutual fund persistence refers to the compelling hypothesis that mutual funds with good (bad) performance records will maintain those good (bad) results over time. An extensive body of literature has been devoted to this predictive phenomenon since the early studies of Brown et al. [7], Grinblatt and Titman [23], Hendricks et al. [25], and Goetzmann and Ibbotson [22]. We extend this persistence focus on the NSBM results obtained by our model. In other words, this section aims to be an original and further contribution to the persistence literature and tests for

whether fund companies maintain their relative NSBM rankings over time for the different management stages considered in our network model. If the persistence hypothesis is accepted, then those companies with high (low) NSBM efﬁciency rankings in a speciﬁc management stage will maintain their high (low) efﬁciency rankings over time. Nonparametric statistics based on contingency tables have been used frequently in the persistence literature since the ﬁrst applications by Brown and Goetzmann [8], Kahn and Rudd [34] and Malkiel [39], among others. However, the arbitrary determination of efﬁciency groups to be compared with other efﬁciency groups in subsequent years may be an important shortcoming of

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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10

Table 6 Summary statistics of the efﬁciency clusters. 2005

2006

2007

2008

2009

2010

Portfolio Stage Top Winners Winners Losers Bottom Losers

0.98 0.75 0.45 0.23

(16) (7) (44) (31)

0.97 0.67 0.47 0.23

(19) (11) (26) (39)

0.97 (16) 0.71 (12) 0.44 (28) 0.23 (36)

0.96 0.70 0.46 0.23

(23) (13) (34) (23)

0.96 0.67 0.44 0.22

(18) (15) (41) (14)

0.98 0.70 0.43 0.23

(13) (16) (30) (25)

0.99 0.77 0.52 0.29

(14) (5) (29) (26)

0.97 0.75 0.57 0.32

(22) (28) (17) (7)

Marketing Stage Top Winners Winners Losers Bottom Losers

0.97 (18) 0.76 (13) 0.51 (26) 0.34 (41)

0.96 0.71 0.53 0.31

(24) (15) (21) (35)

0.96 0.73 0.49 0.29

(21) (15) (32) (24)

0.97 0.79 0.54 0.24

(19) (16) (50) (8)

0.99 0.84 0.59 0.43

(15) (10) (44) (19)

0.98 0.77 0.54 0.34

(15) (11) (28) (30)

0.98 0.82 0.58 0.43

(17) (9) (19) (29)

0.99 0.85 0.71 0.58

(18) (20) (22) (14)

Operational Stage Top Winners Winners Losers Bottom Losers

0.98 (23) 0.78 (7) 0.51 (31) 0.35 (37)

0.99 0.75 0.55 0.33

(26) (13) (27) (29)

0.97 (25) 0.74 (15) 0.54 (27) 0.33 (25)

0.97 0.77 0.56 0.32

(24) (12) (39) (18)

0.99 0.85 0.61 0.46

(19) (5) (39) (25)

0.99 0.77 0.56 0.34

(16) (8) (26) (34)

0.99 0.84 0.61 0.46

(21) (3) (22) (28)

1.00 0.91 0.72 0.57

(18) (4) (39) (13)

Overall efﬁciency Top Winners Winners Losers Bottom Losers

0.96 (17) 0.76 (12) 0.51 (25) 0.34 (44)

0.98 0.76 0.52 0.30

(16) (20) (25) (34)

0.96 0.75 0.48 0.29

0.94 (24) 0.70 (19) 0.47 (45) 0.15 (5)

0.97 0.78 0.58 0.43

(16) (8) (37) (27)

0.95 0.70 0.48 0.32

(16) (15) (23) (30)

0.97 0.78 0.52 0.38

(15) (11) (32) (16)

0.99 0.85 0.73 0.59

(17) (6) (32) (19)

(15) (21) (31) (25)

2011

2012

This table illustrates the average efﬁciency scores per cluster and year. The statistics shown are for those companies included in the persistence analysis. The number of companies for each cluster is in brackets.

this nonparametric approach. Thus, those groups usually based on efﬁciency medians and quartiles might affect the accuracy of the persistence ﬁndings in the sense that adjacent groups may not have signiﬁcant efﬁciency differences between them. This concern is especially relevant in small mutual fund samples [14]. Our approach to persistence is based on contingency tables, but efﬁciency groups are not exogenously determined through median or quartile breakpoints. We propose divisive clustering techniques to design robust efﬁciency groups rather than merely considering median or quartile groups with the same number of companies. This divisive clustering approach begins with one large cluster containing all fund companies. This group is divided until C representative efﬁciency clusters with the largest dissimilarity between any two of its efﬁciency observations are selected.14 According to the standards in the persistence literature, we initially identify two (C ¼2) consistent efﬁciency groups of companies for each management stage and year: Winners (W) and Losers (L). Then, the divisive clustering technique splits up these groups to obtain four clusters (C ¼4) for each management stage and year (Top Winners, Winners, Losers, and Bottom Losers). Table 6 summarises the average efﬁciency scores obtained by cluster and year. These statistics show that clusters are signiﬁcantly different in terms of efﬁciency to form accurate contingency tables to contrast the persistence hypothesis. The comparison of the initially obtained W and L groups in two consecutive years allows for the identiﬁcation of the 2 2 contingency tables displayed in Table 7. Several nonparametric tests 14 DIANA algorithm was applied to obtain the efﬁciency clusters. DIANA is included in the package ‘Cluster’ of the R project for Statistical Computing (Version 1.14.4, August 2013). This divisive approach seems to be more appropriate for our concentrated sample than agglomerative techniques because it initially ﬁnds a few consistent large clusters from a unique efﬁciency group rather than combining the nearest efﬁciency observations until only one large cluster remains, as agglomerative techniques do. In any case, for our sample, the clusters obtained by both techniques are quite similar and robust against outliers. Detailed cluster dendrograms are available upon request.

previously used in the persistence literature are applied to these contingency tables. Table 7 shows a signiﬁcant persistence in NSBM efﬁciency rankings for all the management stages and years considered in our study, although less signiﬁcance is observed between 2008–2009 and 2011–2012. This result is robust across all the 2 2 tests. In addition, Cochran's Y-test conﬁrms this persistence from 2005 to 2012. Thus, the best (worst) managed companies at the different management stages included in our model are usually the same throughout our sample period. To look more deeply at persistence using nonparametric tests, we use the 4 4 contingency tables that result when comparing the four efﬁciency clusters (Top Winners, Winners, Losers, and Bottom Losers) over two consecutive years. Table 8 presents the main results. First, we ﬁnd a signiﬁcant chi-square value for each management stage for nearly all the consecutive periods. Again, this result supports a strong persistence in the NSBM efﬁciency rankings obtained by the Spanish fund companies in our sample period. As with the 2 2 contingency tables, this 4 4 analysis ﬁnds a decrease in the signiﬁcance of persistence between 2008– 2009 and 2011–2012, which might be explained by the ﬁnancial crisis and a new industry competition map, respectively. Future studies are needed to properly justify these potential explanations. Finally, the Haberman [24] analysis of residuals identiﬁes those efﬁciency groups responsible for the persistence. Table 8 presents a signiﬁcantly higher persistence of the companies included in the Top W clusters than in the other 4 4 table cells, and this result is robust across nearly all periods and management stages. Thus, these persistence results are strongly caused by the best companies in terms of efﬁciency, as this result is robust for portfolio management, for the marketing activities and for the operational management of the company. Furthermore, we pay detailed attention to the number of companies that have performed consistently well. Table 9 shows that very few companies perform at an excellent level over a long time period. In our sample, only 4, 5, and 6 companies perform consistently at an excellent level over periods longer than 6 years

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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Table 7 NSBM efﬁciency persistence (2 2 contingency tables). Portfolio Stage

WW

WL

LW

LL

Malkiel Z-test Winners

Malkiel Z-test Losers

B&G Z-test

K&R χ2 test

Cochran Y-test

2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012

17 19 24 19 16 17 15

6 11 4 17 17 12 4

13 10 11 16 13 5 35

62 55 53 41 42 50 20

4.506nn 3.902nn 5.196nn 1.875 1.898 3.972nn 1.060

2.495n 2.651nn 3.437nn 1.490 1.470 2.884nn 0.623

4.613nn 4.401nn 5.310nn 2.363n 2.360n 4.405nn 1.212

26.528nn 22.252nn 38.806nn 5.739n 5.764n 24.097nn 1.511

10.235nn

Marketing Stage 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012

WW 24 24 22 14 15 17 19

WL 7 15 14 21 10 9 7

LW 15 13 12 12 11 10 19

LL 52 43 44 46 52 48 29

Malkiel Z-test Winners 4.280nn 2.893nn 3.003nn 1.588 3.338nn 3.629nn 2.216n

Malkiel Z-test Losers 2.911nn 2.414n 2.407n 1.233 2.102n 2.430n 1.631

B&G Z-test 4.760nn 3.649nn 3.709nn 1.982n 3.723nn 4.088nn 2.674nn

K&R χ2 test 26.790nn 14.200nn 14.811nn 4.041n 15.559nn 19.077nn 7.573nn

Cochran Y-test 9.789nn

Operational Stage 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012

WW 24 25 23 15 15 15 11

WL 6 14 17 21 9 9 13

LW 14 16 12 11 9 10 11

LL 54 40 40 46 55 50 39

Malkiel Z-test Winners 4.634nn 2.641nn 2.535n 1.833 3.875nn 3.508nn 1.726

Malkiel Z-test Losers 3.078nn 2.204n 2.223n 1.457 2.373n 2.219n 1.196

B&G Z-test 5.010nn 3.354nn 3.282nn 2.297n 4.188nn 3.885nn 2.060n

K&R χ2 test 30.950nn 11.831nn 11.366nn 5.481n 20.646nn 17.227nn 4.409n

Cochran Y-test 9.629nn

Overall Efﬁciency 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012

WW 22 25 26 15 16 20 12

WL 7 11 10 28 8 11 14

LW 13 12 16 10 15 7 11

LL 56 47 40 40 49 46 37

Malkiel Z-test Winners 4.512nn 3.752nn 3.201nn 1.184 3.224nn 3.859nn 1.661

Malkiel Z-test Losers 2.925nn 2.931nn 2.566n 1.098 1.975n 2.952nn 1.222

B&G Z-test 4.897nn 4.505nn 3.938nn .598 3.582nn 4.488nn 2.028n

K&R χ2 test 28.916nn 22.673nn 16.828nn 2.606 14.295nn 23.608nn 4.251n

Cochran Y-test 10.123nn

The 2 2 contingency tables are obtained by comparing the efﬁciency clusters W and L of two consecutive years. Therefore, WW (LL) shows the number of winners (losers) in two consecutive years. WL (LW) indicates the number of winners (losers) in the ﬁrst year that become losers (winners) in the next year. The following nonparametric tests use the information provided by these 2 2 contingency tables. The Z-test applied by Malkiel [39] compares the number of winners (losers) in two consecutive years with the number of winners (losers) in the ﬁrst year. The Z-test N(0,1) contrasts the persistence hypothesis, including the probability of a winner (loser) being a winner (loser) in the next year. This probability takes different values for each compared year because the number of winners and losers is different due to our clustering approach. Brown and Goetzmann [8] propose an odds ratio that represents the number of persistent companies to those that are not persistent. Brown and Goetzmann [8] develop a Z-test N(0,1) to contrast the persistence hypothesis based on this odds ratio. Kahn and Rudd [34] originally apply a chi-square test χ2(1) to contrast for the persistence hypothesis. This statistic is based on both actual and expected number of companies being WW, WL, LW and LL in two consecutive years. Similar to the Z-test applied by Malkiel [39], the expected frequencies are calculated in our sample for each year. Finally, Cochran [11] uses the aggregate information from the 2 2 contingency tables to provide a persistence test for the entire sample period. This Cochran's Y-test N(0,1) is based on the number of 2 2 contingency tables, the number of winners (losers) in the ﬁrst year, and the relation between persistent companies and those that are not persistent. n

5% signiﬁcance level; 1% signiﬁcance level.

nn

at the Portfolio Stage, the Marketing Stage and the Operational Stage, respectively. In this small set, we ﬁnd large bank-owned companies managing many mutual funds and fund types together with small independent companies specialising in a few mutual funds and fund types. This result indicates that both diversiﬁcation and specialisation strategies may be successful in terms of efﬁciency with properly developed strategies. 5.3. The search for locally efﬁcient mutual fund companies This analysis extends the previous results based on global best practice frontiers. We follow SBM Variation III by Tone [50] to identify locally efﬁcient companies, deﬁned as efﬁcient companies in reference to local groups of competitors with similar management resources. The comparison between globally and locally efﬁcient companies allows us to identify the sensitivity of efﬁciency scores to reference frontiers in the concentrated Spanish fund market. Our clustering proposal is based on the assets managed by the fund companies in our sample, in which a large number of small fund companies manage a residual market asset share and a

reduced number of large fund companies dominate the industry. We assume the hypothesis that companies with clusteringhomogeneous size should have quite similar management resources to reach efﬁciency at every management stage in our network structure. We propose ﬁve size clusters based on homogeneous dendrogram heights. As with the identiﬁcation of contingency tables in the persistence analysis, we follow the divisive clustering approach proposed by DIANA algorithm (footnote 14) to ﬁnd robust size clusters. Table 10 presents the average assets managed by cluster as a metric to highlight that the large size differences between clusters also correspond to different management resources under our clustering hypothesis. The search for the maximal friend facets has been different for each stage and cluster. A total of 19,112 reference combinations are examined to ﬁnd the maximal friends facets required to apply SBM Variation III. In those clusters with few efﬁcient companies, the maximal friends are easily found according to the algorithm proposed by Tone [50]. However, those clusters with more efﬁcient companies involve much greater computational resources. For example, if we ﬁnd 13 efﬁcient companies at the Portfolio Stage (Cluster 5 in 2007), then in the worst case, we run 7C6 ¼ 1716 SBM

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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Table 8 NSBM efﬁciency persistence (4 4 contingency tables). Portfolio Stage

Marketing Stage

Operational Stage

Overall Efﬁciency

2006 2005

Top W

W

L

Bot L

χ2 test

Top W

W

L

Bot L

χ2 test

Top W

W

L

Bot L

χ2 test

Top W

W

L

Bot L

χ2 test

Top W W L Bot L

7nn 3 6 3

4 3nn 4 0n

3 0 19nn 5

2nn 1 15 23nn

42.4nn

8n 8nn 6 2nn

5 3 3 4

4 2 11nn 6

1nn 0nn 6 29nn

49.5nn

12nn 4n 6 3nn

6n 2 3 2

4 1 15n 11

1nn 0 7 21nn

41.8nn

6n 2 3 4

8nn 6nn 4 2nn

2 3 13nn 10

1nn 1n 5 28nn

47.6nn

2007 2006 Top W W L Bot L

Top W 7n 6nn 3 1nn

W 4 2 2 4

L 5 3 12n 8

Bot L 3n 0nn 9 26nn

χ2 test 37.7nn

Top W 10n 7n 2 3n

W 4 3 7n 1nn

L 8 3 9 12

Bot L 2n 2 3 19nn

χ2 test 36.2nn

Top W 13nn 5 6 2nn

W 3 4 7 1n

L 7 2 11 7

Bot L 3n 2 3n 19nn

χ2 test 39.5nn

Top W 5 8nn 2 1nn

W 5 7 5 4

L 5 3 14nn 9

Bot L 1n 2n 4 20nn

χ2 test 41.2nn

2008 2007 Top W W L Bot L

Top W 13nn 4 4 1nn

W 2 5nn 3 3

L 1nn 3 12 18n

Bot L 0n 0n 9 14n

χ2 test 54.6nn

Top W 10nn 3 5 1n

W 3 6nn 4 2

L 6nn 6 21 17

Bot L 2 0 2 4

χ2 test 25.7nn

Top W 14nn 3 5 1nn

W 2 4 2 4

L 5nn 6 14 14

Bot L 4 2 6 6

χ2 test 23.5nn

Top W 11nn 8 3n 1nn

W 3 4 8 4

L 1nn 7 19 18nn

Bot L 0 2 1 2

χ2 test 35.7nn

2009 2008 Top W W L Bot L

Top W 8n 3 4 3

W 6 2 5 4

L 7 7 21n 8

Bot L 2 1 4 8nn

χ2 test 16.1

Top W 7nn 2 3nn 3

W 3 2 6 0

L 6 11 28 2

Bot L 3 1 13 3

χ2 test 19.1n

Top W 8nn 1 2n 4

W 4 2 5 0

L 10 5 24 8

Bot L 2 4 8 6

χ2 test 16.6

Top W 9nn 1 5 1

W 2 3 3 1

L 10 6 21 1

Bot L 3n 9 16 2

χ2 test 15.8

2010 2009 Top W W L Bot L

Top W 7nn 3 1nn 2

W 5 1 8 2

L 1nn 9 20 4

Bot L 5 2 12 6

χ2 test 24.3nn

Top W 10nn 1 2nn 2

W 0 4nn 6 1

L 2n 5 18 7

Bot L 3 0n 18 9

χ2 test 44.1nn

Top W 12nn 0 2nn 2

W 1 2n 5 0

L 3 2 18n 6

Bot L 3n 1 14 17nn

χ2 test 48.4nn

Top W 9nn 3 2nn 2

W 4 0 7 4

L 1n 3 16n 7

Bot L 2n 2 12 14n

χ2 test 31.8nn

2011 2010 Top W W L Bot L

Top W 8nn 4 1nn 3

W 1 4nn 1 0

L 1n 5 18nn 7

Bot L 3 3 10 15nn

χ2 test 40.5nn

Top W 8nn 4 3 4

W 3 2 3 0n

L 0nn 4 12n 7

Bot L 4 1n 10 19nn

χ2 test 30.1nn

Top W 10nn 3 5 4n

W 1 1 1 0

L 0nn 4 12 11

Bot L 5 0n 8 19nn

χ2 test 28.9nn

Top W 10nn 2 2 3

W 2 6nn 1 1

L 0nn 7 10 20nn

Bot L 4 0n 10nn 6

χ2 test 48.5nn

2012 2011 Top W W L Bot L

Top W 9nn 3 6 4n

W 2n 1 16n 9

L 2 1 4 10n

Bot L 1 0 3 3

χ2 test 19.5n

Top W 7 3 4 4

W 5 4 6 5

L 2 1 7 12

Bot L 3 1 2 8

χ2 test 12.6

Top W 9n 0 5 4

W 2 0 2 0

L 7n 3 12 17

Bot L 3 0 3 7

χ2 test 12.6

Top W 7n 3 6 1

W 2 0 4 0

L 3n 5 17 7

Bot L 3 3 5 8n

χ2 test 17.1n

The 4 4 contingency tables shows the number of mutual fund companies included in the four efﬁciency clusters (Top W, W, L and Bot L) of two consecutive years. The following nonparametric tests use the information provided by these 4 4 tables. As with the 2 2 tables, a new chi-square test χ2(9) is now applied to the 4 4 tables to check for the persistence hypothesis. This test is based on both the actual and expected number of companies for each of the 16 efﬁciency combinations over two consecutive years. The expected frequencies are calculated in our sample for each year. Finally, we apply the Haberman [24] residual analysis to identify those efﬁciency categories responsible for a signiﬁcant chi-square value. This test computes an adjusted residual d N(0,1) based on both the actual and expected number of companies for each of the 16 cells of a 4 4 contingency table. The adjusted residuals for each contingency table cell are not displayed for the sake of brevity, but statistical signiﬁcance is considered for each cell. As with the chi-square test, the expected frequencies are calculated for each year. n

5% signiﬁcance level; 1% signiﬁcance level.

nn

Table 9 Persistence over different sample periods.

Portfolio Stage Marketing Stage Operational Stage Overall Efﬁciency

Over 2 years

Over 3 years

Over 4 years

Over 5 years

Over 6 years

Over 7 years

Over 8 years

15

3

2

2

2

0

2

7

7

1

2

3

1

1

10

9

1

3

1

3

2

12

4

2

2

2

1

1

This table shows the number of companies that have been Top Winner across different consecutive yearly periods.

models to look for maximal friends facets. The number of clusters should not be increased to avoid huge computational resources, otherwise Variation III could be biased.

This local assessment is based on a smaller number of competitors, so it is obvious that the number of efﬁcient companies will increase. Table 10 shows that this increase is really signiﬁcant for most of the management stages, clusters and years. On average, there are almost three locally efﬁcient companies per one globally efﬁcient. Thus, the analysis restricted to local competitors reveals that an important percentage of globally inefﬁcient companies are now considered as locally efﬁcient. Both global and local efﬁciency levels within each cluster and stage are mostly higher for large companies than for small companies. Therefore, efﬁciency is positively affected by the company size. This result conﬁrms the previous evidence in Table 3. This large number of globally inefﬁcient but locally efﬁcient companies across stages and years reveals that the evaluation of efﬁciency in concentrated fund markets is sensitive to the deﬁnition of appropriate reference clusters. Previous studies on metafrontiers and cluster-frontiers also support this ﬁnding, (e.g., [42]). Further research on this issue is necessary to avoid misinterpreting results in concentrated industries.

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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Table 10 Efﬁciency by size clusters. 2005

2006

2007

2008

2009

2010

2011

2012

Cluster 1 Companies (Average assets) Portfolio Stage- GE (LE) Marketing Stage- GE (LE) Operational Stage- GE (LE)

7 5 2 2

7 7 3 4

6 5 1 3

7 6 1 4

7 6 1 3

(16,415) (1) (3) (4)

11 (9,394) 6 (5) 1 (6) 2 (6)

7 5 1 4

5 4 0 3

Cluster 2 Companies (Average assets) Portfolio Stage- GE (LE) Marketing Stage- GE (LE) Operational Stage- GE (LE)

19 ( 2309) 5 (11) 1 (9) 2 (5)

18 ( 3093) 4 (12) 3 (3) 3 (11)

19 ( 3807) 5 (8) 3 (4) 2 (17)

17 ( 3346) 3 (8) 0 (17) 2 (12)

14 ( 2455) 2 (12) 1 (9) 3 (11)

20 ( 1096) 4 (15) 0 (19) 4 (3)

12 ( 2319) 3 (5) 2 (4) 3 (5)

14 ( 2842) 10 (0) 4 (7) 3 (10)

Cluster 3 Companies (Average assets) Portfolio Stage- GE (LE) Marketing Stage- GE (LE) Operational Stage- GE (LE)

22 (972) 8 (3) 1 (21) 2 (6)

28 (921) 6 (12) 0 (6) 4 (5)

28 (936) 5 (18) 1 (27) 2 (15)

29 (851) 9 (5) 3 (15) 1 (1)

32 (671) 8 (16) 1 (27) 3 (1)

20 (706) 6 (4) 0 (7) 1 (17)

31 (599) 9 (4) 1 (30) 3 (1)

20 (673) 7 (9) 2 (18) 4 (10)

Cluster 4 Companies (Average assets) Portfolio Stage- GE (LE) Marketing Stage- GE (LE) Operational Stage- GE (LE)

22 (278) 5 (13) 2 (11) 3 (16)

18 (244) 5 (6) 2 (7) 4 (5)

15 (224) 4 (11) 2 (11) 3 (9)

16 (256) 1 (8) 2 (7) 1 (11)

12 (182) 2 (8) 3 (0) 2 (9)

14 (176) 4 (10) 2 (4) 0 (11)

17 (162) 5 (9) 2 (15) 2 (11)

13 (221) 4 (9) 2 (7) 2 (10)

Cluster 5 Companies (Average assets) Portfolio Stage- GE (LE) Marketing Stage- GE (LE) Operational Stage- GE (LE)

32 (94) 11 (3) 0 (9) 6 (24)

31 (63) 6 (14) 2 (6) 4 (17)

27 (106) 13 (1) 4 (16) 4 (19)

24 (123) 7 (4) 3 (0) 2 (20)

30 (95) 10 (9) 1 (26) 3 (24)

24 (80) 9 (6) 1 (10) 1 (15)

19 (69) 10 (0) 2 (6) 0 (14)

22 (108) 11 (4) 6 (12) 3 (7)

(23,075) (0) (5) (5)

(24,623) (0) (3) (2)

(27,335) (1) (5) (3)

(23,080) (1) (6) (3)

(11,735) (0) (5) (1)

(12,869) (0) (0) (2)

This table shows the number of companies included for each size cluster and year together with the average assets in million € managed per company. GE is the number of globally efﬁcient companies for each size cluster, stage and year. LE is the number of globally inefﬁcient but locally efﬁcient companies for each size cluster, stage and year.

6. Conclusions This study is the ﬁrst evaluation of the efﬁciency of mutual fund companies in a large Euro fund market, i.e., Spain. Based on a NSBM approach proposed by Tone and Tsutsui [51], our paper develops an innovative model that includes three interacting management stages within a fund company: the Portfolio Stage, the Marketing Stage, and the Operational Stage. The assumptions of our approach incorporates the responsibility of a company to its shareholders as a generalizable and innovative contribution to the efﬁciency models of mutual fund companies. The efﬁciency results of this network model show that the linking effects between the management stages in a company are particularly relevant at the Marketing Stage. In addition, we ﬁnd that both the ability to sell mutual funds and the operational function efﬁciency seem to be more important than portfolio management skills for explaining the overall efﬁciency of a fund company. We also ﬁnd that company size seems to play a positive role in the efﬁciency of Spanish fund companies. Finally, we do not detect a signiﬁcant change in efﬁciency patterns before and after the ﬁnancial crisis. Based on the efﬁciency rankings drawn by our network model, we ﬁnd a signiﬁcant persistence phenomenon for all the management stages and years, although less signiﬁcance is observed following the crisis. This result is robust across all the nonparametric tests and contingency tables. This ﬁnding is especially driven by the best companies in terms of efﬁciency. The application of the innovative SBM Variation III to the concentrated Spanish fund industry ﬁnds a large number of globally but locally efﬁcient companies across management stages

and years. This empirical result supports the application of clusterfrontiers in highly concentrated fund industries such as the Spanish mutual fund market. According to these key ﬁndings, we brieﬂy address some managerial implications for the Spanish fund industry. First, performance-based fees instead of asset-based fees would motivate fund managers to perform better. Second, persistence should be deﬁned as a benchmark to evaluate the consistent success or failure of the strategies developed by the fund companies. Finally, the company size should allow companies to determine their real competitors.

Acknowledgements We thank Laura Andreu, Manuel Armada, Mircea Epure, Francisco González, Alexander Kempf, Terry Hallahan, Cristina Ortiz, the participants of the XX AEFIN Forum and the anonymous review process for their insightful comments. We are also grateful to ﬁnancial support provided by Government of Aragón/FEDER Funds (268219/1) and Government of Spain (ECO2013-45568-R). This paper was awarded the 2015 “Antonio Dionis Soler” Research Prize (accésit) by Fundación de Estudios Financieros. Any error is the responsibility of the authors.

Appendix A. SBM model According to the non-oriented VRS approach of the SBM model (A1) proposed by Tone [49], an objective company xko ;yko will be

Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

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considered as efﬁcient at stage k in terms of Pareto–Koopmans when it has no input excesses and no output shortfalls for any k ¼ 1. optimal solution, i.e., ρSBM o Pmk sk 1 i 1 k mk i¼1 x min io k ρSBM ¼ k k k þ ðA1Þ o λ ; s ; s 1 þ 1 Prk skr þ k r ¼ 1 rk y ro

subject to Xk λ þ sk ¼ xko k

Yk λ sk þ ¼ yko k

eλ ¼ 1 k

λk ;sk ;sk þ Z 0;

where Xk ¼ xk1 ;⋯; xkn A Rmk n ; Yk ¼ yk1 ;⋯; ykn A Rrk n . In this ðk;hÞ approach, the link variables Z and their slacks must be included in the sets of ordinary inputs Xk or outputs Yk previously deﬁned. k If we delete the constraint eλ ¼ 1, we address the CRS version of the SBM model. an optimal solution of the above model (A1) be Let kþ . The reference set Ro to the target company at λko ;sk o ; so stage k is deﬁned as those companies corresponding to positive values of the intensity vector. n o k ðA2Þ Ro ¼ j\λj 4 0; j ¼ 1; :::n k k According to Tone [49], the objective company xo ;yo can be projected in terms of the companies included in the reference set Ro at stage k, as follows: X X x ko ¼ xko sk ¼ xj λj y ko ¼ yko þ sko þ ¼ yj λj ðA3Þ o j A Ro

j A Ro

or Zðk;hÞ λ ¼ zðk;hÞ Zðk;hÞ λ ¼ zðk;hÞ 8 k; h ðB3Þ o o ðk;hÞ ðk;hÞ ðk;hÞ tðk;hÞ n AR ¼ z1 ;⋯; zn where Z Restriction (B2) corresponds to the “free” case in which the linking activities are freely determined and keep continuity between input and output. In other words, the link ﬂow may vary in the optimal solution of model (B1). Restriction (B3) corresponds to the “ﬁxed” case, i.e., the linking activities do not change. An objective company will be considered as overall efﬁcient when ρNSBM ¼ 1; therefore, an objective company will be considered as o k efﬁcient at stage k when ρNSBM ¼ 1, with the non-oriented efﬁo ciency at stage k deﬁned by Pmk sk i 1m1k k i¼1 x io k P ðB4Þ ρNSBM ¼ ðk ¼ 1; 2; :::; KÞ o srk þ rk 1 1 þ rk r ¼ 1 yk h

k

ro

where sk ; sk þ are the optimal input and output slacks in model (B1). The reference set Ro to the target company evaluated in (B1) at stage k is deﬁned as the set of companies corresponding to positive values of the intensity vector. n o k Ro ¼ j\λj 40; j ¼ 1; :::n ðB5Þ Furthermore, Tone and Tsutsui [51] propose to extend the original NSBM model to incorporate the inefﬁciency of the intermediate variables into the objective function. This extension includes the slacks sðf ;kÞ– of the intermediate input to stage k at link (f,k), and the slacks sðk;hÞ þ of the intermediate output from stage k at link (k,h). The extension of the non-oriented version of the NSBM model under VRS is set as follows: K P

'¼ ρNSBM o

min

k¼1

λk ; sk ; sk þ ; sðf ;kÞ ; sðk;hÞ þ P K

" wk 1 m "

wk

k¼1

1þr

k

þ

kþ

Pmk

P1 f A Pk

P1 h A Fk

t ðf ;kÞ

t ðk;hÞ

ski i ¼ 1 xk io

Prk

skr þ r ¼ 1 ykro

þ þ

P

sðff ;kÞ f A P k zðf ;kÞ fo

P

þ sðk;hÞ h h A F k zðk;hÞ ho

# #

ðB6Þ Appendix B. Network SBM model and extension

subject to

After setting exogenously the relative importance wk of stage k in the overall efﬁciency measure, NSBM (Tone and Tsutsui [51]) evaluates the n o non-oriented overall efﬁciency of a target company xko ;yko ; zðk;hÞ under the VRS assumption, as follows: o

K P Pmk ski wk 1 m1k i ¼ 1 xk min io ρNSBM ¼ k k k þ k ¼K1 ðB1Þ o P i λ ;s ;s P kh skr þ rk 1 w 1 þ rk k r¼1 y k¼1

ro

subject to Xk λ þ sk ¼ xko k

Yk λ ̶sk þ ¼ yko k

Xk λ þ sk ¼ xko Yk λ ̶sk þ ¼ yko eλ ¼ 1ðk ¼ 1; 2; …; KÞ k

k

k

Zðf :kÞ λ þ sðf :kÞ ¼ zðfo :kÞ Zðf :kÞ λ ¼ Zðf :kÞ λ 8 f; k k

f

k

Zðk;hÞ λ –sðk;hÞ þ ¼ zðk;hÞ Zðk;hÞ λ ¼ Zðk;hÞ λ 8 k; h o k

h

k

λk ;sk ;sk þ ; sðf ;kÞ ;sðk;hÞ þ Z 0 8 f; k; h where Pk is the set of stages having the link (f,k) A L (antecessor of stage k), and t(f,k) is the number of intermediate variables in that link; and Fk is the set of stages having the link (k,h) A L (successor of stage k), and t(k,h) is the number of intermediate variables in that link. A company will be overall efﬁcient in model (B6) when the optimal input and output slacks (sk ;sk þ ) together with optimal ðf ;kÞ– ðk;hÞ þ ;s ) result in. intermediate input and output slacks (s

eλ ¼ 1ðk ¼ 1; 2; …; KÞ k

References

λk ;sk ;sk þ Z 0 8 k

PK k where Xk ¼ xk1 ;⋯; xkn A Rmk n ; Yk ¼ yk1 ;⋯; ykn A Rrk n ; k¼1w

¼ 1;wk Z0 8 k. Notice that if we delete the constraint eλ ¼ 1, we assume the CRS version of the NSBM model. According to Tone and Tsutsui [51], the restrictions related to link variables zoðk;hÞ can be added to the above model (B1), as follows: k

Zðk;hÞ λ ¼ Zðk;hÞ λ 8 k; h h

k

ðB2Þ

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Please cite this article as: Sánchez-González C, et al. The efﬁciency of mutual fund companies: Evidence from an innovative network SBM approach. Omega (2016), http://dx.doi.org/10.1016/j.omega.2016.10.003i

The efficiency of mutual fund companies: Evidence from an innovative network SBM approach

The efficiency of mutual fund companies: Evidence from an innovative network SBM approach

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