Stochastic frontiers of efficiency for Brazilian investment funds: A panel data analysis

“Stochastic frontiers of efficiency for Brazilian investment funds: a panel data analysis” AUTHORS Luis Ferruz Agudo https://orcid.org/0000-0002-3816-9747 João Serafim Tusi da Silveira https://orcid.org/0000-0002-0720-5020 Daniel Knebel Baggio https://orcid.org/0000-0002-6167-2682 Isoé Nícolas Schneider https://orcid.org/0000-0002-2806-5135 Maria Margarete Baccin Brizolla https://orcid.org/0000-0002-5120-0729 ARTICLE INFO Luis Ferruz Agudo, João Serafim Tusi da Silveira, Daniel Knebel Baggio, Isoé Nícolas Schneider and Maria Margarete Baccin Brizolla (2019). Stochastic frontiers of efficiency for Brazilian investment funds: a panel data analysis. Investment Management and Financial Innovations, 16(4), 352-365. doi:10.21511/imfi.16(4).2019.30 DOI http://dx.doi.org/10.21511/imfi.16(4).2019.30 RELEASED ON Thursday, 26 December 2019 RECEIVED ON Monday, 23 September 2019 ACCEPTED ON Tuesday, 10 December 2019 LICENSE This work is licensed under a Creative Commons Attribution 4.0 International License JOURNAL "Investment Management and Financial Innovations" ISSN PRINT 1810-4967 ISSN ONLINE 1812-9358 PUBLISHER LLC “Consulting Publishing Company “Business Perspectives” FOUNDER LLC “Consulting Publishing Company “Business Perspectives” NUMBER OF REFERENCES 52 NUMBER OF FIGURES 0 NUMBER OF TABLES 4 © The author(s) 2021. This publication is an open access article. businessperspectives.org 352 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 Abstract Foundations, methodological and empirical possibilities of measurement and analysis in the performance of financial investments within investment funds have been developed since they were once introduced in the 1970s, thus establishing a path of growing acceptance in financial markets and universities’ academies. The first approaches over the efficiency of these funds, considering their stochastic implications, occurred in the late 1990s and have evolved with the help of SFA – Stochastic Frontier Analysis, although it still needs more careful verification. This article measured and analyzed the stochastic frontier of efficiency over 33 different Brazilian investment funds from 2012 to 2015. For doing so, Battese and Coelli’s (1995) specifications was used. It shows the effects of inefficiencies, which are defined as explicit functions of specific factors in the context of panel data funds. They are estimated by the maximum likelihood method. Sharpe ratios (SR) were also calculated for comparative purposes. Based on these two indicators (SFA and SR), the most recommendable funds to invest and the ones in which the application should not be performed were identified. Such procedures have stimulated the necessary and promising studies, as well as future researches, which, in turn, may establish new methodological formulation as an efficient and effective instrument to choose the best and the safest funds to invest. Luis Ferruz Agudo (Spain), João Serafim Tusi da Silveira (Brazil), Daniel Knebel Baggio (Brazil), Isoé Nícolas Schneider (Brazil), Maria Margarete Baccin Brizolla (Brazil) Stochastic frontiers of efficiency for Brazilian investment funds: a panel data analysis Received on: 23rd of September, 2019 Accepted on: 10th of December, 2019 INTRODUCTION Investment funds are one of the most important investment options in today’s financial market, due to their increasing quantity and to the options available, and for the importance they have in domestic savings and in the allocation of resources in productive activities (Amaral, Vilaça, Barbosa, & Bressan, 2004). They are the determinants for the economic development of regions, where resources are applied (Baggio, 2012). According to Fundação Getúlio Vargas [FGV] (2017), Brazilian funds market is the tenth largest in the world, with approximately 3% out of the total world equity. Currently, more than 15,000 funds are under management in Brazil, and are also notable for the variety of products offered and the diversity of investors (Brazilian Association of Financial and Capital Market Entities [ANBIMA], 2017). The underlying idea of efficiency ratios is that individuals act as risk enemies who expect greater profitability for taking greater risks. The measures of efficiency, when relating average profitability with risk, indicate how the portfolio is rewarding in terms of profitability, the assumed risk. © Luis Ferruz Agudo, João Serafim Tusi da Silveira, Daniel Knebel Baggio, Isoé Nícolas Schneider, Maria Margarete Baccin Brizolla, 2019 Luis Ferruz Agudo, Doctor in Accounting and Finance, Department of Accounting and Finance, University of Zaragoza, Spain. João Serafim Tusi da Silveira, Doctor in Production Engineering, Professor, Federal University of Santa Catarina, Brazil. Daniel Knebel Baggio, Doctor in Accounting and Finance, Professor, Universidade Regional Integrada e das Missões e Universidade Regional do Noroeste do Estado do Rio Grande do Sul – UNIJUI, Brazil. Isoé Nícolas Schneider, Master in Regional Development, DACEC, Universidade Regional do Noroeste do Estado do Rio Grande do Sul – UNIJUÍ, Brazil. Maria Margarete Baccin Brizolla, Doctor in Accounting and Administration, Professor, Universidade Regional do Noroeste do Estado do Rio Grande do Sul – UNIJUI, Brazil. efficiency, performance, investment funds Keywords JEL Classification G23, G24 This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International license, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. www.businessperspectives.org LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, Sumy, 40022, Ukraine BUSINESS PERSPECTIVES 353 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 The literature is rich on performance evaluation of investment funds. Recently, some authors have used different methodologies to contrast the efficiency’s performance of investments based on Data Envelopment Analysis (DEA) and/or Stochastic Frontier Analysis (SFA) (Galan, Ramos, & Veiga, 2015; Mamatzkis & Xu, 2016), among others. These two methodological approaches configure the determination of efficiency’s frontiers. The DEA methodology is non-parametric, deterministic, and efficiency’s frontier is determined by mathematical programming. SFA methodology is parametric, non-deterministic, and stochastic efficiency frontier is determined econometrically. Data Envelopment Analysis considers the manager’s inefficiency as all the inefficiencies registered by the fund, or how close it was to be totally efficient. On the other hand, in Stochastic Frontier Analysis, the inefficiency of the manager is deducted from the total inefficiency of the fund, subtracting from it the part beyond its control. In this regard, we sought to contribute to a deeper knowledge in the analysis of the efficiency of Brazilian investments funds, by identifying the variables which impact either positively or negatively the funds’ efficiency. The use of Stochastic Frontier Analysis turned it all possible, despite its infrequent use in the investment analysis of Brazilian investment funds. In this regard, we sought to contribute to a deeper knowledge in the analysis of the efficiency of Brazilian investments funds, by identifying the variables which impact either positively or negatively the funds’ efficiency. The use of Stochastic Frontier Analysis turned it all possible, despite its infrequent use in the investment analysis of Brazilian investment funds. From important and significant variables identified in the efficiency model, performance rankings of investment funds were established in order to help investors in their decision-making. Yet, to help fund managers who may compare their financial products performance with the ones from other institutions. Therefore, this study can be recognized as original by the econometric method used to measure the funds efficiency, and for the variables found and the effects they have on efficiency. Next to the introduction, a review on the literature over performance measurements and investment funds efficiency is presented. After that, the aim of the article, and then the models of stochastic frontiers and the econometric model specifications are detailed. Section 4 presents the results and the debate. Finally, the conclusion and the bibliographic references are presented. 1. LITERATURE REVIEW Many performance measures have been used since the pioneering theory of portfolios, which was developed by Markowitz (1952). In the understanding of Vargas (2006), Baggio, Silveira, Schneider, Maciel and Oliva (2018) and since it is based on a portfolio theory, the Sharpe Index (1964) should be used to evaluate the performance of diverse portfolios, once it measures the risk through standard deviation. When this ratio is applied to a poor diversified portfolio, it is often undervalued for the excessive risk, which could be reduced by a proper diversification. Thus, it would not be entirely correct to apply the Sharpe Index to specialized portfolios, which by definition do not embrace any diversification. For such cases, the Capital Asset Pricing Model (CAPM) is recommended, once it advocates the securities and portfolios should yield according to their systematic risk, measured by beta. This process leads to ratios such as the ones used by Treynor (1965) and Jensen (1968). Jensen (1968) was a pioneer in the analysis of predictive capacity of investment fund managers. This author evaluated the capacity of 115 US mutual funds from 1945 to 1964 using a model derived from Sharpe (1964), the Capital Asset Pricing Model (CAPM). He concluded that there is little evidence that any individual fund can perform better than expected. Over time, new and more sophisticated forms of performance measurement have been developed, such as market timing and conditional performance measures, which are not based on histori- 354 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 cal returns. They consider the state of the economy every time there is profit and the ability of managers to provide the extraordinary returns. Treynor and Mazuy (1966) have analyzed the annual return of 57 US funds and assumed that in only one of the funds, the hypothesis of market timing was not rejected. Merton (1981), on the other hand, has formalized the analysis of value creation by market timing, in which the manager predicts the highest market return in relation to the risk-free asset, and vice versa, but cannot predict its magnitude. Henrikson and Merton (1981) have performed both tests, parametric and non-parametric, in order to measure the funds’ performance according to market timing. It did not require though, restrictive market assumptions in equilibrium and it followed rationality and efficiency tests considered by Fama (1970). Henrikson (1984) applied these tests in the American market from 1968 to 1980 in 116 funds, and he has found only three funds with a positive market timing ability, so, proving their non-existence. Grinblatt and Titman (1989) compared the abnormal returns of passive and active investment funds during the period from 1975 to 1984, and they got the conclusion that some of the highest performance can be considered the result of active management of the funds. Carhart (1997) analyzed the fund performance investment during the period from 1962 to 1993. The result has confirmed the hypothesis of lack of skill on the part of the managers. Adding to it, the moment factor of Jegadeesh and Titman (1993), which corresponds to the difference between shortterm gaining returns and losing portfolios, to the three-factor model of Fama and French (1993), Mayorga and Marcos (1996) introduced in their analysis the incidence of rates and costs passed on to investment funds management, without obtaining the results significantly different from those obtained in previous studies. Franz and Figueiredo (2003) found no evidence of market timing ability in 29 Brazilian mutual stock funds from 1995 to 2000. Barbosa and Sarto (2007) studied a sample of nine ANBID categories (currently ANBIMA) of Brazilian investment funds, based on the performance measures of Treynor (1965), Sharpe (1966), and Jensen (1968), verifying that the management classification is accompanied by strong similarities, according to different measures. Malacrida, Yamamoto, Lima, and Pimentel (2007) compared the performance of Brazil’s variable income funds with Ibovespa’s benchmark and assumed that many managers cannot overcome the benchmark over the years. This article presents the results of a study, which was carried out by Casaccia (2009), Baggio, Silveira, Schneider, Maciel, and Oliva (2018), examining the Brazilian variable income funds from different performance measures. The conclusion is there are no substantial distinctions among the applied performance measures. Leusin and Brito (2008), in turn, found the evidence of market timing ability in a minority of fund managers from 1998 to 2003, apparently due to greater predictability of large differences in the returns between the stock market and the risk-free interest rate. Fama and French (2010) analyzed the American funds from 1984 to 2006 in order to show whether the performance occurs by skill, or merely luck. The results showed that the net return obtained by the investors was lower than CAPM benchmarks and than three and four factor models, concluding that few funds can cover their costs. Baggio, Ferruz, and Marco (2010) analyzed the relationship between the performance and the increase in the equity of Brazilian variable income investment funds, considering 459 funds from January 1997 to December 2006. Comparing the averages of the annual, semi-annual, and quarterly results, the persistence of the performance and the relation between it and future movements of capital was shown, especially in the short periods. From 1998 to 2009, Matos and Nave (2012) detected a level of unusual persistence in the stock funds due to the manager’s expertise. In the research of 75 different Ibovespa assets funds from January 1998 to December 2008, 355 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 Silva (2012) identified those which were the result of simply luck and those obtained through the ability of their managers, using the methodology proposed by Fama and French (1993). For the analysis of fund performance, Silva (2012) used the methodology proposed by Fama and French (2010) and verified that most of the funds that outperformed had this kind of performance due to chance, while three of them showed a truly superior performance due to their manager’s skills. According to the studies and the research summarized so far, it can be noticed the great attention given to indicate the best investment to make since the creation of classic performance measures. Also, if managers could be efficient compared to the market; and whether efficiency has occurred because of the manager’s skill or pure luck. With the incorporation of the efficiency frontier analysis to the studies and research on the profitability of investment funds, the possibilities of forecasting and planning the portfolio management have been significantly amplified with the support of sturdier methods of multidimensional analysis, such as the Data Envelopment Analysis (DEA) and the Stochastic Frontier Analysis (SFA). Ceretta and Costa (2001) investigated the performance of stock investment funds by Data Envelopment Analysis, sampling 106 funds in the free portfolio mode from December 1997 to November 1999. They identified seven dominant funds, which were confronted with seven least efficient funds, highlighting the differences in attributes and considerations among them. Santos, Silveira, Costa, and Da Silva (2005) evaluated the performance of 307 Brazilian mutual stock funds using the stochastic frontiers. The researchers listed the top ten actively managed funds and the last ten in the period from April 2001 to July 2003. They found out that the efficiency of a fund increases along with larger administrative skills to win the market. They also found that portfolios with low volatility tend to be more efficient; and that there was no relationship between the size of the fund and its performance, although this may have been clouded by a survival bias. De Resende Baima and Costa (2006) checked if the investment expenses and the size of pension funds are directly or inversely related with their performance in the period of 1998–2002. Such authors learned that expenses and the size of pension funds’ portfolios are inversely related to the investments’ performance. Such findings support the idea that active management is not a good strategy. Berggrun, Mongrut, Umaña, and Varga (2014) investigated the performance persistence of stock funds in the Brazilian market between 2000 and 2012. They found the evidence that performance endures once there is significant adjusted risk of bid-ask spread between portfolios of better and worse performance. Besides, it can be noticed that such spread happens mostly due to a lower performance of funds in the lower decile, underlining that some fund managers do not have enough skills to win back the investment costs. Fonseca, Kanitz, and Bassani (2014) checked in their study the performance of 46 Brazilian funds of private equity and venture capital from 1990 to 2013, in comparison to the American market. The internal rate of return (IRR) of Brazilian funds is higher than the average of American funds in the period. Between 1990 and 1997, the funds had lower average performance than private equity funds in the USA, while between 1998 and 2008, the Brazilian funds outperformed the American funds. Therefore, it reflects a learning curve in the Brazilian industry of private equity, and that Brazil is more cyclical than the USA. Galan, Ramos, and Veiga (2015) estimated the efficiency of a mutual funds sample invested in the United States through stochastic production function. They found that the underlying technology had economies of scale both at the bottom and at the top level of the company, and that informational asymmetry had a significant influence on the efficiency. In addition, they also found that domestic funds were more efficient than foreign funds, which invested in the US; that funds directly sold to investors were more efficient than the ones sold to financial intermediaries; and the level of inefficiency’s persistence was globally high. While in ethical and corporate-oriented funds, the ineffi- 356 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 ciency’s persistence was higher, whereas in funds for growth companies, it was lower. Rebeschini and Leal (2016) tested the version of arbitrage pricing theory (APT) with Brazilian funds of stock investment between 2002 and 2012 by using four macroeconomic factors and a single market factor. The only ones to present the consistent signal of coefficients and high significance frequencies in all periods and fund categories were market risk and the structure of interest rate. Mamatzkis and Xu (2016) examined the performance of Chinese mutual funds and the impact of managerial attributes on fund performance over the period from 2005 to 2013, using SFA and other traditional fund performance methods such as Jensen alpha and Sharpe Index. The study revealed that team management in a large fund had a negative impact on its performance; funds managed by long-term managers performed poorer than relatively new fund managers, and that only managers with a Master’s Degree had a positive impact on the fund performance. Maestri and Malaquias (2018) analyzed 6,002 multimarket funds from September 2009 to December 2015 and they concluded that portfolio composition is the factor, which explains best a significant change in the funds’ performance. Yet, the best returns adjusted to risk were delivered by less experienced managers, funds, which invested more in fixed income, managers with greater quantity of funds, and larger funds. In this brief context of empirical experiments discussed so far, it becomes clear that the recent use of DEA and SFA methods has risen the efficiency frontier analysis of investment funds. 2. AIMS AND METHODS The goal of this work is to apply the SFA method on panel data of Investment Funds in Credit Rights (FIDC) of the Brazilian ANBIMA Agro, Commerce, and Industry categories, active from 2012 to 2015. The goal is also to evaluate its relative efficiency and persistence in those years, including Sharpe Index to identify the most and the least recommendable by these two different approaches. 2.1. The Stochastic Frontier Analysis (SFA) model applied to panel data The theoretical basis of the SFA model originates from Aigner, Lovell, and Schmidt (1977) and their proposition of a stochastic frontier production function, considering the additional error of the variable, i V added to the non-negative random variable, i U : ( ) ln , i i ii y X VU β = +− 1,2,..., .in= (1) The random variable Vi accounts for errors and other random factors, such as weather effects, crisis, strikes, etc. in the value of the production variable, along with combined effects of not specified input variables in the production function. The term V is independent and identically distributed; it has a normal distribution with zero mean and constant variance. The model defined in (1) is called production function of stochastic frontier because the product’s values are bounded by the stochastic random variable, ( ) exp . ii XV β + The random component i V can be positive or negative and thus the stochastic production frontier varies over the deterministic part of the frontier, ( ) exp . i X β When this model was incepted in 1977, it was regarded as the calculation of average technical efficiency for all the observations, except its estimate for each Decision Making Unit (DMU). The solution to the decomposition problem came five years later with Jondrow, Lovell, Materov, and Schmidt (1982). Six years later, Battese and Coelli (1988) elaborated a generalization of those results for panel data i U and semi-normal distribution. They took the function of frontier production as a basis: ( ) ln ln , , it it i y fpf X βε = + (2) where 1,...,in= and Tt ,...,1= index of the DMUs and the time, respectively, it y is the production volume of the i-th DMU at time t, it X is a matrix of the inputs associated with i-th DMU at time t, β is the vector of parameters to be estimated, , 0 it it i i V UU ε =+< has the components defined as (1). 357 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 Thus, for Battese and Coelli (1988), the technical efficiency of a given DMU is defined as the ratio between its average production (in original units) at a given efficiency level and the corresponding average production being i U zero, that is: ( ) ( ) | , . | 0, it i it i it i it Ey U X ET Ey U X == (3) In the case where the frontier production function is defined by the logarithm of production, the production of i-th DMU at time t is ( ) exp , it y and its corresponding measure of technical efficiency is ( ) exp . ii ET U= (4) This measure is equivalent to the ratio between the production of i-th DMU in a given period t: ( ) ( ) exp exp it it it i y X VU β = ++ (5) and the corresponding volume of production, where Ui is equal to zero, that is, ( ) exp . it it XV β + (6) Putting aside the two-stage models used so far, Kumbhakar, Ghosh, and McGuckin (1991), Reifschneider and Stevenson (1991), and Huang and Liu (1992) proposed the models in which frontier parameters and those of the inefficiency equation are estimated simultaneously. Such formulations presume the existence of associated distribution to the cross-sectional data of sample firms. Battese and Coelli (1995) extended the Huang and Liu’s model (1992) to a panel data and created a specification, where efficiency is expressed as a function of specific variables, including “time trend” and random term. Since this model assigns a structure to the technical efficiency, it is possible to analyze the simultaneous variation of production frontier and efficiency by discriminating the trends associated with frontier dislocations from those related to the dissemination (or not) of best practice. This specification has the advantage of softening the hypothesis of technical efficiency levels and technological frontier invariant over time. Thus, itititit UVXy −++= ββ 0 (7) and 0, it it it it y XV ββ =++ 00, it it U ββ = − (8) where it y denotes the production/service of DMU i at time ,t it X is an input vector associated with the units under analysis in each observation period, β are the parameters to be estimated ( 0 β is the intercept of the production frontier), it V are the stochastic shocks assumed as iid in a normal distribution ( ) 2 0, v N σ and distributed independently of the , it U it U are non-negative random variables associated to the production inefficiency, and they have, by assumption, a normal distribution shortened with mean it Z δ and variance 2, σ it Z is a vector of explanatory variables associated with technical inefficiency of the firms involved in the production process, and δ is a vector of unknown coefficients to be estimated. The technical efficiency it U is, by hypothesis, a function of “explanatory” it Z variables and a vector of unknown coefficients, . δ It is expected that this set of variables be associated with the deviations of production observed in relation to stochastic frontier, ( ) exp . it it XV β + The individual effects related to , it U can be specified as , it it it UZ W δ = + (9) where the random variable Wit is defined by the truncation of a normal distribution with zero mean and variance 2, σ provided that the truncation point is in , it Z δ − i.e., . it it WZ δ ≥− This hypothesis is consistent with the fact that it U has a non-negative truncated distribution ( ) 2 ,. it NZ δσ The basic assumption of this model is that it U and it V are independently distributed throughout 1,2,...,tT= and 1,2,..., .in= The efficiency of firm i at time t of observation is defined by ( ) ( ) exp exp . it it it it TE U Z W δ = −= −− (10) And it is based on a mean conditioned to the hypotheses given. It is important to observe that , it it i t i t Z WZ W δδ ′ ′′ +> + for ,ii ′ ≠ does not necessarily imply that , it it i t i t Z WZ W δδ ′ ′ ′′ ′′ +> + for .tt ′≠ 358 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 Consequently, the same ordering of DMUs in terms of technical efficiency of production is not applied to all the periods. 2.2. Specification of the econometric model The empirical version of the stochastic frontier analysis model, applied to panel data (Equations 7 to 10, section 2), is 01 23 ln ln ln ln it it it it it it RENTA RISCA PATLA TADA V U ββ ββ =++ + + +− (11) and 01 23 , it it it it U TEMPO RENTS RISCS δδ δδ =++ ++ (12) where it RENTA denotes the profitability of fund i in year ,t expressed as a percentage, where 1i= to 33 and 1t= (2012) to 4 (2015) – these indexes are also valid for the other variables of the model, 0 β is the constant coefficient (intercept of the profitability frontier) and 1, β 2 β , and 3 β are the coefficients of the explanatory variables it RISCA (annual risk – in units of monthly standard deviation of yields), it PATLA (annual equity – in R$ 1,00 ) and it TADA (annual management fee – in percentage), respectively, it V are stochastic shocks, it U are non-negative random variables associated to inefficiency of profitability, which have, by assumption, truncated normal distribution with mean it Z δ and variance 2 , σ it Z is a vector of explanatory variables (Equation 12) associated with the funds technical innefficiency, defined by it TEMPO (years), it RENTS (semester return) and it RISCS (semester risk) in the present case, and 0 δ is the constant coefficient and 1 , δ 2 δ , and 3 δ are the coefficients of time, semiannual profitability and semiannual risk, respectively. The explanatory variables included in the profitability function (Equation 11) were defined as being the most common in the studies and in the research on investment funds profitability found in the specialized literature. By exposing the explanatory variables on the inefficiency function (Equation 12), we intend to verify the meanings and the impact of their influence on efficiency, as well as the calculated time trend and the semiannual risk and return – the definition of these last two variables walks side by side with the understanding of Ceretta and Costa Jr (2001). The FRONTIER Version 4.1 software, available at the Center for Efficiency and Productivity Analysis (CEPA) (2018), was used to quantify the efficiency on stochastic frontier panel of Brazilian FIDC Agro, Commerce, and Industry categories. It follows the parameters of Battese and Corra (1977), where 2 V σ and 2 U σ are replaced by 2 22 VU σσσ = + and 22 , U γσσ = respectively, which indicates the influence of the one-sided component on global variance and represents the relative importance of the term inefficiency in the panel adjustment. Under these conditions, γ must be between 0 and 1, at the iteration’s initialization of the maximization algorithm. This estimation process makes it possible to include two vectors of explanatory variables. The first one influences the level of frontier profitability (Equation 11), while the second one influences the technical inefficiency (Equation 12). Such characteristics are found in the stochastic frontier efficiency model with panel data, designed by Battese and Coelli (1995). The data used were extracted from the information system of the Brazilian Association of Financial and Capital Market Entities (ANBIMA) through formal request. For the composition of the surveyed funds, all investment funds of FIDC Agro, Commerce, and Industry categories of ANBIMA were taken into account, totaling 223 existing funds in the period from 2011 to 2015. Among those, we selected the active ones from 2012 to 2015, neglecting the year of 2011, once it would have reduced the quota of funds to be analyzed. 3. RESULTS AND DISCUSSION Table 1 presents the results regarding the descriptive analysis of the investment funds analyzed. It is noteworthy that the funds obtained positive average returns in three of the four years analyzed. It also stands out that the higher the profitability, the greater the risk involved. 359 Investment Management and Financial Innovations, Volume 16, Issue 4, 2019 http://dx.doi.org/10.21511/imfi.16(4).2019.30 Table 1. Descriptive analysis Source: Elaborated by the authors from the research data. Code Institution Annual management fee 2012 2013 2014 2015 Average Standard deviation Profitability Risk Profitability Risk Profitability Risk Profitability Risk 130702 BEM 0.27% 8.59% 0.11% 8.22% 0.10% 11.03% 0.07% 13.51% 0.11% 10.34% 2.46% 130710 BEM 0.27% 8.45% 0.47% 2.95% 16.05% 8.03% 0.32% 11.97% 0.36% 7.85% 3.71% 156876 CITIBANK 0.02% 7.98% 0.10% 7.90% 0.14% 11.38% 0.07% 13.93% 0.11% 10.30% 2.92% 156884 CITIBANK 0.02% 11.76% 0.36% 23.51% 1.41% 46.08% 0.53% 38.78% 0.51% 30.03% 15.39% 166391 CONCORDIA 0.15% 9.91% 0.13% 9.49% 0.12% 12.41% 0.06% 1.64% 3.37% 8.36% 4.66% 166405 CONCORDIA 0.15% 8.38% 0.39% 9.92% 0.52% –2.09% 5.03% –5.48% 3.41% 2.68% 7.62% 180580 CONCORDIA 1.35% 5.99% 1.45% 14.51% 3.32% 4.03% 118.41% 3.68% 0.12% 7.05% 5.08% 187501 BEM 0.10% 0.59% 2.24% 1.01% 1.86% 5.40% 1.29% 12.77% 0.10% 4.94% 5.65% 187518 BEM 0.10% –16.15% 0.27% –21.82% 0.21% –28.75% 0.45% –44.73% 1.07% –27.86% 12.37% 199461 OLIVEIRA TRUST DTVM 0.50% –45.26% 49.08% –8.91% 33.63% 561.74% 99.81% 14.49% 13.63% 130.51% 288.53% 199761 BB DTVM S.A 0.01% 8.41% 0.11% 8.05% 0.10% 10.81% 0.06% 13.23% 0.10% 10.13% 2.40% 199877 BB DTVM S.A 0.01% 56.16% 5.16% –35.81% 4.27% –78.75% 4.75% –93.12% 14.99% –37.88% 67.26% 223514 CAIXA 0.20% –0.36% 0.09% 0.24% 0.09% 0.17% 0.08% 0.19% 0.10% 0.06% 0.28% 223522 CAIXA 0.20% –11.85% 8.75% –8.49% 5.17% 4.95% 2.96% 21.61% 0.93% 1.56% 15.21% 226467 CAIXA 0.20% –22.27% 0.17% –33.33% 0.85% –47.46% 1.71% –35.24% 0.45% –34.58% 10.32% 226475 CAIXA 0.20% 13.92% 0.25% 14.62% 0.32% –72.71% 22.85% 11.89% 0.96% –8.07% 43.11% 226904 CITIBANK 0.73% 13.45% 0.12% 13.01% 0.12% 15.86% 0.12% 19.20% 0.51% 15.38% 2.84% 237728 OLIVEIRA TRUST DTVM 0.10% 10.38% 0.14% 0.92% 2.26% 0.70% 3.10% 0.97% 3.69% 3.24% 4.76% 237841 SOCOPA 1.50% 12.90% 0.19% 13.21% 0.21% 14.25% 0.27% 18.28% 0.33% 14.66% 2.48% 237868 SOCOPA 1.50% 35.73% 2.85% –35.55% 4.29% –8.02% 5.54% –7.43% 3.29% –3.81% 29.45% 237914 BEM 0.24% 6.00% 0.03% 5.92% 0.10% 5.87% 0.11% 7.58% 0.60% 6.34% 0.83% 237922 OLIVEIRA TRUST DTVM 0.10% 1.57% 2.19% 4.82% 3.70% 7.80% 1.59% 14.30% 1.24% 7.12% 5.42% 239631 BNY MELLON 0.60% 27.69% 0.39% 16.75% 0.30% 15.46% 0.53% 15.32% 0.18% 18.81% 5.96% 240567 PLANNER 1.35% 10.62% 0.14% –59.24% 18.31% –54.72% 10.31% –4.15% 1.33% –26.87% 35.33% 242691 CONCORDIA 1.50% –2.15% 2.09% –3.02% 0.52% –0.47% 0.27% 2.84% 0.33% –0.70% 2.59% 244351 OLIVEIRA TRUST DTVM 0.10% 10.46% 0.15% 0.92% 2.26% 0.70% 3.10% 0.97% 3.69% 3.26% 4.80% 252484 BNY MELLON 1.50% –68.21% 18.23% –2.86% 0.93% –50.51% 14.18% –0.34% 1.04% –30.48% 34.14% 253979 CITIBANK 0.42% –51.27% 5.20% –98.88% 30.49% 999.77% 372.46% –15.68% 1.51% 208.49% 528.62% 255610 SOCOPA 0.65% –5.44% 5.44% 19.05% 4.24% 24.29% 8.41% –70.12% 19.88% –8.06% 43.36% 257508 SOCOPA 1.50% 11.07% 0.14% 10.59% 0.13% 14.80% 0.09% 18.15% 0.14% 13.65% 3.54% 257516 SOCOPA 1.50% 24.96% 3.36% –8.01% 2.20% 5.63% 2.87% 17.29% 1.54% 9.97% 14.38% 259721 GRADUAL CCTVM S A 0.50% 21.65% 2.97% 24.74% 4.34% 28.77% 2.35% 4.79% 3.31% 19.99% 10.55% 261114 CITIBANK 0.22% –52.33% 4.66% –90.03% 189.60% 77.33% 123.31% –32.66% 23.22% –24.42% 71.89% Total average –1.56% 3.56% –5.93% 10.06% 46.78% 24.46% –0.96% 3.22% 10.36% 39.03%