بهترین عملکرد خانواده های صندوق سرمایه گذاریه آمریکا از 1993-2008: شواهدی از مدل نوین دو مرحله ای DEA برای تجزیه و تحلیل بهره وری

When analyzing relative performance, especially at the institutional level, the traditional data envelopment analysis (DEA) models do not recognize vastly different and important activities as separate functions and therefore cannot identify which function may be the main source of inefficiency. We propose a novel two-stage DEA model that decomposes the overall efficiency of a decision-making unit into two components and demonstrate its applicability by assessing the relative performance of 66 large mutual fund families in the US over the period 1993–2008. By decomposing the overall efficiency into operational management efficiency and portfolio management efficiency components, we reveal the best performers, the families that deteriorated in performance, and those that improved in their performance over the sample period. We also make frontier projections for poorly performing mutual fund families and highlight how the portfolio managers have managed their funds relative to the others during financial crisis periods.

The mutual fund industry in the US is by far the largest such industry in the world, managing US$11.2 trillion in assets by the end of 2009. In this paper, we propose a novel data envelopment analysis (DEA) model to investigate the relative performance of 66 large (in terms of total funds) mutual fund families in the US over the 16-year period 1993–2008. Research on individual mutual fund performance is vast and is spread widely across different markets (Treynor, 1965, Sharpe, 1966, Jensen, 1968, Hendricks et al., 1993, Goetzmann and Ibbotson, 1994, Malkiel, 1995, Elton et al., 1996, Carhart, 1997 and Blake and Morey, 2000). However, the focus on the performance at the mutual fund family level is limited only to a few (Tower and Zheng, 2008 and Elton et al., 2007), possibly due to the complex nature of the analysis involved. This paper fills this gap by focusing on the relative performance of mutual fund families. This is an important area of study, as investors in mutual funds generally tend to invest in funds within the same mutual fund family rather than across a number of families. The reasons for investing within one mutual fund family include convenience in searching for investment opportunities and recordkeeping (Kempf and Ruenzi, 2008) and flexibility of switching funds without additional sales charges and restrictions imposed by the fund family (Elton et al., 2006 and Elton et al., 2007). We investigate the relative performance of large mutual fund families using a novel two-stage DEA model where the overall efficiency of a mutual fund family is decomposed into two components, namely, operational management efficiency and portfolio management efficiency; that is, we conceptualize fund family management as a two-stage process that consists of an operational management stage (stage 1) and a portfolio management stage (stage 2). Therefore, the overall efficiency of a fund family is a composition of operational management efficiency and portfolio management efficiency. The aim of decomposing the overall efficiency is to capture which of the two stages may have greater influence on the overall efficiency of the mutual fund family. Hence, our study is of interest to all stakeholders: the investors, the fund managers, and the management companies of mutual fund families. Previous studies of mutual fund family performance consider overall return as the measure of performance. Kapur and Timmerman (2005) note that when the share market has performed very well, the absolute return-based performance of mutual funds is an unreliable measure of managerial ability. They acknowledge that during a bullish market, it is more appropriate to remunerate fund managers based on relative performance rather than on absolute performance. Cooper et al. (2004) argue that DEA, which is a non-parametric method, is ideal for assessing relative performance.1 DEA models have the advantage of assessing performance in a multi-dimensional framework; that is, they can accommodate multiple inputs and multiple outputs. For the efficiency decomposition, we propose a novel two-stage DEA model with i1 inputs to stage 1, D intermediate measures, i2 inputs to stage 2 (in addition to the intermediate measures), and s outputs from stage 2. The proposed model aligns with the network approach of Färe and Whittaker (1995). The novel aspect of our model stems from several methodological advances. Unlike previous work, we model efficiencies of both stages simultaneously and therefore our model adopts a non-standard approach. The proposed DEA model not only assesses the overall performance, it decomposes the overall efficiency into two components associated with the performance of each stage. Such decomposition of efficiency is not possible in the previous network approach of Färe and Whittaker (1995). Furthermore, our approach is not restrictive in terms of orientation as in Kao and Hwang’s (2008) two-stage model, which is valid only under the constant returns-to-scale (CRS) assumption. Our approach can be applied under CRS as well as variable returns-to-scale (VRS) situations. Holod and Lewis (2011) propose a two-stage DEA model to resolve the deposit dilemma. However, their model is not capable of obtaining separate efficiency estimates for each stage. In addition to the decomposition of overall efficiency, another major difference between our model and that of Holod and Lewis (2011) is that our model allows new variables in the second stage as inputs in addition to the intermediate variables that link stages 1 and 2. The proposed two-stage DEA model is applied to investigate the relative performance of the mutual fund families as follows. In the first stage, we focus on the operational management efficiency of each mutual fund family by considering how efficiently they make use of inputs, such as marketing and distribution expenses and management fees, in producing the output, which is the net asset value. In the second stage, we focus on portfolio management efficiency by estimating how efficiently the mutual fund families make use of inputs, such as fund size, standard deviation of the returns, turnover ratio, expense ratio, and net asset value, in producing the output, which is the average return of the fund family; that is, the mutual fund family application presented in this paper is an illustration of the general two-stage DEA model with i1 = 2, D = 1, i2 = 4, and s = 1. Although there is one output from the first stage and one output from the second stage in this particular application, the DEA model proposed in this paper works under multiple inputs, outputs, and intermediate measures. In our formulation, we treat net asset value (NAV), which is the output variable of the first stage, as an input variable in the second stage; that is, net asset value is modeled as an intermediate variable that links stage 1 and stage 2. Holod and Lewis (2011) treat deposits in the same way in the two-stage DEA model they use in assessing bank performance. Brown et al. (2001) point out that even though relative performance appears to be the overriding concern of fund managers as well as their clients, considerably less attention is directed towards the equally important question of assessing the relative performance of portfolios. In this paper, we make a significant contribution to the literature on this issue by providing a methodology that is robust and flexible. Our modeling approach is general and hence can be applied to assess the performance of other financial institutions as well. For instance, it can be applied to assess the operational management efficiency and portfolio management efficiency of finance sector institutions, such as insurance companies, banks and credit unions. The rest of the paper is organized as follows. Section 2 discusses the background of our study. Section 3 provides a general description of the proposed two-stage DEA model. Specific details regarding the formulation of the DEA model are provided in Appendix A, and the model used for frontier projection is given in Appendix B. Section 4 is devoted to a discussion of the data, sample selection, and calibrating the input–output variables used in the DEA model. The results are presented in Section 5, and Section 6 concludes the paper.

The mutual fund industry in the US is the largest such industry in the world, and numerous studies have investigated its fund performance at the individual mutual fund level. Studies at the individual fund level fail to reveal information on the performance of the fund family to which the individual fund belongs. This is important to investors who invest in funds within the same mutual fund family rather than across a number of families for various reasons, including practical convenience. For them, the information on how a given mutual fund family as a whole may have performed relative to other mutual fund families is crucial. Studies have paid little attention to this issue. In this study, we fill this gap by proposing a novel two-stage DEA model to analyze the relative performance of large US mutual fund families over the period 1993–2008. Unlike the traditional performance measures, the proposed DEA model allows a combination of several performance measures, such as returns, fees and charges, risk of investment, stock selection style and portfolio management skills, and operational management skills, into a single measure in evaluating the overall performance of a mutual fund family relative to other families in the sample. The proposed two-stage DEA model provides greater insight into the performance of mutual fund families by decomposing the overall efficiency into two components: operational efficiency and portfolio efficiency. This is a significant contribution to the DEA literature, as the two-stage DEA model proposed in the past literature does not discuss decomposition of overall efficiency into different components. In addition to mutual fund families, the proposed DEA model can also be applied to the other financial institutions, such as banks, insurance companies and credit unions. Numerical evaluation of the proposed DEA model over the period 1993–2008 reveals that the proposed model is able to highlight the mutual fund families that may have managed their portfolios well during financial crisis periods as well as which of the two components, operational management or portfolio management, may have been the contributory factor to their good or bad performance. This useful information can help investors make informed decisions and enables administrators of fund families to judge how well their portfolio managers have performed relative to their competitors.