Resources Policy 39 (2014) 54–60
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Precious metal mutual fund performance appraisal using DEA modeling Ioannis E. Tsolas n National Technical University of Athens, School of Applied Mathematics and Physics, 9 Iroon Polytechniou, Zografou Campus, Athens 157 80, Greece
art ic l e i nf o
a b s t r a c t
Article history: Received 30 December 2010 Received in revised form 25 October 2013 Accepted 8 November 2013 Available online 27 November 2013
The purpose of this paper is to evaluate the performance of a sample of sixty-two precious metal mutual funds by applying a two-stage procedure. In the ﬁrst stage, data envelopment analysis (DEA) is used to measure the relative efﬁciency of funds. In the second stage, a Tobit model is employed to identify the drivers of performance. The purpose for and intended contribution of this paper is twofold: to provide consolidated measures of relative performance of precious metal mutual funds using for ﬁrst time the DEA framework and to explain fund performance by employing a Tobit model. Correlation results among DEA-based performance measures and traditional indicators of fund performance (Sharpe ratio and Jensen's α) are mixed; no correlation has been found for the Sharpe ratio; whereas in the case of Jensen's α, the correlation is not high. Moreover, the mean-variance efﬁciency hypothesis holds for the inefﬁcient funds of the sample. In addition, DEA-based fund performance can be explained by fund size, fund persistence, and beta coefﬁcient. & 2013 Elsevier Ltd. All rights reserved.
JEL classiﬁcation: C14 G20 G23 Keywords: Precious metal mutual funds Efﬁciency Data envelopment analysis
Introduction Mutual funds are portfolios of stock-exchange securities and/or bonds consisting of shares with the purpose of echoing the overall market. Fund prices are quoted daily on the market, providing a margin for the various types of costs (e.g. management costs and costs for buying and selling securities) (Chiodi et al., 2003). Precious metal mutual funds (e.g. gold mutual funds) are similar in deﬁnition to stock mutual funds, in that they invest in a portfolio of shares of mining companies or in tangible metal. Investors who purchase precious metal mutual funds hope to experience greater returns in the long run by buying shares in groups rather than individually. Trading in key precious metals (e.g. gold, silver, platinum, and palladium) comprised a US$0.4 trillion in December 2008, about 9 percent of the trading in commodity markets (e.g. precious metals, oil, agricultural, and other resource commodities) (Batten et al., 2010). Investors can take a position in precious metal price risk by investing in precious metal mutual funds. On average, gold mutual funds provide greater absolute returns than an investment directly in gold itself. Investors expecting a change in the gold price (positive or negative) can expect the gold mutual funds to change
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even more gold, but evidence also supports the assertions that mutual fund returns are disrupted by no-gold-related risk. In regard to empirical research on the correlation between gold and the stock market, see Blose (2010). The prices of precious metal mining stocks do not always move in the same direction as the market price of precious metals. This is due to a number of factors such as mining cost, which can vary signiﬁcantly among precious metal mining companies and the length of mine life; for instance, a long mine life is associated with better geological conditions; whereas a short mine life implies that a deeper, more costly process will be necessary to extract the precious metal. Precious metal mutual funds offer a diversiﬁed portfolio of precious metal mining stocks, and savvy investors should seek funds based on their aggregated performance measures (Blose, 1996). The performance evaluation of mutual funds has become an important issue for both fund managers and researchers. The performance of mutual funds since the pioneering works of Sharpe (1964, 1966), Treynor (1965), and Jensen (1968, 1969) has been investigated using mainly the Capital Asset Pricing Model (CAPM). The CAPM-based performance measurement techniques are within the risk-return framework and are dependent on two factors: the benchmark portfolio used and risk measurement. Most studies investigate the performance of mutual funds while taking into account the expected excess return of the portfolio and a risk measure without incorporating cost categories such as the transaction costs and management fees charged by the funds (Galagedera and Silvapulle, 2002; Murthi et al., 1997; Sengupta and Zohar, 2001).
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Since the late nineties, there has been a growing body of research applying DEA (Charnes et al., 1978) on mutual fund performance evaluation. DEA was ﬁrst proposed by Murthi et al. (1997) as a measure of portfolio performance. It can easily capture the multidimensional aspect of mutual fund performance and alleviate some of the problems associated with CAPM-based performance measures. DEA, based on the efﬁciency measurement method of Farrell (1957), permits appraisal and rank of precious metal mutual funds in a risk-return framework using other variables such as the expense ratio. A DEA-based performance measure is important because it enables investors to potentially pinpoint the reasons behind poor performance of funds; moreover, it assists fund managers in the performance appraisal for their funds (Alexakis and Tsolas, 2011). The present study offers two main contributions into the ﬁnance literature. In a ﬁrst stage, the performance of a sample of precious metal mutual funds is assessed using DEA modeling. In the second stage, a Tobit model is employed to identify the performance drivers. The ﬁrst stage of analysis deals with the derivation of consolidated fund performance measures, the classiﬁcation of funds into efﬁcient and inefﬁcient, the analysis of slacks to test whether the mean-variance efﬁciency hypothesis holds for the underperformer funds, and the comparison of traditional indices of fund performance with the derived DEA measures. The second stage deals with Tobit regression analysis. In this paper, the following questions are addressed: (1) What is the most efﬁcient level of risk and other transaction cost associated with sampled precious metal mutual fund returns? (2) Which are the top performers among the sampled precious metal mutual funds? (3) Is there statistical signiﬁcant correlation among the proposed DEA-based performance measures and the traditional indices of fund performance evaluation? (4) Does the mean-variance efﬁciency hypothesis holds for the underperformer funds? (5) Which are the drivers of fund performance? The rest of the paper unfolds as follows: Section 2 reviews the literature on DEA-based mutual fund performance evaluation. Section 3 brieﬂy outlines DEA methodology and the proposed model. The data, along with identiﬁcation of inputs and outputs for the case of precious metal mutual fund industry, are reported in Section 4. Section 5 presents and discusses the results of the two stages of the analysis. Section 6 provides some policy implications, and the last section concludes.
Survey of DEA-based mutual fund performance evaluation In recent years, a growing body of studies has applied frontier estimation methodologies for evaluating the performance of mutual funds. The methods on efﬁciency measurement use either a parametric or a nonparametric approach (Førsund et al., 1980). Studies that apply the parametric approach in frontier analysis to mutual funds include the works by Briec and Lesourd (2000), where an application of the stochastic parametric approach is provided, and Annaert et al. (2003), who apply the stochastic Bayesian approach (van den Broeck et al., 1994). The ﬁrst use of DEA to assess fund performance dates back to the pioneering work by Murthi et al. (1997), who developed the DEA portfolio efﬁciency index (DPEI) to evaluate the performance of mutual funds using costs (inputs) and returns (output). They modiﬁed the basic idea employed in the Sharpe index (Sharpe, 1966) by incorporating transaction costs. The motivation of Murthi et al. (1997) to use DEA was to overcome a number of
shortcomings of traditional two-dimensional (risk-return) performance measures. DEA offers a multidimensional performance analysis compared to the above two-dimensional performance measures, since it does not require any theoretical model as a benchmark. Moreover, DEA-based performance is a combination of multiple fund attributes. These include mean returns (outputs), risk (total or systematic), expenses (e.g. transaction costs and administration fees), loads (subscription or/and redemption costs), minimum initial investment, and net asset value (inputs) (See Morey and Morey, 1999; Choi and Murthi, 2001; Sengupta and Zohar, 2001; Anderson et al., 2004). The analysis has been extended to introduce other output variables such as a stochastic dominance indicator (Basso and Funari, 2001, 2005) and input variables such as an ethical indicator (Basso and Funari, 2003), value-at-risk (VaR), and conditional value-at-risk (CVaR) measures (Chen and Lin, 2006). For recent reviews, see Galagedera (2003) and Glawischnig and Sommersguter-Reichmann (2010). Employing essentially radial DEA models like CCR (Charnes et al., 1978) or BCC (Banker et al., 1984) models without or with weight restrictions (McMullen and Strong, 1998; Glawischnig and Sommersguter-Reichmann, 2010) and non-radial DEA models like the directional distance function (Chambers et al., 1998) or the range-adjusted measure (RAM) of performance (Cooper et al., 1999), the efﬁciency of funds is compared within a category or between several categories. Other approaches that appear in the relevant literature are the minimum convex input requirement set (MCIRS) approach (Chang, 2004), the concept of order m frontier (Daraio and Simar, 2006), the concept of α-quantile efﬁciency scores (Daouia and Simar, 2007), as well as DEA modeling based on the mean-variance (Briec et al., 2004) and mean-varianceskewness framework (Joro and Na, 2006; Briec et al., 2007). Briec and Kerstens (2009) extended the multi-horizon mean-variance portfolio analysis of Morey and Morey (1999), and more recently, Bãdin et al. (2010) presented a data-driven approach for conditional efﬁciency measures of mutual funds. A recent classiﬁcation of modeling approaches by Brandouy et al. (2013) distinguishes models directly derived from production theory, models combining a fund traditional performance measure (e.g. Sharpe ratio) with other variables, models based on portfolio theory, and hedonic price models (Kerstens et al., 2011).
Conceptual framework DEA methodology DEA methodology was ﬁrst proposed by Charnes et al. (1978) to evaluate the relative efﬁciency of production units, referred to as decision-making units (DMUs). This is a nonparametric method, in that it does not require assumptions regarding the shape of the production frontier using simultaneously multiple inputs and outputs. In portfolio management, the objective is to analyze the performance of investment portfolios. Risk (volatility or variance) and the return of a portfolio are analogous to inputs and outputs in model of production; in the DEA setting, other variables that reﬂect cost can be incorporated into the input side of the DEA. Also in the DEA setting, the use of mutual funds such as DMUs may raise some questions about the homogeneity of those mutual funds. It is worth noting that the objective of the DEA is to measure the relative efﬁciency among similar units that share the same technology (procedure) for similar goals (outputs, returns), by using similar resources (inputs). DEA maps a piecewise linear convex isoquant (i.e. a nonparametric efﬁcient frontier) over data points to determine the efﬁciency of each of the DMUs relative to the isoquant. DEA accomplishes this by constructing the efﬁcient frontier from a linear combination of the perfectly
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efﬁcient funds and determines fund deviations from that frontier that represent performance inefﬁciencies. The efﬁciency scores of DMUs are bounded between zero and one, with fully efﬁcient funds having an efﬁciency score of one. A DEA model can be formulated in two versions: input and output orientation. An input orientation analysis determines the proportional reduction of the inputs without changing the output level for an inefﬁcient fund to become DEA efﬁcient. An output orientation analysis provides information on the proportional expansion of output levels of an inefﬁcient fund that is necessary, along with the maintenance of current input levels, for the fund to become DEA efﬁcient. Apart from the input- and output-oriented efﬁciency measures there are also the so called non-oriented or graph efﬁciency measures. In the mutual fund rating literature, examples include the works of Briec et al. (2004, 2007) and Briec and Kerstens (2009). Input orientation analysis is most cited in the relevant literature and in particular the BCC (Banker et al., 1984) model. This is due to the fact that the input-oriented BCC model is translation invariant with respect to output variables, and thus it can be used to overcome the possible problem posed by the presence of negative returns. DEA input orientation analysis deﬁnes an efﬁciency measure of a fund by its position relative to the frontier of the best fund performance established mathematically by the ratio of the weighted sum of outputs to the weighted sum of inputs. The estimated frontier of best performance characterizes the efﬁciency of funds and identiﬁes inefﬁciencies (Alexakis and Tsolas, 2011). More generally, in a DEA framework (Charnes et al., 1978), the management of n mutual funds, j¼1,…,n, is characterized by a set of k inputs X A ℜm þ to produce quantities of outputs Y A ℜ ; the amounts of the ith input and rth output, used by the jth mutual fund are denoted by xij and yrj, respectively. The following VRS input-oriented BCC (Banker et al., 1984), or value-based model (Thanassoulis, 2001) (1) can be used to assess the performance of funds. k
h ¼ ∑ μr yrjo þ ω r¼1
∑ vi xijo ¼ 1
∑ μr yrj ∑ vr xrj þ ω r 0
j ¼ 1; 2; …; j0 ; …n
r ¼ 1; 2; …; k
vi Z ε ω free on sign
r ¼ 1; 2; …; m
( Yj ¼
j ¼ 1; 2; :::; n
Y nj 4 0
Y nj r0
Simar and Wilson (2007) claim that this DEA/Tobit two-stage approach is invalid due, among other factors, to complicated and unknown serial correlation among the estimated efﬁciencies. In addition, it can lead to inaccuracies if the number of the units located on the efﬁcient frontier represents a large proportion of the sample (Nahra et al., 2009). Simar and Wilson (2007) propose in the second-stage bootstrap procedures truncated (rather than Tobit) regression analysis. See Johnson and Kuosmanen (2012) for additional qualiﬁcation of these conclusions. Estimation method alternatives to Tobit regression have appeared in the relevant literature. Ordinary least squares (OLS) linear regression has proved to be a consistent estimator (Banker and Natarajan, 2008; McDonald, 2009). McDonald (2009) further argued that DEA scores are more consistent with a fractional logit model; whereas Estelle et al. (2010) conclude that multiple regression approaches such as nonparametric regression, OLS, Tobit, and fractional logit provide very similar results. Recent contributions to this bulk of literature are the works of Ramalho et al. (2010) and Guan and Chen (2012), who employed partial least squares regression (PLSR) to the second stage of DEA formulation modeling regression.
Data and identiﬁcation of input and output variables Data
Two-stage approach A two-stage approach is applied in this research, combining the input-oriented BCC (BCC-I) model in the ﬁrst stage with a censored Tobit regression model in the second. The BCC-I model provides the most efﬁcient level of the value factors of the sample funds and the best funds (top performers), whereas the censored Tobit model is used to examine whether fund-speciﬁc factors interfere with the fund ratings produced. Regression analysis The ﬁrst-stage inefﬁciency score is the dependent variable that is regressed on the explanatory variables according to the model: j ¼ 1; 2; :::; n
Y nj ¼ βZ j þuj :
where ε 40, a convenient small positive number (non-Archimedean), see also Charnes et al. (1994), μr ¼output weights estimated by the model and vi ¼input weights estimated by the model.
Y j ¼ f ðZ j ; βÞ þ uj ;
where Y j is the dependent variable, Z j and β are vectors of explanatory variables and unknown parameters, respectively, uj is the error term and n is the number of observations. The ﬁrst stage of the analysis produces DEA efﬁciency fund ratings that are distributed between zero and unity; therefore, the fund rating becomes a limited dependent variable in the second stage of analysis. To analyze such type of data, a censored Tobit model (Tobin, 1958) is usually applied as an appropriate multivariate statistical model (Hoff, 2007; Sueyoshi et al., 2010). When the dependent variable Y j is censored at zero, the Tobit model may be described as follows (Greene, 1997)
The input and output variables on sixty-two precious metal mutual funds were used in this study. The annual data, publicly available on the Google Finance website (www.google.com/ﬁnance), is from Morningstar, which provides data on net assets, risk measures (i.e. standard deviations and the beta coefﬁcient (β) of the CAPM), annualized returns, fund characteristics and traditional indices (Sharpe ratio and Jensen's α) of mutual fund performance evaluation. Sixty-two funds were analyzed due to the availability of complete information on these funds. Input and output variable speciﬁcation for DEA There is no consensus among researchers and investors as to which input and output variables should be unambiguously included in a DEA fund performance model. One output variable, namely, the annualized 3-yr return, is considered in this paper to capture the medium-term gross performances (Galagedera and Silvapulle, 2002). The input variables used in the DEA analysis are the following: (i) standard deviation of 3-yr gross performance as a measure of risk; (ii) operating expenses generally referred to as the management expense ratio (MER); (iii) front load; and (iv) deferred load. The BCC-I model is used to examine whether
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the fund managers have employed inputs (risk, MER, front and deferred load) efﬁciently to produce output (annualized yearly returns). Risk is proxied by standard deviation (i.e. the dispersion of return) that represents the fund's total risk, which may be important for the not-well-diversiﬁed small funds. The MER is the percentage of fund assets paid for operating expenses and management fees, including administrative fees and all other assetbased costs incurred by the fund except brokerage costs. The front load, or sales charge, as a percentage of investment, is the entry fee paid by the investors at the time of purchasing shares of mutual funds, while the deferred load is the fee paid when shares are sold. Descriptive statistics of inputs and outputs used in the DEA assessment are presented in Table 1. Variable speciﬁcations for the Tobit regression model The second stage of analysis involves explaining the variation in the DEA-based relative inefﬁciencies by Tobit regression model that include independent variables to proxy a fund's operational characteristics. The explanatory variables include the logarithm of the fund's net assets, which controls for fund size, persistence (i.e. annualized 1-yr return) that reﬂects momentum, and beta coefﬁcient to proxy the systematic risk that cannot be further reduced through diversiﬁcation.
Results The following section ﬁrst presents and discusses the results of the BCC-I model (ﬁrst stage), before turning to the second-stage Tobit regression results. First stage analysis Precious metal mutual fund performance The estimated efﬁciency scores of precious metal mutual funds derived using the BCC-I model are summarized in Table 2. The
Table 1 Descriptive statistics of precious metal mutual funds data used in the assessments.
Min Max Mean Median Standard deviation Q1 Q3 Number of funds: 62
3 yr-standard deviation (%)
Frond load (%)
Deferred 3 yr-returns (%) load (%)
25.72 36.32 30.08 29.96 1.77 29.24 30.89
0.26 3.57 1.46 1.29 0.57 1.05 1.87
0.00 5.75 1.20 0.00 2.26 0.00 0.00
0.00 5.00 0.60 0.00 1.32 0.00 1.00
26.12 12.50 17.17 16.70 2.56 18.93 15.72
mean efﬁciency is 87 percent; whereas the median efﬁciency is of the order of 87 percent. Out of the sixty-two funds, four (6 percent of the total sample) were found relatively efﬁcient. The results indicate that there is scope for efﬁciency improvement in fund performance by minimizing inputs of about 13 percent (¼ 1 0.87) (Table 2). Using the results of the dual of Model (1), one can discriminate among funds that have excelled in performance; these could, therefore, be proposed as benchmarks across sampled funds. Among the four efﬁcient funds, one could further differentiate based on the frequency of their appearance in the reference sets of the inefﬁcient funds, an idea ﬁrstly developed by Charnes et al. (1985) (See also: Adler et al., 2002). The frequency of appearance of an efﬁcient fund in an inefﬁcient fund's reference set provides information on how many inefﬁcient funds are affected by the presence of the efﬁcient fund. Therefore, one can further rank the efﬁcient funds. Corresponding results for the top efﬁcient funds are included in Table 3. The top four funds that can be used as benchmarks are: First Eagle Gold Fund, A (SGGDX); First Eagle Gold Fund, C (FEGOX); First Eagle Gold Fund, I (FEGIX); and Vanguard Precious Metals and Mining Fund, Investor (VGPMX). A comparison among nonparametric and traditional indices of precious metal mutual fund performance Table 4 shows the results of the correlation analysis among DEA-based (nonparametric) and traditional indices (Sharpe ratio and Jensen's α) of mutual fund performance evaluation. From the correlation analysis, the following ﬁndings emerge: First, Sharpe ratio and Jensen's α indicators are positively correlated to each other across the sampled precious metal mutual funds. This is an expected ﬁnding, since the measures by Sharpe (1966) and Jensen (1968) are highly correlated in terms of fund ranking (see also Daraio and Simar, 2006). Second, DEA-based indicators are not highly correlated with Jensen's α, and they are not correlated with the Sharpe ratio. This is not a surprise, due to the different perspectives taken by the two approaches. To investigate further among the nonparametric and traditional indices in the comparative analysis of mutual funds management, a back-testing analysis comparing DEA-based ratings and traditional ratings may be employed (Brandouy et al., 2013; MatallínSáez et al., 2014). The issue is beyond the scope of the current paper, but we look forward to seeing more research addressing this issue.
Table 3 The top efﬁciency precious metal mutual funds.
Notes: 3 yr-standard deviation: standard deviation of 3 yr gross performance, MER: management expense ratio, 3 yr-returns: annualized 3-yr return, Q1: ﬁrst quartile, and Q3: third quartile.
Appearance in the reference set (number of times)
SGGDX FEGOX FEGIX VGPMX
11 17 58 16
Table 2 Mean (standard deviation), median, quartiles (Q1 and Q3), min, max values of efﬁciency measures, number and percentage of efﬁcient funds.
Efﬁcient and inefﬁcient funds Inefﬁcient funds
Efﬁcient funds, number (%)
87.11% (5.43%) 86.22% (4.37%)
SD ¼ standard deviation, Q1 ¼ ﬁrst quartile, and Q3 ¼ third quartile.
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Table 4 Correlation matrix among DEA and traditional indices for the sampled precious metal mutual funds. Jensen's α
BCC-I Pearcon's correlation coefﬁcient BCC-I 1 Jensen's α 0.568* (0.000) Sharpe index 0.159 (0.217) Kendall's rank correlation coefﬁcient BCC-I 1 Jensen's α 0.277* (0.002) Sharpe index 0.001 (0.990) Spearman's rank correlation coefﬁcient BCC-I 1 Jensen's α 0.403* (0.001) Sharpe index 0.002 (0.990)
Min Max Mean Median Standard deviation Q1 Q3
1.63 7.72 5.72 6.10 1.44 5.05 6.85
44.35 28.03 35.40 35.10 2.96 37.89 33.92
0.47 1.30 0.65 0.61 0.17 0.52 0.75
Table 7 Results of Tobit regression for fund efﬁciency. Variable
Notes: p-values in parentheses. n
1 0.726* (0.000)
Notes: size: logarithm of funds' net assets; persist: funds' annualized 1 yr-return; beta: beta coefﬁcient.
1 0.562* (0.000)
Size Sharpe index
1 0.618* (0.000)
Table 6 Explanatory variables. Descriptive statistics.
Correlation is statistically signiﬁcant at a level of 1%.
Table 5 Mean slacks in inputs (3 yr-standard deviation, 3 yr-beta, MER, frond load and deferred load).
t-Ratios signiﬁcant at a level of 1%.
Frond load (%)
Deferred load (%)
The DEA measures that stem from Model (1) yield only ﬁrststage measures of mutual fund performance. What is not known is the reason for variations in such performance patterns, and it is evident that DEA metrics may not be enough for both consulting purposes and policy analysis. Therefore, a second-stage analysis is called for, as performance may be affected not only by inadequate fund management but also by other explanatory variables. In the sequential step that follows DEA, mutual fund performance measures are regressed using the Tobit regression methodology to identify the impact of a series of explanatory variables listed in Table 6. Between the DEA and Tobit regression, this study uses as dependent variable the transformed variable “h′ ¼1 h”, where h is the performance metric derived from Model (1). For computational purposes, Greene (1997) suggested the use of censoring at zero for Tobit regression (see also Sueyoshi et al., 2010)
Notes: size: logarithm of funds' net assets; persist: funds' annualized 1 yr-return; beta: beta coefﬁcient. p-Values in parentheses
Second stage analysis – Tobit regressions
Panel A: censored Tobit model (dependent variable (DEA run 1) ¼ 1 h) Constant 0.1420 0.0820 1.73 (0.089) Size 0.0123 0.0042 2.89* (0.005) Persist 0.7422 0.2049 3.62* (0.001) Beta 0.1179 0.0362 3.26* (0.002) Sigma 0.0464 0.0044 Log likelihood ¼90.235
3yr-standard deviation (%)
Analysis of slacks In the ﬁrst stage analysis, the sources of inefﬁciency for the non-efﬁcient funds can be identiﬁed by examining the slacks of the input variables. Table 5 depicts the relative mean slacks (absolute mean slack of an input divided by the mean value of the input) of the input variables (Murthi et al., 1997) (see also Daraio and Simar, 2006; Alexakis and Tsolas, 2011). A striking result derived is that risk measured by the standard deviation has no slacks throughout all funds. This is consistent with the notion that mutual funds are on average mean-variance efﬁcient (Murthi et al., 1997). With respect to the other input variables, the slacks for MER are the largest, indicating that this direction may be of higher priority for the precious metal mutual fund managers.
50% 40% 30% 20% 10% 0%
Efficiency Fig. 1. Distribution of efﬁciency measures of funds. BBC-I1: four-input/one-output model (base case); BCC-I2: ﬁve-input/one-output model.
The results of the analysis explaining the performance scores derived by the DEA are given in Table 7. The effect of the logarithm of a fund's net assets and 1-yr returns, which control for fund size and persistence respectively, are signiﬁcant in explaining fund efﬁciency at the 0.01 level; the signs of variables are negative as expected. The beta coefﬁcient is signiﬁcant in explaining fund efﬁciency at the 0.01 level; according to the ﬁndings, high-beta funds seem to be more inefﬁcient compared to the low-beta funds. An interesting topic to be examined further is the use of control variables found to be statistically signiﬁcant after the Tobit regression in the input side of DEA. Fund size has been selected to perform such analysis; the results are available upon request from the author. The distribution of efﬁciency scores (Table 2) produced using the four input and one output variables described in Section 4 (base case) and the efﬁciency scores produced by adding fund size in the input side of DEA (ﬁve-input/one-output model) are presented in Fig. 1. As it can be seen from this ﬁgure, the use of fund size decreases the discriminating power of the BBC-I model by providing more funds as efﬁcient.
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Policy implications The information provided in the previous section can be interpreted in different ways, according to the objectives of the reader/user. More speciﬁcally, it can be used by ﬁnancial analysts to monitor the performance of precious metal mutual funds industry at a sectorial level. Financial investors could acquire more information on their investments by the derived metrics and could use the potential competitors scenario to compare mutual fundholding politics. Fund managers may be interested in monitoring the performance of their funds, along with their efﬁciency. The best-in-class funds may be candidates to be picked up by investors that aim to be exposed in the precious metal investing market. Hence, the proposed approach can be a useful tool for practitioners and investors.
Conclusions This paper summarizes a study carried out by employing DEA to monitor the performance of a sample of precious metal mutual funds. DEA is a nonparametric methodology; therefore, it does not need to assume a particular functional form for the returngenerating process. In contrast to traditional methods, the applied methodology provides an efﬁciency index for each mutual fund under evaluation relative to the best set of funds. A series of research questions presented in the ﬁrst section are addressed in this study. In order to address these questions, the BCC-I model was employed. The empirical results, providing answers to Questions (1) and (2), indicate that there is scope for efﬁciency improvement by decreasing inputs of about 13 percent. Moreover, the derived DEA scores can be used to discriminate among funds that have excelled in performance and, therefore, could be proposed as benchmark funds from those in the sample. Results that provide answers to Question (3) do not point out positive links in terms of Pearson's correlation coefﬁcient and rank correlation coefﬁcients, among DEA-based performance measures and Sharpe ratio; DEA scores are not highly correlated with Jensen's α. The mean-variance efﬁciency hypothesis holds for the inefﬁcient funds of the sample (Question (4)). In addition, to provide answers to Question (5), this paper uses a Tobit regression model to examine factors that signiﬁcantly inﬂuence mutual fund performance. A series of variables were employed to examine the model. The results revealed that DEA-based fund performance can be explained by fund size, persistence, and beta coefﬁcient. An understanding of the DEA-based performance of the sampled funds and of the factors that affect them can be extremely beneﬁcial to both practitioners and investors and can provide helpful references for future studies.
Acknowledgments The author acknowledges the constructive comments of two anonymous reviewers who helped him to signiﬁcantly improve the quality of this article.
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